TSTP Solution File: ITP280^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP280^1 : 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 03:30:57 EDT 2023
% Result : Timeout 299.99s 300.35s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.52/2.56 % Problem : ITP280^1 : TPTP v8.1.2. Released v8.1.0.
% 2.52/2.56 % Command : do_cvc5 %s %d
% 2.56/2.78 % Computer : n012.cluster.edu
% 2.56/2.78 % Model : x86_64 x86_64
% 2.56/2.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.56/2.78 % Memory : 8042.1875MB
% 2.56/2.78 % OS : Linux 3.10.0-693.el7.x86_64
% 2.56/2.78 % CPULimit : 300
% 2.56/2.78 % WCLimit : 300
% 2.56/2.78 % DateTime : Sun Aug 27 10:35:42 EDT 2023
% 2.56/2.78 % CPUTime :
% 5.16/5.33 %----Proving TH0
% 5.16/5.33 %------------------------------------------------------------------------------
% 5.16/5.33 % File : ITP280^1 : TPTP v8.1.2. Released v8.1.0.
% 5.16/5.33 % Domain : Interactive Theorem Proving
% 5.16/5.33 % Problem : Sledgehammer problem VEBT_Space 00398_018442
% 5.16/5.33 % Version : [Des22] axioms.
% 5.16/5.33 % English :
% 5.16/5.33
% 5.16/5.33 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.16/5.33 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.16/5.33 % Source : [Des22]
% 5.16/5.33 % Names : 0076_VEBT_Space_00398_018442 [Des22]
% 5.16/5.33
% 5.16/5.33 % Status : Theorem
% 5.16/5.33 % Rating : 0.77 v8.1.0
% 5.16/5.33 % Syntax : Number of formulae : 11117 (6321 unt; 860 typ; 0 def)
% 5.16/5.33 % Number of atoms : 25845 (11910 equ; 0 cnn)
% 5.16/5.33 % Maximal formula atoms : 71 ( 2 avg)
% 5.16/5.33 % Number of connectives : 99808 (2428 ~; 483 |;1427 &;87236 @)
% 5.16/5.33 % ( 0 <=>;8234 =>; 0 <=; 0 <~>)
% 5.16/5.33 % Maximal formula depth : 39 ( 5 avg)
% 5.16/5.33 % Number of types : 60 ( 59 usr)
% 5.16/5.33 % Number of type conns : 2776 (2776 >; 0 *; 0 +; 0 <<)
% 5.16/5.33 % Number of symbols : 804 ( 801 usr; 57 con; 0-8 aty)
% 5.16/5.33 % Number of variables : 22270 (1711 ^;20086 !; 473 ?;22270 :)
% 5.16/5.33 % SPC : TH0_THM_EQU_NAR
% 5.16/5.33
% 5.16/5.33 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.16/5.33 % from the van Emde Boas Trees session in the Archive of Formal
% 5.16/5.33 % proofs -
% 5.16/5.33 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.16/5.33 % 2022-02-18 17:11:08.526
% 5.16/5.33 %------------------------------------------------------------------------------
% 5.16/5.33 % Could-be-implicit typings (59)
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Set__Oset_It__List__Olist_It__Int__Oint_J_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Filter__Ofilter_It__Int__Oint_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__List__Olist_It__Real__Oreal_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
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% 5.16/5.33 thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
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% 5.16/5.33 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 5.16/5.33 thf(ty_n_t__Complex__Ocomplex,type,
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% 5.16/5.33 thf(ty_n_t__Set__Oset_I_Eo_J,type,
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% 5.16/5.33 thf(ty_n_t__Real__Oreal,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Rat__Orat,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Num__Onum,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Nat__Onat,type,
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% 5.16/5.33
% 5.16/5.33 thf(ty_n_t__Int__Oint,type,
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% 5.16/5.33
% 5.16/5.33 % Explicit typings (801)
% 5.16/5.33 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
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% 5.16/5.33 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
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% 5.16/5.33 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
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% 5.16/5.33
% 5.16/5.33 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
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% 5.16/5.33
% 5.16/5.33 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
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% 5.16/5.33
% 5.16/5.33 thf(sy_c_Archimedean__Field_Ofrac_001t__Real__Oreal,type,
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% 5.16/5.33
% 5.16/5.33 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
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% 5.16/5.33
% 5.16/5.33 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
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% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 5.16/5.33 bNF_re1962705104956426057at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 5.16/5.33 bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
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% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.16/5.33 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_Eo_J_001_062_It__Real__Oreal_M_Eo_J,type,
% 5.16/5.33 bNF_re4521903465945308077real_o: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > $o ) > ( real > $o ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( real > real > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.16/5.33 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.16/5.33 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.16/5.33 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.16/5.33 bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 5.16/5.33 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.16/5.33 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.16/5.33 bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.16/5.33 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.16/5.33 bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.16/5.33 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.16/5.33 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 5.16/5.33 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.33 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.16/5.33 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 5.16/5.33 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 5.16/5.33 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.16/5.33 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.16/5.33 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 5.16/5.33 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.16/5.33 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.16/5.33 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_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,
% 5.16/5.33 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.33 bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.16/5.33 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.16/5.33 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_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__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.16/5.33 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.16/5.33 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.33 bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.16/5.33 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Binomial_Obinomial,type,
% 5.16/5.33 binomial: nat > nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 5.16/5.33 gbinomial_complex: complex > nat > complex ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 5.16/5.33 gbinomial_int: int > nat > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 5.16/5.33 gbinomial_nat: nat > nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 5.16/5.33 gbinomial_rat: rat > nat > rat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 5.16/5.33 gbinomial_real: real > nat > real ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 5.16/5.33 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 5.16/5.33 bit_and_not_num: num > num > option_num ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 5.16/5.33 bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 5.16/5.33 bit_concat_bit: nat > int > int > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 5.16/5.33 bit_or_not_num_neg: num > num > num ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 5.16/5.33 bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Code____Numeral__Ointeger,type,
% 5.16/5.33 bit_ri7632146776885996613nteger: code_integer > code_integer ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 5.16/5.33 bit_ri7919022796975470100ot_int: int > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 5.16/5.33 bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 5.16/5.33 bit_ri631733984087533419it_int: nat > int > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 5.16/5.33 bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 5.16/5.33 bit_se725231765392027082nd_int: int > int > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 5.16/5.33 bit_se727722235901077358nd_nat: nat > nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Code____Numeral__Ointeger,type,
% 5.16/5.33 bit_se3928097537394005634nteger: nat > code_integer > code_integer ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 5.16/5.33 bit_se8568078237143864401it_int: nat > int > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 5.16/5.33 bit_se8570568707652914677it_nat: nat > nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 5.16/5.33 bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 5.16/5.33 bit_se2159334234014336723it_int: nat > int > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 5.16/5.33 bit_se2161824704523386999it_nat: nat > nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
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% 5.16/5.33 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.16/5.33 princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.16/5.33 princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.16/5.33 finite_card_o: set_o > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.16/5.33 finite_card_complex: set_complex > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.16/5.33 finite_card_int: set_int > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 5.16/5.33 finite_card_list_nat: set_list_nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.16/5.33 finite_card_nat: set_nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.16/5.33 finite_card_set_nat: set_set_nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.16/5.33 finite_card_char: set_char > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.16/5.33 finite3207457112153483333omplex: set_complex > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.16/5.33 finite_finite_int: set_int > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.16/5.33 finite_finite_nat: set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.16/5.33 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__Int__Oint_001t__Nat__Onat,type,
% 5.16/5.33 bij_betw_int_nat: ( int > nat ) > set_int > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.16/5.33 bij_be8532844293280997160at_nat: ( list_nat > nat ) > set_list_nat > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.16/5.33 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Int__Oint,type,
% 5.16/5.33 bij_betw_nat_int: ( nat > int ) > set_nat > set_int > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.33 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Obij__betw_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.16/5.33 bij_be5333170631980326235at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 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,
% 5.16/5.33 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.16/5.33
% 5.16/5.33 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,
% 5.16/5.33 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 5.16/5.33 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 5.16/5.33 comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.33 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
% 5.16/5.33 comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oid_001_Eo,type,
% 5.16/5.33 id_o: $o > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 5.16/5.33 id_nat: nat > nat ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Int__Oint_001t__Nat__Onat,type,
% 5.16/5.33 inj_on_int_nat: ( int > nat ) > set_int > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.16/5.33 inj_on_list_nat_nat: ( list_nat > nat ) > set_list_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Int__Oint,type,
% 5.16/5.33 inj_on_nat_int: ( nat > int ) > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.33 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 5.16/5.33 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 5.16/5.33 inj_on2178005380612969504at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.16/5.33 inj_on_real_real: ( real > real ) > set_real > $o ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.16/5.33 inj_on_set_nat_nat: ( set_nat > nat ) > set_set_nat > $o ).
% 5.16/5.33
% 5.16/5.33 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_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.16/5.33 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 5.16/5.33
% 5.16/5.33 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,
% 5.16/5.33 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 ).
% 5.16/5.33
% 5.16/5.33 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.16/5.34 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.16/5.34 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 5.16/5.34
% 5.16/5.34 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,
% 5.16/5.34 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 5.16/5.34 map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 5.16/5.34 map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.16/5.34 map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.16/5.34 map_fu1532550112467129777l_real: ( real > nat > rat ) > ( ( ( nat > rat ) > nat > rat ) > real > real ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > real > real > real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 5.16/5.34 map_fu7146612038024189824t_real: ( real > nat > rat ) > ( ( nat > rat ) > real ) > ( ( nat > rat ) > nat > rat ) > real > real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Omap__fun_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 5.16/5.34 map_fu1856342031159181835at_o_o: ( real > nat > rat ) > ( $o > $o ) > ( ( nat > rat ) > $o ) > real > $o ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.16/5.34 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun__Def_Ois__measure_001t__Int__Oint,type,
% 5.16/5.34 fun_is_measure_int: ( int > nat ) > $o ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun__Def_Opair__leq,type,
% 5.16/5.34 fun_pair_leq: set_Pr8693737435421807431at_nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Fun__Def_Opair__less,type,
% 5.16/5.34 fun_pair_less: set_Pr8693737435421807431at_nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 5.16/5.34 gcd_Gcd_int: set_int > int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 5.16/5.34 gcd_Gcd_nat: set_nat > nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_Obezw,type,
% 5.16/5.34 bezw: nat > nat > product_prod_int_int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_Obezw__rel,type,
% 5.16/5.34 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 5.16/5.34 gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 5.16/5.34 gcd_gcd_int: int > int > int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 5.16/5.34 gcd_gcd_nat: nat > nat > nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 5.16/5.34 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 5.16/5.34 abs_abs_Code_integer: code_integer > code_integer ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 5.16/5.34 abs_abs_complex: complex > complex ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 5.16/5.34 abs_abs_int: int > int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 5.16/5.34 abs_abs_rat: rat > rat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 5.16/5.34 abs_abs_real: real > real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 5.16/5.34 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 5.16/5.34 minus_minus_complex: complex > complex > complex ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 5.16/5.34 minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 5.16/5.34 minus_minus_int: int > int > int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 5.16/5.34 minus_minus_nat: nat > nat > nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 5.16/5.34 minus_minus_rat: rat > rat > rat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 5.16/5.34 minus_minus_real: real > real > real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.16/5.34 minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 5.16/5.34 minus_minus_set_int: set_int > set_int > set_int ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.16/5.34 minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.16/5.34 minus_minus_set_real: set_real > set_real > set_real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.16/5.34 minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
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% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
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% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 5.16/5.34 one_on7984719198319812577d_enat: extended_enat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
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% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 5.16/5.34 one_one_nat: nat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 5.16/5.34 one_one_rat: rat ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 5.16/5.34 one_one_real: real ).
% 5.16/5.34
% 5.16/5.34 thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
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% 5.17/5.34
% 5.17/5.34 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.17/5.34 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 5.17/5.34 at_infinity_real: filter_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.17/5.34 append_int: list_int > list_int > list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.17/5.34 append_nat: list_nat > list_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oconcat_001_Eo,type,
% 5.17/5.34 concat_o: list_list_o > list_o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oconcat_001t__Int__Oint,type,
% 5.17/5.34 concat_int: list_list_int > list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 5.17/5.34 concat_nat: list_list_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oconcat_001t__Real__Oreal,type,
% 5.17/5.34 concat_real: list_list_real > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.17/5.34 foldr_real_real: ( real > real > real ) > list_real > real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 5.17/5.34 last_nat: list_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.17/5.34 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.17/5.34 cons_int: int > list_int > list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.17/5.34 cons_nat: nat > list_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.17/5.34 nil_int: list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.17/5.34 nil_nat: list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 5.17/5.34 map_complex_real: ( complex > real ) > list_complex > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__Int__Oint_001t__Real__Oreal,type,
% 5.17/5.34 map_int_real: ( int > real ) > list_int > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.17/5.34 map_nat_real: ( nat > real ) > list_nat > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.17/5.34 map_real_real: ( real > real ) > list_real > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__Set__Oset_It__Nat__Onat_J_001t__Real__Oreal,type,
% 5.17/5.34 map_set_nat_real: ( set_nat > real ) > list_set_nat > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.17/5.34 map_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 5.17/5.34 map_VEBT_VEBT_real: ( vEBT_VEBT > real ) > list_VEBT_VEBT > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.17/5.34 set_o2: list_o > set_o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.17/5.34 set_complex2: list_complex > set_complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.17/5.34 set_int2: list_int > set_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 5.17/5.34 set_list_o2: list_list_o > set_list_o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 5.17/5.34 set_list_int2: list_list_int > set_list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 5.17/5.34 set_list_nat2: list_list_nat > set_list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Real__Oreal_J,type,
% 5.17/5.34 set_list_real2: list_list_real > set_list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.17/5.34 set_nat2: list_nat > set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.17/5.34 set_real2: list_real > set_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.17/5.34 set_set_nat2: list_set_nat > set_set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.17/5.34 tl_nat: list_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001_Eo,type,
% 5.17/5.34 nth_o: list_o > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.17/5.34 nth_complex: list_complex > nat > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.17/5.34 nth_int: list_int > nat > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.17/5.34 nth_nat: list_nat > nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.17/5.34 nth_real: list_real > nat > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.17/5.34 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.17/5.34 replicate_complex: nat > complex > list_complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.17/5.34 replicate_int: nat > int > list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.17/5.34 replicate_nat: nat > nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.17/5.34 replicate_real: nat > real > list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.17/5.34 replicate_set_nat: nat > set_nat > list_set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.17/5.34 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.17/5.34 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Osubseqs_001_Eo,type,
% 5.17/5.34 subseqs_o: list_o > list_list_o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 5.17/5.34 subseqs_int: list_int > list_list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 5.17/5.34 subseqs_nat: list_nat > list_list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Osubseqs_001t__Real__Oreal,type,
% 5.17/5.34 subseqs_real: list_real > list_list_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.17/5.34 take_nat: nat > list_nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oupt,type,
% 5.17/5.34 upt: nat > nat > list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oupto,type,
% 5.17/5.34 upto: int > int > list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oupto__aux,type,
% 5.17/5.34 upto_aux: int > int > list_int > list_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_List_Oupto__rel,type,
% 5.17/5.34 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_OSuc,type,
% 5.17/5.34 suc: nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.17/5.34 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.17/5.34 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.17/5.34 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.17/5.34 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Onat_Opred,type,
% 5.17/5.34 pred: nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Complex__Ocomplex,type,
% 5.17/5.34 semiri3842193898606819883omplex: set_complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 5.17/5.34 semiring_1_Nats_int: set_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 semiri4939895301339042750nteger: nat > code_integer ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.17/5.34 semiri8010041392384452111omplex: nat > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.17/5.34 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.17/5.34 semiri1314217659103216013at_int: nat > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.17/5.34 semiri1316708129612266289at_nat: nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.17/5.34 semiri681578069525770553at_rat: nat > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.17/5.34 semiri5074537144036343181t_real: nat > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.17/5.34 size_size_list_o: list_o > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.17/5.34 size_s3451745648224563538omplex: list_complex > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.17/5.34 size_size_list_int: list_int > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 5.17/5.34 size_s2710708370519433104list_o: list_list_o > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
% 5.17/5.34 size_s533118279054570080st_int: list_list_int > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.17/5.34 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Real__Oreal_J_J,type,
% 5.17/5.34 size_s6660260683639930848t_real: list_list_real > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.17/5.34 size_size_list_nat: list_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.17/5.34 size_size_list_real: list_real > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.17/5.34 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.17/5.34 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.17/5.34 size_size_num: num > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.17/5.34 size_size_char: char > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oint__decode,type,
% 5.17/5.34 nat_int_decode: nat > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oint__encode,type,
% 5.17/5.34 nat_int_encode: int > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.17/5.34 nat_list_encode: list_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.17/5.34 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.17/5.34 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.17/5.34 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.17/5.34 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.17/5.34 nat_set_decode: nat > set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.17/5.34 nat_set_encode: set_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.17/5.34 nat_triangle: nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_NthRoot_Oroot,type,
% 5.17/5.34 root: nat > real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_NthRoot_Osqrt,type,
% 5.17/5.34 sqrt: real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_OBitM,type,
% 5.17/5.34 bitM: num > num ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oinc,type,
% 5.17/5.34 inc: num > num ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.17/5.34 neg_nu7009210354673126013omplex: complex > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.17/5.34 neg_numeral_dbl_int: int > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.17/5.34 neg_numeral_dbl_rat: rat > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.17/5.34 neg_numeral_dbl_real: real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
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% 5.17/5.34
% 5.17/5.34 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 5.17/5.34 power_power_rat: rat > nat > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 5.17/5.34 power_power_real: real > nat > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.17/5.34 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 5.17/5.34 product_Pair_int_int: int > int > product_prod_int_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.17/5.34 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 5.17/5.34 product_Pair_num_num: num > num > product_prod_num_num ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.17/5.34 produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.17/5.34 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.17/5.34 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.17/5.34 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.17/5.34 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.17/5.34
% 5.17/5.34 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,
% 5.17/5.34 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.17/5.34
% 5.17/5.34 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,
% 5.17/5.34 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 5.17/5.34 produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.17/5.34 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.17/5.34 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.17/5.34
% 5.17/5.34 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,
% 5.17/5.34 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.17/5.34
% 5.17/5.34 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,
% 5.17/5.34 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.17/5.34
% 5.17/5.34 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,
% 5.17/5.34 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.17/5.34 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.17/5.34
% 5.17/5.34 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,
% 5.17/5.34 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.17/5.34 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.17/5.34 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.17/5.34 product_fst_int_int: product_prod_int_int > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.17/5.34 product_snd_int_int: product_prod_int_int > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.17/5.34 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_OAbs__Rat,type,
% 5.17/5.34 abs_Rat: product_prod_int_int > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_OFract,type,
% 5.17/5.34 fract: int > int > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_OFrct,type,
% 5.17/5.34 frct: product_prod_int_int > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_ORep__Rat,type,
% 5.17/5.34 rep_Rat: rat > product_prod_int_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.17/5.34 field_5140801741446780682s_real: set_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.17/5.34 field_7254667332652039916t_real: rat > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Onormalize,type,
% 5.17/5.34 normalize: product_prod_int_int > product_prod_int_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Opcr__rat,type,
% 5.17/5.34 pcr_rat: product_prod_int_int > rat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Opositive,type,
% 5.17/5.34 positive: rat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Oquotient__of,type,
% 5.17/5.34 quotient_of: rat > product_prod_int_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rat_Oratrel,type,
% 5.17/5.34 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_OReal,type,
% 5.17/5.34 real2: ( nat > rat ) > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Ocauchy,type,
% 5.17/5.34 cauchy: ( nat > rat ) > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Ocr__real,type,
% 5.17/5.34 cr_real: ( nat > rat ) > real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Opcr__real,type,
% 5.17/5.34 pcr_real: ( nat > rat ) > real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Opositive,type,
% 5.17/5.34 positive2: real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Orealrel,type,
% 5.17/5.34 realrel: ( nat > rat ) > ( nat > rat ) > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Orep__real,type,
% 5.17/5.34 rep_real: real > nat > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real_Ovanishes,type,
% 5.17/5.34 vanishes: ( nat > rat ) > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.17/5.34 real_V2521375963428798218omplex: set_complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_OReals_001t__Real__Oreal,type,
% 5.17/5.34 real_V470468836141973256s_real: set_real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.17/5.34 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.17/5.34 real_V3694042436643373181omplex: complex > complex > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.17/5.34 real_V975177566351809787t_real: real > real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.17/5.34 real_V1022390504157884413omplex: complex > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.17/5.34 real_V7735802525324610683m_real: real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.17/5.34 real_V4546457046886955230omplex: real > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.17/5.34 real_V1803761363581548252l_real: real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.17/5.34 real_V2046097035970521341omplex: real > complex > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.17/5.34 real_V1485227260804924795R_real: real > real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
% 5.17/5.34 algebr932160517623751201me_int: int > int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
% 5.17/5.34 algebr934650988132801477me_nat: nat > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.17/5.34 divide1717551699836669952omplex: complex > complex > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 5.17/5.34 divide_divide_int: int > int > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.17/5.34 divide_divide_nat: nat > nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.17/5.34 divide_divide_rat: rat > rat > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.17/5.34 divide_divide_real: real > real > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.17/5.34 dvd_dvd_complex: complex > complex > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.17/5.34 dvd_dvd_int: int > int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.17/5.34 dvd_dvd_nat: nat > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.17/5.34 dvd_dvd_rat: rat > rat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.17/5.34 dvd_dvd_real: real > real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.17/5.34 modulo_modulo_int: int > int > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.17/5.34 modulo_modulo_nat: nat > nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 zero_n356916108424825756nteger: $o > code_integer ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.17/5.34 zero_n1201886186963655149omplex: $o > complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.17/5.34 zero_n2684676970156552555ol_int: $o > int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 5.17/5.34 zero_n2687167440665602831ol_nat: $o > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.17/5.34 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.17/5.34 zero_n3304061248610475627l_real: $o > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.17/5.34 suminf_real: ( nat > real ) > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.17/5.34 summable_real: ( nat > real ) > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.17/5.34 sums_real: ( nat > real ) > real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.17/5.34 collect_complex: ( complex > $o ) > set_complex ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 5.17/5.34 collect_int: ( int > $o ) > set_int ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 5.17/5.34 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 5.17/5.34 collect_nat: ( nat > $o ) > set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.17/5.34 collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).
% 5.17/5.34
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% 5.17/5.34 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.17/5.34 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.17/5.34 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.17/5.34 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d,type,
% 5.17/5.34 vEBT_V8646137997579335489_i_l_d: nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p,type,
% 5.17/5.34 vEBT_V8346862874174094_d_u_p: nat > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p__rel,type,
% 5.17/5.34 vEBT_V1247956027447740395_p_rel: nat > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d__rel,type,
% 5.17/5.34 vEBT_V5144397997797733112_d_rel: nat > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt,type,
% 5.17/5.34 vEBT_VEBT_cnt: vEBT_VEBT > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_Ocnt__rel,type,
% 5.17/5.34 vEBT_VEBT_cnt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace,type,
% 5.17/5.34 vEBT_VEBT_space: vEBT_VEBT > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H,type,
% 5.17/5.34 vEBT_VEBT_space2: vEBT_VEBT > nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace_H__rel,type,
% 5.17/5.34 vEBT_VEBT_space_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_VEBT__Space_OVEBT__internal_Ospace__rel,type,
% 5.17/5.34 vEBT_VEBT_space_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.17/5.34 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.17/5.34 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.17/5.34 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.17/5.34 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.17/5.34 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.17/5.34 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.17/5.34 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.17/5.34 fChoice_real: ( real > $o ) > real ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001_Eo,type,
% 5.17/5.34 member_o: $o > set_o > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 5.17/5.34 member_Code_integer: code_integer > set_Code_integer > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.17/5.34 member_complex: complex > set_complex > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Int__Oint,type,
% 5.17/5.34 member_int: int > set_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.17/5.34 member_list_o: list_o > set_list_o > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.17/5.34 member_list_int: list_int > set_list_int > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.17/5.34 member_list_nat: list_nat > set_list_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__List__Olist_It__Real__Oreal_J,type,
% 5.17/5.34 member_list_real: list_real > set_list_real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Nat__Onat,type,
% 5.17/5.34 member_nat: nat > set_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.17/5.34 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.17/5.34 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Rat__Orat,type,
% 5.17/5.34 member_rat: rat > set_rat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Real__Oreal,type,
% 5.17/5.34 member_real: real > set_real > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.17/5.34 member_set_nat: set_nat > set_set_nat > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.17/5.34 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.17/5.34
% 5.17/5.34 thf(sy_v_va____,type,
% 5.17/5.34 va: nat ).
% 5.17/5.34
% 5.17/5.34 % Relevant facts (10216)
% 5.17/5.34 thf(fact_0_False,axiom,
% 5.17/5.34 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ va ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % False
% 5.17/5.34 thf(fact_1__C3_OIH_C_I3_J,axiom,
% 5.17/5.34 ! [X: nat] :
% 5.17/5.34 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ va ) ) )
% 5.17/5.34 => ( ( X
% 5.17/5.34 = ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.34 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ X ) ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ ( suc @ X ) ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % "3.IH"(3)
% 5.17/5.34 thf(fact_2__C3_OIH_C_I4_J,axiom,
% 5.17/5.34 ! [X: nat] :
% 5.17/5.34 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ va ) ) )
% 5.17/5.34 => ( ( X
% 5.17/5.34 = ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.34 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ X ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ X ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % "3.IH"(4)
% 5.17/5.34 thf(fact_3__C3_OIH_C_I1_J,axiom,
% 5.17/5.34 ! [X: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ va ) ) )
% 5.17/5.34 => ( ( X
% 5.17/5.34 = ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.34 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ X ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ X ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % "3.IH"(1)
% 5.17/5.34 thf(fact_4_space__cnt,axiom,
% 5.17/5.34 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_cnt @ T ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % space_cnt
% 5.17/5.34 thf(fact_5_div2__Suc__Suc,axiom,
% 5.17/5.34 ! [M: nat] :
% 5.17/5.34 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div2_Suc_Suc
% 5.17/5.34 thf(fact_6_divide__le__eq__numeral1_I1_J,axiom,
% 5.17/5.34 ! [B: real,W: num,A: real] :
% 5.17/5.34 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.17/5.34 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % divide_le_eq_numeral1(1)
% 5.17/5.34 thf(fact_7_divide__le__eq__numeral1_I1_J,axiom,
% 5.17/5.34 ! [B: rat,W: num,A: rat] :
% 5.17/5.34 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.17/5.34 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % divide_le_eq_numeral1(1)
% 5.17/5.34 thf(fact_8_le__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.34 ! [A: real,B: real,W: num] :
% 5.17/5.34 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.34 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_divide_eq_numeral1(1)
% 5.17/5.34 thf(fact_9_le__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.34 ! [A: rat,B: rat,W: num] :
% 5.17/5.34 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.34 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_divide_eq_numeral1(1)
% 5.17/5.34 thf(fact_10_of__nat__numeral,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_numeral
% 5.17/5.34 thf(fact_11_of__nat__numeral,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( numeral_numeral_real @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_numeral
% 5.17/5.34 thf(fact_12_of__nat__numeral,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_numeral
% 5.17/5.34 thf(fact_13_of__nat__numeral,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_numeral
% 5.17/5.34 thf(fact_14_of__nat__numeral,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_numeral
% 5.17/5.34 thf(fact_15_semiring__norm_I86_J,axiom,
% 5.17/5.34 ! [M: num] :
% 5.17/5.34 ( ( bit1 @ M )
% 5.17/5.34 != one ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(86)
% 5.17/5.34 thf(fact_16_semiring__norm_I84_J,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( one
% 5.17/5.34 != ( bit1 @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(84)
% 5.17/5.34 thf(fact_17_semiring__norm_I89_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( bit1 @ M )
% 5.17/5.34 != ( bit0 @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(89)
% 5.17/5.34 thf(fact_18_semiring__norm_I88_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( bit0 @ M )
% 5.17/5.34 != ( bit1 @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(88)
% 5.17/5.34 thf(fact_19_of__nat__mult,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 5.17/5.34 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mult
% 5.17/5.34 thf(fact_20_of__nat__mult,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.17/5.34 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mult
% 5.17/5.34 thf(fact_21_of__nat__mult,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.17/5.34 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mult
% 5.17/5.34 thf(fact_22_of__nat__mult,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.17/5.34 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mult
% 5.17/5.34 thf(fact_23_of__nat__mult,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.17/5.34 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mult
% 5.17/5.34 thf(fact_24_numeral__Bit1__div__2,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_Bit1_div_2
% 5.17/5.34 thf(fact_25_numeral__Bit1__div__2,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_Bit1_div_2
% 5.17/5.34 thf(fact_26_of__nat__le__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_le_iff
% 5.17/5.34 thf(fact_27_of__nat__le__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_le_iff
% 5.17/5.34 thf(fact_28_of__nat__le__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_le_iff
% 5.17/5.34 thf(fact_29_of__nat__le__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_le_iff
% 5.17/5.34 thf(fact_30_numeral__eq__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( numera6690914467698888265omplex @ M )
% 5.17/5.34 = ( numera6690914467698888265omplex @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_eq_iff
% 5.17/5.34 thf(fact_31_numeral__eq__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( numeral_numeral_real @ M )
% 5.17/5.34 = ( numeral_numeral_real @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_eq_iff
% 5.17/5.34 thf(fact_32_numeral__eq__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( numeral_numeral_rat @ M )
% 5.17/5.34 = ( numeral_numeral_rat @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_eq_iff
% 5.17/5.34 thf(fact_33_numeral__eq__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( numeral_numeral_nat @ M )
% 5.17/5.34 = ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_eq_iff
% 5.17/5.34 thf(fact_34_numeral__eq__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( numeral_numeral_int @ M )
% 5.17/5.34 = ( numeral_numeral_int @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_eq_iff
% 5.17/5.34 thf(fact_35_semiring__norm_I13_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.34 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(13)
% 5.17/5.34 thf(fact_36_semiring__norm_I71_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(71)
% 5.17/5.34 thf(fact_37_semiring__norm_I87_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( bit0 @ M )
% 5.17/5.34 = ( bit0 @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(87)
% 5.17/5.34 thf(fact_38_semiring__norm_I11_J,axiom,
% 5.17/5.34 ! [M: num] :
% 5.17/5.34 ( ( times_times_num @ M @ one )
% 5.17/5.34 = M ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(11)
% 5.17/5.34 thf(fact_39_semiring__norm_I12_J,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( times_times_num @ one @ N )
% 5.17/5.34 = N ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(12)
% 5.17/5.34 thf(fact_40_semiring__norm_I68_J,axiom,
% 5.17/5.34 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(68)
% 5.17/5.34 thf(fact_41_old_Onat_Oinject,axiom,
% 5.17/5.34 ! [Nat: nat,Nat2: nat] :
% 5.17/5.34 ( ( ( suc @ Nat )
% 5.17/5.34 = ( suc @ Nat2 ) )
% 5.17/5.34 = ( Nat = Nat2 ) ) ).
% 5.17/5.34
% 5.17/5.34 % old.nat.inject
% 5.17/5.34 thf(fact_42_nat_Oinject,axiom,
% 5.17/5.34 ! [X2: nat,Y2: nat] :
% 5.17/5.34 ( ( ( suc @ X2 )
% 5.17/5.34 = ( suc @ Y2 ) )
% 5.17/5.34 = ( X2 = Y2 ) ) ).
% 5.17/5.34
% 5.17/5.34 % nat.inject
% 5.17/5.34 thf(fact_43_of__nat__eq__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ( semiri8010041392384452111omplex @ M )
% 5.17/5.34 = ( semiri8010041392384452111omplex @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_eq_iff
% 5.17/5.34 thf(fact_44_of__nat__eq__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ( semiri5074537144036343181t_real @ M )
% 5.17/5.34 = ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_eq_iff
% 5.17/5.34 thf(fact_45_of__nat__eq__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ( semiri681578069525770553at_rat @ M )
% 5.17/5.34 = ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_eq_iff
% 5.17/5.34 thf(fact_46_of__nat__eq__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.17/5.34 = ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_eq_iff
% 5.17/5.34 thf(fact_47_of__nat__eq__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ( semiri1314217659103216013at_int @ M )
% 5.17/5.34 = ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_eq_iff
% 5.17/5.34 thf(fact_48_semiring__norm_I73_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(73)
% 5.17/5.34 thf(fact_49_semiring__norm_I90_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ( bit1 @ M )
% 5.17/5.34 = ( bit1 @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(90)
% 5.17/5.34 thf(fact_50_numeral__le__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_le_iff
% 5.17/5.34 thf(fact_51_numeral__le__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_le_iff
% 5.17/5.34 thf(fact_52_numeral__le__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_le_iff
% 5.17/5.34 thf(fact_53_numeral__le__iff,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_le_iff
% 5.17/5.34 thf(fact_54_mult__numeral__left__semiring__numeral,axiom,
% 5.17/5.34 ! [V: num,W: num,Z: complex] :
% 5.17/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.17/5.34 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_left_semiring_numeral
% 5.17/5.34 thf(fact_55_mult__numeral__left__semiring__numeral,axiom,
% 5.17/5.34 ! [V: num,W: num,Z: real] :
% 5.17/5.34 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.17/5.34 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_left_semiring_numeral
% 5.17/5.34 thf(fact_56_mult__numeral__left__semiring__numeral,axiom,
% 5.17/5.34 ! [V: num,W: num,Z: rat] :
% 5.17/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.17/5.34 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_left_semiring_numeral
% 5.17/5.34 thf(fact_57_mult__numeral__left__semiring__numeral,axiom,
% 5.17/5.34 ! [V: num,W: num,Z: nat] :
% 5.17/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.17/5.34 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_left_semiring_numeral
% 5.17/5.34 thf(fact_58_mult__numeral__left__semiring__numeral,axiom,
% 5.17/5.34 ! [V: num,W: num,Z: int] :
% 5.17/5.34 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.17/5.34 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_left_semiring_numeral
% 5.17/5.34 thf(fact_59_numeral__times__numeral,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.34 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_times_numeral
% 5.17/5.34 thf(fact_60_numeral__times__numeral,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.34 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_times_numeral
% 5.17/5.34 thf(fact_61_numeral__times__numeral,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.34 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_times_numeral
% 5.17/5.34 thf(fact_62_numeral__times__numeral,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.34 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_times_numeral
% 5.17/5.34 thf(fact_63_numeral__times__numeral,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.34 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_times_numeral
% 5.17/5.34 thf(fact_64_num__double,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.17/5.34 = ( bit0 @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % num_double
% 5.17/5.34 thf(fact_65_semiring__norm_I69_J,axiom,
% 5.17/5.34 ! [M: num] :
% 5.17/5.34 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(69)
% 5.17/5.34 thf(fact_66_semiring__norm_I83_J,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( one
% 5.17/5.34 != ( bit0 @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(83)
% 5.17/5.34 thf(fact_67_semiring__norm_I85_J,axiom,
% 5.17/5.34 ! [M: num] :
% 5.17/5.34 ( ( bit0 @ M )
% 5.17/5.34 != one ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(85)
% 5.17/5.34 thf(fact_68_semiring__norm_I14_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.34 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(14)
% 5.17/5.34 thf(fact_69_semiring__norm_I15_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.34 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(15)
% 5.17/5.34 thf(fact_70_semiring__norm_I72_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.34 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(72)
% 5.17/5.34 thf(fact_71_semiring__norm_I70_J,axiom,
% 5.17/5.34 ! [M: num] :
% 5.17/5.34 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.17/5.34
% 5.17/5.34 % semiring_norm(70)
% 5.17/5.34 thf(fact_72_Suc__le__mono,axiom,
% 5.17/5.34 ! [N: nat,M: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.17/5.34 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_le_mono
% 5.17/5.34 thf(fact_73_le__cube,axiom,
% 5.17/5.34 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_cube
% 5.17/5.34 thf(fact_74_le__refl,axiom,
% 5.17/5.34 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.17/5.34
% 5.17/5.34 % le_refl
% 5.17/5.34 thf(fact_75_le__trans,axiom,
% 5.17/5.34 ! [I: nat,J: nat,K: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ( ord_less_eq_nat @ J @ K )
% 5.17/5.34 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_trans
% 5.17/5.34 thf(fact_76_mem__Collect__eq,axiom,
% 5.17/5.34 ! [A: complex,P: complex > $o] :
% 5.17/5.34 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.17/5.34 = ( P @ A ) ) ).
% 5.17/5.34
% 5.17/5.34 % mem_Collect_eq
% 5.17/5.34 thf(fact_77_mem__Collect__eq,axiom,
% 5.17/5.34 ! [A: real,P: real > $o] :
% 5.17/5.34 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.17/5.34 = ( P @ A ) ) ).
% 5.17/5.34
% 5.17/5.34 % mem_Collect_eq
% 5.17/5.34 thf(fact_78_mem__Collect__eq,axiom,
% 5.17/5.34 ! [A: list_nat,P: list_nat > $o] :
% 5.17/5.34 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.17/5.34 = ( P @ A ) ) ).
% 5.17/5.34
% 5.17/5.34 % mem_Collect_eq
% 5.17/5.34 thf(fact_79_mem__Collect__eq,axiom,
% 5.17/5.34 ! [A: set_nat,P: set_nat > $o] :
% 5.17/5.34 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.17/5.34 = ( P @ A ) ) ).
% 5.17/5.34
% 5.17/5.34 % mem_Collect_eq
% 5.17/5.34 thf(fact_80_mem__Collect__eq,axiom,
% 5.17/5.34 ! [A: nat,P: nat > $o] :
% 5.17/5.34 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.17/5.34 = ( P @ A ) ) ).
% 5.17/5.34
% 5.17/5.34 % mem_Collect_eq
% 5.17/5.34 thf(fact_81_mem__Collect__eq,axiom,
% 5.17/5.34 ! [A: int,P: int > $o] :
% 5.17/5.34 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.17/5.34 = ( P @ A ) ) ).
% 5.17/5.34
% 5.17/5.34 % mem_Collect_eq
% 5.17/5.34 thf(fact_82_Collect__mem__eq,axiom,
% 5.17/5.34 ! [A2: set_complex] :
% 5.17/5.34 ( ( collect_complex
% 5.17/5.34 @ ^ [X3: complex] : ( member_complex @ X3 @ A2 ) )
% 5.17/5.34 = A2 ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_mem_eq
% 5.17/5.34 thf(fact_83_Collect__mem__eq,axiom,
% 5.17/5.34 ! [A2: set_real] :
% 5.17/5.34 ( ( collect_real
% 5.17/5.34 @ ^ [X3: real] : ( member_real @ X3 @ A2 ) )
% 5.17/5.34 = A2 ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_mem_eq
% 5.17/5.34 thf(fact_84_Collect__mem__eq,axiom,
% 5.17/5.34 ! [A2: set_list_nat] :
% 5.17/5.34 ( ( collect_list_nat
% 5.17/5.34 @ ^ [X3: list_nat] : ( member_list_nat @ X3 @ A2 ) )
% 5.17/5.34 = A2 ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_mem_eq
% 5.17/5.34 thf(fact_85_Collect__mem__eq,axiom,
% 5.17/5.34 ! [A2: set_set_nat] :
% 5.17/5.34 ( ( collect_set_nat
% 5.17/5.34 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 5.17/5.34 = A2 ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_mem_eq
% 5.17/5.34 thf(fact_86_Collect__mem__eq,axiom,
% 5.17/5.34 ! [A2: set_nat] :
% 5.17/5.34 ( ( collect_nat
% 5.17/5.34 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 5.17/5.34 = A2 ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_mem_eq
% 5.17/5.34 thf(fact_87_Collect__mem__eq,axiom,
% 5.17/5.34 ! [A2: set_int] :
% 5.17/5.34 ( ( collect_int
% 5.17/5.34 @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 5.17/5.34 = A2 ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_mem_eq
% 5.17/5.34 thf(fact_88_Collect__cong,axiom,
% 5.17/5.34 ! [P: real > $o,Q: real > $o] :
% 5.17/5.34 ( ! [X4: real] :
% 5.17/5.34 ( ( P @ X4 )
% 5.17/5.34 = ( Q @ X4 ) )
% 5.17/5.34 => ( ( collect_real @ P )
% 5.17/5.34 = ( collect_real @ Q ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_cong
% 5.17/5.34 thf(fact_89_Collect__cong,axiom,
% 5.17/5.34 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.17/5.34 ( ! [X4: list_nat] :
% 5.17/5.34 ( ( P @ X4 )
% 5.17/5.34 = ( Q @ X4 ) )
% 5.17/5.34 => ( ( collect_list_nat @ P )
% 5.17/5.34 = ( collect_list_nat @ Q ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_cong
% 5.17/5.34 thf(fact_90_Collect__cong,axiom,
% 5.17/5.34 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.17/5.34 ( ! [X4: set_nat] :
% 5.17/5.34 ( ( P @ X4 )
% 5.17/5.34 = ( Q @ X4 ) )
% 5.17/5.34 => ( ( collect_set_nat @ P )
% 5.17/5.34 = ( collect_set_nat @ Q ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_cong
% 5.17/5.34 thf(fact_91_Collect__cong,axiom,
% 5.17/5.34 ! [P: nat > $o,Q: nat > $o] :
% 5.17/5.34 ( ! [X4: nat] :
% 5.17/5.34 ( ( P @ X4 )
% 5.17/5.34 = ( Q @ X4 ) )
% 5.17/5.34 => ( ( collect_nat @ P )
% 5.17/5.34 = ( collect_nat @ Q ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_cong
% 5.17/5.34 thf(fact_92_Collect__cong,axiom,
% 5.17/5.34 ! [P: int > $o,Q: int > $o] :
% 5.17/5.34 ( ! [X4: int] :
% 5.17/5.34 ( ( P @ X4 )
% 5.17/5.34 = ( Q @ X4 ) )
% 5.17/5.34 => ( ( collect_int @ P )
% 5.17/5.34 = ( collect_int @ Q ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Collect_cong
% 5.17/5.34 thf(fact_93_eq__imp__le,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( M = N )
% 5.17/5.34 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % eq_imp_le
% 5.17/5.34 thf(fact_94_le__square,axiom,
% 5.17/5.34 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_square
% 5.17/5.34 thf(fact_95_le__antisym,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.34 => ( M = N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_antisym
% 5.17/5.34 thf(fact_96_dvd__antisym,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ M @ N )
% 5.17/5.34 => ( ( dvd_dvd_nat @ N @ M )
% 5.17/5.34 => ( M = N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_antisym
% 5.17/5.34 thf(fact_97_mult__le__mono,axiom,
% 5.17/5.34 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ( ord_less_eq_nat @ K @ L )
% 5.17/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_le_mono
% 5.17/5.34 thf(fact_98_mult__le__mono1,axiom,
% 5.17/5.34 ! [I: nat,J: nat,K: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_le_mono1
% 5.17/5.34 thf(fact_99_mult__le__mono2,axiom,
% 5.17/5.34 ! [I: nat,J: nat,K: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_le_mono2
% 5.17/5.34 thf(fact_100_nat__le__linear,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.17/5.34
% 5.17/5.34 % nat_le_linear
% 5.17/5.34 thf(fact_101_Suc__mult__le__cancel1,axiom,
% 5.17/5.34 ! [K: nat,M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_mult_le_cancel1
% 5.17/5.34 thf(fact_102_Nat_Oex__has__greatest__nat,axiom,
% 5.17/5.34 ! [P: nat > $o,K: nat,B: nat] :
% 5.17/5.34 ( ( P @ K )
% 5.17/5.34 => ( ! [Y: nat] :
% 5.17/5.34 ( ( P @ Y )
% 5.17/5.34 => ( ord_less_eq_nat @ Y @ B ) )
% 5.17/5.34 => ? [X4: nat] :
% 5.17/5.34 ( ( P @ X4 )
% 5.17/5.34 & ! [Y3: nat] :
% 5.17/5.34 ( ( P @ Y3 )
% 5.17/5.34 => ( ord_less_eq_nat @ Y3 @ X4 ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Nat.ex_has_greatest_nat
% 5.17/5.34 thf(fact_103_div__times__less__eq__dividend,axiom,
% 5.17/5.34 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.17/5.34
% 5.17/5.34 % div_times_less_eq_dividend
% 5.17/5.34 thf(fact_104_times__div__less__eq__dividend,axiom,
% 5.17/5.34 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.17/5.34
% 5.17/5.34 % times_div_less_eq_dividend
% 5.17/5.34 thf(fact_105_le__num__One__iff,axiom,
% 5.17/5.34 ! [X: num] :
% 5.17/5.34 ( ( ord_less_eq_num @ X @ one )
% 5.17/5.34 = ( X = one ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_num_One_iff
% 5.17/5.34 thf(fact_106_Suc__mult__cancel1,axiom,
% 5.17/5.34 ! [K: nat,M: nat,N: nat] :
% 5.17/5.34 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.17/5.34 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.17/5.34 = ( M = N ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_mult_cancel1
% 5.17/5.34 thf(fact_107_transitive__stepwise__le,axiom,
% 5.17/5.34 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 5.17/5.34 => ( ! [X4: nat,Y: nat,Z2: nat] :
% 5.17/5.34 ( ( R @ X4 @ Y )
% 5.17/5.34 => ( ( R @ Y @ Z2 )
% 5.17/5.34 => ( R @ X4 @ Z2 ) ) )
% 5.17/5.34 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 5.17/5.34 => ( R @ M @ N ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % transitive_stepwise_le
% 5.17/5.34 thf(fact_108_nat__induct__at__least,axiom,
% 5.17/5.34 ! [M: nat,N: nat,P: nat > $o] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 => ( ( P @ M )
% 5.17/5.34 => ( ! [N2: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.17/5.34 => ( ( P @ N2 )
% 5.17/5.34 => ( P @ ( suc @ N2 ) ) ) )
% 5.17/5.34 => ( P @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % nat_induct_at_least
% 5.17/5.34 thf(fact_109_full__nat__induct,axiom,
% 5.17/5.34 ! [P: nat > $o,N: nat] :
% 5.17/5.34 ( ! [N2: nat] :
% 5.17/5.34 ( ! [M2: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 5.17/5.34 => ( P @ M2 ) )
% 5.17/5.34 => ( P @ N2 ) )
% 5.17/5.34 => ( P @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % full_nat_induct
% 5.17/5.34 thf(fact_110_not__less__eq__eq,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.17/5.34
% 5.17/5.34 % not_less_eq_eq
% 5.17/5.34 thf(fact_111_Suc__n__not__le__n,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_n_not_le_n
% 5.17/5.34 thf(fact_112_le__Suc__eq,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.17/5.34 = ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 | ( M
% 5.17/5.34 = ( suc @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_Suc_eq
% 5.17/5.34 thf(fact_113_Suc__le__D,axiom,
% 5.17/5.34 ! [N: nat,M3: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( suc @ N ) @ M3 )
% 5.17/5.34 => ? [M4: nat] :
% 5.17/5.34 ( M3
% 5.17/5.34 = ( suc @ M4 ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_le_D
% 5.17/5.34 thf(fact_114_le__SucI,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_SucI
% 5.17/5.34 thf(fact_115_le__SucE,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.17/5.34 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 => ( M
% 5.17/5.34 = ( suc @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % le_SucE
% 5.17/5.34 thf(fact_116_Suc__leD,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.17/5.34 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_leD
% 5.17/5.34 thf(fact_117_div__mult2__eq,axiom,
% 5.17/5.34 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.34 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.17/5.34 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_mult2_eq
% 5.17/5.34 thf(fact_118_div__le__dividend,axiom,
% 5.17/5.34 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.17/5.34
% 5.17/5.34 % div_le_dividend
% 5.17/5.34 thf(fact_119_div__le__mono,axiom,
% 5.17/5.34 ! [M: nat,N: nat,K: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.34 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_le_mono
% 5.17/5.34 thf(fact_120_of__nat__dvd__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.17/5.34 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_dvd_iff
% 5.17/5.34 thf(fact_121_of__nat__dvd__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.34 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_dvd_iff
% 5.17/5.34 thf(fact_122_of__nat__dvd__iff,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.34 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_dvd_iff
% 5.17/5.34 thf(fact_123_div__mult2__numeral__eq,axiom,
% 5.17/5.34 ! [A: nat,K: num,L: num] :
% 5.17/5.34 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.17/5.34 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_mult2_numeral_eq
% 5.17/5.34 thf(fact_124_div__mult2__numeral__eq,axiom,
% 5.17/5.34 ! [A: int,K: num,L: num] :
% 5.17/5.34 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.17/5.34 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_mult2_numeral_eq
% 5.17/5.34 thf(fact_125_Suc__div__le__mono,axiom,
% 5.17/5.34 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_div_le_mono
% 5.17/5.34 thf(fact_126_n__not__Suc__n,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( N
% 5.17/5.34 != ( suc @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % n_not_Suc_n
% 5.17/5.34 thf(fact_127_Suc__inject,axiom,
% 5.17/5.34 ! [X: nat,Y4: nat] :
% 5.17/5.34 ( ( ( suc @ X )
% 5.17/5.34 = ( suc @ Y4 ) )
% 5.17/5.34 => ( X = Y4 ) ) ).
% 5.17/5.34
% 5.17/5.34 % Suc_inject
% 5.17/5.34 thf(fact_128_lift__Suc__antimono__le,axiom,
% 5.17/5.34 ! [F: nat > set_int,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_antimono_le
% 5.17/5.34 thf(fact_129_lift__Suc__antimono__le,axiom,
% 5.17/5.34 ! [F: nat > rat,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_antimono_le
% 5.17/5.34 thf(fact_130_lift__Suc__antimono__le,axiom,
% 5.17/5.34 ! [F: nat > num,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_antimono_le
% 5.17/5.34 thf(fact_131_lift__Suc__antimono__le,axiom,
% 5.17/5.34 ! [F: nat > nat,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_antimono_le
% 5.17/5.34 thf(fact_132_lift__Suc__antimono__le,axiom,
% 5.17/5.34 ! [F: nat > int,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_antimono_le
% 5.17/5.34 thf(fact_133_lift__Suc__antimono__le,axiom,
% 5.17/5.34 ! [F: nat > real,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_antimono_le
% 5.17/5.34 thf(fact_134_lift__Suc__mono__le,axiom,
% 5.17/5.34 ! [F: nat > set_int,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_mono_le
% 5.17/5.34 thf(fact_135_lift__Suc__mono__le,axiom,
% 5.17/5.34 ! [F: nat > rat,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_mono_le
% 5.17/5.34 thf(fact_136_lift__Suc__mono__le,axiom,
% 5.17/5.34 ! [F: nat > num,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_mono_le
% 5.17/5.34 thf(fact_137_lift__Suc__mono__le,axiom,
% 5.17/5.34 ! [F: nat > nat,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_mono_le
% 5.17/5.34 thf(fact_138_lift__Suc__mono__le,axiom,
% 5.17/5.34 ! [F: nat > int,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_mono_le
% 5.17/5.34 thf(fact_139_lift__Suc__mono__le,axiom,
% 5.17/5.34 ! [F: nat > real,N: nat,N3: nat] :
% 5.17/5.34 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.34 => ( ( ord_less_eq_nat @ N @ N3 )
% 5.17/5.34 => ( ord_less_eq_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % lift_Suc_mono_le
% 5.17/5.34 thf(fact_140_of__nat__mono,axiom,
% 5.17/5.34 ! [I: nat,J: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mono
% 5.17/5.34 thf(fact_141_of__nat__mono,axiom,
% 5.17/5.34 ! [I: nat,J: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mono
% 5.17/5.34 thf(fact_142_of__nat__mono,axiom,
% 5.17/5.34 ! [I: nat,J: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mono
% 5.17/5.34 thf(fact_143_of__nat__mono,axiom,
% 5.17/5.34 ! [I: nat,J: nat] :
% 5.17/5.34 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.34 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % of_nat_mono
% 5.17/5.34 thf(fact_144_mult__of__nat__commute,axiom,
% 5.17/5.34 ! [X: nat,Y4: complex] :
% 5.17/5.34 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y4 )
% 5.17/5.34 = ( times_times_complex @ Y4 @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_of_nat_commute
% 5.17/5.34 thf(fact_145_mult__of__nat__commute,axiom,
% 5.17/5.34 ! [X: nat,Y4: real] :
% 5.17/5.34 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y4 )
% 5.17/5.34 = ( times_times_real @ Y4 @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_of_nat_commute
% 5.17/5.34 thf(fact_146_mult__of__nat__commute,axiom,
% 5.17/5.34 ! [X: nat,Y4: rat] :
% 5.17/5.34 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y4 )
% 5.17/5.34 = ( times_times_rat @ Y4 @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_of_nat_commute
% 5.17/5.34 thf(fact_147_mult__of__nat__commute,axiom,
% 5.17/5.34 ! [X: nat,Y4: nat] :
% 5.17/5.34 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y4 )
% 5.17/5.34 = ( times_times_nat @ Y4 @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_of_nat_commute
% 5.17/5.34 thf(fact_148_mult__of__nat__commute,axiom,
% 5.17/5.34 ! [X: nat,Y4: int] :
% 5.17/5.34 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y4 )
% 5.17/5.34 = ( times_times_int @ Y4 @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % mult_of_nat_commute
% 5.17/5.34 thf(fact_149_mult__numeral__1__right,axiom,
% 5.17/5.34 ! [A: complex] :
% 5.17/5.34 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1_right
% 5.17/5.34 thf(fact_150_mult__numeral__1__right,axiom,
% 5.17/5.34 ! [A: real] :
% 5.17/5.34 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1_right
% 5.17/5.34 thf(fact_151_mult__numeral__1__right,axiom,
% 5.17/5.34 ! [A: rat] :
% 5.17/5.34 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1_right
% 5.17/5.34 thf(fact_152_mult__numeral__1__right,axiom,
% 5.17/5.34 ! [A: nat] :
% 5.17/5.34 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1_right
% 5.17/5.34 thf(fact_153_mult__numeral__1__right,axiom,
% 5.17/5.34 ! [A: int] :
% 5.17/5.34 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1_right
% 5.17/5.34 thf(fact_154_mult__numeral__1,axiom,
% 5.17/5.34 ! [A: complex] :
% 5.17/5.34 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1
% 5.17/5.34 thf(fact_155_mult__numeral__1,axiom,
% 5.17/5.34 ! [A: real] :
% 5.17/5.34 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1
% 5.17/5.34 thf(fact_156_mult__numeral__1,axiom,
% 5.17/5.34 ! [A: rat] :
% 5.17/5.34 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1
% 5.17/5.34 thf(fact_157_mult__numeral__1,axiom,
% 5.17/5.34 ! [A: nat] :
% 5.17/5.34 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1
% 5.17/5.34 thf(fact_158_mult__numeral__1,axiom,
% 5.17/5.34 ! [A: int] :
% 5.17/5.34 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % mult_numeral_1
% 5.17/5.34 thf(fact_159_divide__numeral__1,axiom,
% 5.17/5.34 ! [A: complex] :
% 5.17/5.34 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % divide_numeral_1
% 5.17/5.34 thf(fact_160_divide__numeral__1,axiom,
% 5.17/5.34 ! [A: real] :
% 5.17/5.34 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % divide_numeral_1
% 5.17/5.34 thf(fact_161_divide__numeral__1,axiom,
% 5.17/5.34 ! [A: rat] :
% 5.17/5.34 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.17/5.34 = A ) ).
% 5.17/5.34
% 5.17/5.34 % divide_numeral_1
% 5.17/5.34 thf(fact_162_num_Oexhaust,axiom,
% 5.17/5.34 ! [Y4: num] :
% 5.17/5.34 ( ( Y4 != one )
% 5.17/5.34 => ( ! [X22: num] :
% 5.17/5.34 ( Y4
% 5.17/5.34 != ( bit0 @ X22 ) )
% 5.17/5.34 => ~ ! [X32: num] :
% 5.17/5.34 ( Y4
% 5.17/5.34 != ( bit1 @ X32 ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % num.exhaust
% 5.17/5.34 thf(fact_163_div__mult2__eq_H,axiom,
% 5.17/5.34 ! [A: nat,M: nat,N: nat] :
% 5.17/5.34 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.17/5.34 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_mult2_eq'
% 5.17/5.34 thf(fact_164_div__mult2__eq_H,axiom,
% 5.17/5.34 ! [A: int,M: nat,N: nat] :
% 5.17/5.34 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.34 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_mult2_eq'
% 5.17/5.34 thf(fact_165_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.34 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.17/5.34 thf(fact_166_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.17/5.34 ! [M: nat,N: nat] :
% 5.17/5.34 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.34 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.17/5.34 thf(fact_167_numeral__Bit0__div__2,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_Bit0_div_2
% 5.17/5.34 thf(fact_168_numeral__Bit0__div__2,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_Bit0_div_2
% 5.17/5.34 thf(fact_169_eval__nat__numeral_I3_J,axiom,
% 5.17/5.34 ! [N: num] :
% 5.17/5.34 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.17/5.34 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % eval_nat_numeral(3)
% 5.17/5.34 thf(fact_170_even__of__nat,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.17/5.34 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_of_nat
% 5.17/5.34 thf(fact_171_even__of__nat,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.34 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_of_nat
% 5.17/5.34 thf(fact_172_even__of__nat,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.34 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_of_nat
% 5.17/5.34 thf(fact_173_even__Suc__div__two,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.34 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_Suc_div_two
% 5.17/5.34 thf(fact_174_odd__Suc__div__two,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.34 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % odd_Suc_div_two
% 5.17/5.34 thf(fact_175_numeral__le__real__of__nat__iff,axiom,
% 5.17/5.34 ! [N: num,M: nat] :
% 5.17/5.34 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.17/5.34 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.17/5.34
% 5.17/5.34 % numeral_le_real_of_nat_iff
% 5.17/5.34 thf(fact_176_even__Suc__Suc__iff,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.17/5.34 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_Suc_Suc_iff
% 5.17/5.34 thf(fact_177_even__Suc,axiom,
% 5.17/5.34 ! [N: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.17/5.34 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_Suc
% 5.17/5.34 thf(fact_178_even__mult__iff,axiom,
% 5.17/5.34 ! [A: code_integer,B: code_integer] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.17/5.34 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.34 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_mult_iff
% 5.17/5.34 thf(fact_179_even__mult__iff,axiom,
% 5.17/5.34 ! [A: nat,B: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.17/5.34 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.34 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_mult_iff
% 5.17/5.34 thf(fact_180_even__mult__iff,axiom,
% 5.17/5.34 ! [A: int,B: int] :
% 5.17/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.17/5.34 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.34 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_mult_iff
% 5.17/5.34 thf(fact_181_dvd__mult__div__cancel,axiom,
% 5.17/5.34 ! [A: code_integer,B: code_integer] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.34 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.17/5.34 = B ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_mult_div_cancel
% 5.17/5.34 thf(fact_182_dvd__mult__div__cancel,axiom,
% 5.17/5.34 ! [A: nat,B: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.34 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.17/5.34 = B ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_mult_div_cancel
% 5.17/5.34 thf(fact_183_dvd__mult__div__cancel,axiom,
% 5.17/5.34 ! [A: int,B: int] :
% 5.17/5.34 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.34 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.17/5.34 = B ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_mult_div_cancel
% 5.17/5.34 thf(fact_184_dvd__div__mult__self,axiom,
% 5.17/5.34 ! [A: code_integer,B: code_integer] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.34 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.17/5.34 = B ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_div_mult_self
% 5.17/5.34 thf(fact_185_dvd__div__mult__self,axiom,
% 5.17/5.34 ! [A: nat,B: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.34 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.17/5.34 = B ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_div_mult_self
% 5.17/5.34 thf(fact_186_dvd__div__mult__self,axiom,
% 5.17/5.34 ! [A: int,B: int] :
% 5.17/5.34 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.34 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.17/5.34 = B ) ) ).
% 5.17/5.34
% 5.17/5.34 % dvd_div_mult_self
% 5.17/5.34 thf(fact_187_even__two__times__div__two,axiom,
% 5.17/5.34 ! [A: code_integer] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.34 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.17/5.34 = A ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_two_times_div_two
% 5.17/5.34 thf(fact_188_even__two__times__div__two,axiom,
% 5.17/5.34 ! [A: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.34 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.34 = A ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_two_times_div_two
% 5.17/5.34 thf(fact_189_even__two__times__div__two,axiom,
% 5.17/5.34 ! [A: int] :
% 5.17/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.34 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.17/5.34 = A ) ) ).
% 5.17/5.34
% 5.17/5.34 % even_two_times_div_two
% 5.17/5.34 thf(fact_190_div2__even__ext__nat,axiom,
% 5.17/5.34 ! [X: nat,Y4: nat] :
% 5.17/5.34 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.34 = ( divide_divide_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.34 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.17/5.34 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y4 ) )
% 5.17/5.34 => ( X = Y4 ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div2_even_ext_nat
% 5.17/5.34 thf(fact_191_enat__ord__number_I1_J,axiom,
% 5.17/5.34 ! [M: num,N: num] :
% 5.17/5.34 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.17/5.34 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % enat_ord_number(1)
% 5.17/5.34 thf(fact_192_div__dvd__div,axiom,
% 5.17/5.34 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.34 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.34 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.17/5.34 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.17/5.34 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_dvd_div
% 5.17/5.34 thf(fact_193_div__dvd__div,axiom,
% 5.17/5.34 ! [A: nat,B: nat,C: nat] :
% 5.17/5.34 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.34 => ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.34 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.17/5.34 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_dvd_div
% 5.17/5.34 thf(fact_194_div__dvd__div,axiom,
% 5.17/5.34 ! [A: int,B: int,C: int] :
% 5.17/5.34 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.34 => ( ( dvd_dvd_int @ A @ C )
% 5.17/5.34 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.17/5.34 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.17/5.34
% 5.17/5.34 % div_dvd_div
% 5.17/5.35 thf(fact_195_dvd__trans,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.35 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_trans
% 5.17/5.35 thf(fact_196_dvd__trans,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_int @ B @ C )
% 5.17/5.35 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_trans
% 5.17/5.35 thf(fact_197_dvd__trans,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_trans
% 5.17/5.35 thf(fact_198_dvd__refl,axiom,
% 5.17/5.35 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_refl
% 5.17/5.35 thf(fact_199_dvd__refl,axiom,
% 5.17/5.35 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_refl
% 5.17/5.35 thf(fact_200_dvd__refl,axiom,
% 5.17/5.35 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_refl
% 5.17/5.35 thf(fact_201_complete__real,axiom,
% 5.17/5.35 ! [S: set_real] :
% 5.17/5.35 ( ? [X5: real] : ( member_real @ X5 @ S )
% 5.17/5.35 => ( ? [Z3: real] :
% 5.17/5.35 ! [X4: real] :
% 5.17/5.35 ( ( member_real @ X4 @ S )
% 5.17/5.35 => ( ord_less_eq_real @ X4 @ Z3 ) )
% 5.17/5.35 => ? [Y: real] :
% 5.17/5.35 ( ! [X5: real] :
% 5.17/5.35 ( ( member_real @ X5 @ S )
% 5.17/5.35 => ( ord_less_eq_real @ X5 @ Y ) )
% 5.17/5.35 & ! [Z3: real] :
% 5.17/5.35 ( ! [X4: real] :
% 5.17/5.35 ( ( member_real @ X4 @ S )
% 5.17/5.35 => ( ord_less_eq_real @ X4 @ Z3 ) )
% 5.17/5.35 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % complete_real
% 5.17/5.35 thf(fact_202_dvdE,axiom,
% 5.17/5.35 ! [B: code_integer,A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.35 => ~ ! [K2: code_integer] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdE
% 5.17/5.35 thf(fact_203_dvdE,axiom,
% 5.17/5.35 ! [B: real,A: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ B @ A )
% 5.17/5.35 => ~ ! [K2: real] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdE
% 5.17/5.35 thf(fact_204_dvdE,axiom,
% 5.17/5.35 ! [B: rat,A: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ B @ A )
% 5.17/5.35 => ~ ! [K2: rat] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdE
% 5.17/5.35 thf(fact_205_dvdE,axiom,
% 5.17/5.35 ! [B: nat,A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.35 => ~ ! [K2: nat] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdE
% 5.17/5.35 thf(fact_206_dvdE,axiom,
% 5.17/5.35 ! [B: int,A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.35 => ~ ! [K2: int] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdE
% 5.17/5.35 thf(fact_207_dvdI,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdI
% 5.17/5.35 thf(fact_208_dvdI,axiom,
% 5.17/5.35 ! [A: real,B: real,K: real] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( times_times_real @ B @ K ) )
% 5.17/5.35 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdI
% 5.17/5.35 thf(fact_209_dvdI,axiom,
% 5.17/5.35 ! [A: rat,B: rat,K: rat] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( times_times_rat @ B @ K ) )
% 5.17/5.35 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdI
% 5.17/5.35 thf(fact_210_dvdI,axiom,
% 5.17/5.35 ! [A: nat,B: nat,K: nat] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( times_times_nat @ B @ K ) )
% 5.17/5.35 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdI
% 5.17/5.35 thf(fact_211_dvdI,axiom,
% 5.17/5.35 ! [A: int,B: int,K: int] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( times_times_int @ B @ K ) )
% 5.17/5.35 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvdI
% 5.17/5.35 thf(fact_212_dvd__def,axiom,
% 5.17/5.35 ( dvd_dvd_Code_integer
% 5.17/5.35 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.17/5.35 ? [K3: code_integer] :
% 5.17/5.35 ( A3
% 5.17/5.35 = ( times_3573771949741848930nteger @ B2 @ K3 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_def
% 5.17/5.35 thf(fact_213_dvd__def,axiom,
% 5.17/5.35 ( dvd_dvd_real
% 5.17/5.35 = ( ^ [B2: real,A3: real] :
% 5.17/5.35 ? [K3: real] :
% 5.17/5.35 ( A3
% 5.17/5.35 = ( times_times_real @ B2 @ K3 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_def
% 5.17/5.35 thf(fact_214_dvd__def,axiom,
% 5.17/5.35 ( dvd_dvd_rat
% 5.17/5.35 = ( ^ [B2: rat,A3: rat] :
% 5.17/5.35 ? [K3: rat] :
% 5.17/5.35 ( A3
% 5.17/5.35 = ( times_times_rat @ B2 @ K3 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_def
% 5.17/5.35 thf(fact_215_dvd__def,axiom,
% 5.17/5.35 ( dvd_dvd_nat
% 5.17/5.35 = ( ^ [B2: nat,A3: nat] :
% 5.17/5.35 ? [K3: nat] :
% 5.17/5.35 ( A3
% 5.17/5.35 = ( times_times_nat @ B2 @ K3 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_def
% 5.17/5.35 thf(fact_216_dvd__def,axiom,
% 5.17/5.35 ( dvd_dvd_int
% 5.17/5.35 = ( ^ [B2: int,A3: int] :
% 5.17/5.35 ? [K3: int] :
% 5.17/5.35 ( A3
% 5.17/5.35 = ( times_times_int @ B2 @ K3 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_def
% 5.17/5.35 thf(fact_217_dvd__mult,axiom,
% 5.17/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult
% 5.17/5.35 thf(fact_218_dvd__mult,axiom,
% 5.17/5.35 ! [A: real,C: real,B: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ A @ C )
% 5.17/5.35 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult
% 5.17/5.35 thf(fact_219_dvd__mult,axiom,
% 5.17/5.35 ! [A: rat,C: rat,B: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ A @ C )
% 5.17/5.35 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult
% 5.17/5.35 thf(fact_220_dvd__mult,axiom,
% 5.17/5.35 ! [A: nat,C: nat,B: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.35 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult
% 5.17/5.35 thf(fact_221_dvd__mult,axiom,
% 5.17/5.35 ! [A: int,C: int,B: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ A @ C )
% 5.17/5.35 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult
% 5.17/5.35 thf(fact_222_dvd__mult2,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult2
% 5.17/5.35 thf(fact_223_dvd__mult2,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ A @ B )
% 5.17/5.35 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult2
% 5.17/5.35 thf(fact_224_dvd__mult2,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ A @ B )
% 5.17/5.35 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult2
% 5.17/5.35 thf(fact_225_dvd__mult2,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.35 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult2
% 5.17/5.35 thf(fact_226_dvd__mult2,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.35 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult2
% 5.17/5.35 thf(fact_227_dvd__mult__left,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_left
% 5.17/5.35 thf(fact_228_dvd__mult__left,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_left
% 5.17/5.35 thf(fact_229_dvd__mult__left,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_left
% 5.17/5.35 thf(fact_230_dvd__mult__left,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_left
% 5.17/5.35 thf(fact_231_dvd__mult__left,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_left
% 5.17/5.35 thf(fact_232_dvd__triv__left,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_left
% 5.17/5.35 thf(fact_233_dvd__triv__left,axiom,
% 5.17/5.35 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_left
% 5.17/5.35 thf(fact_234_dvd__triv__left,axiom,
% 5.17/5.35 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_left
% 5.17/5.35 thf(fact_235_dvd__triv__left,axiom,
% 5.17/5.35 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_left
% 5.17/5.35 thf(fact_236_dvd__triv__left,axiom,
% 5.17/5.35 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_left
% 5.17/5.35 thf(fact_237_mult__dvd__mono,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_dvd_mono
% 5.17/5.35 thf(fact_238_mult__dvd__mono,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_real @ C @ D )
% 5.17/5.35 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_dvd_mono
% 5.17/5.35 thf(fact_239_mult__dvd__mono,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_rat @ C @ D )
% 5.17/5.35 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_dvd_mono
% 5.17/5.35 thf(fact_240_mult__dvd__mono,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_nat @ C @ D )
% 5.17/5.35 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_dvd_mono
% 5.17/5.35 thf(fact_241_mult__dvd__mono,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.35 => ( ( dvd_dvd_int @ C @ D )
% 5.17/5.35 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_dvd_mono
% 5.17/5.35 thf(fact_242_dvd__mult__right,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_right
% 5.17/5.35 thf(fact_243_dvd__mult__right,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_right
% 5.17/5.35 thf(fact_244_dvd__mult__right,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_right
% 5.17/5.35 thf(fact_245_dvd__mult__right,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_right
% 5.17/5.35 thf(fact_246_dvd__mult__right,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.35 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_right
% 5.17/5.35 thf(fact_247_dvd__triv__right,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_right
% 5.17/5.35 thf(fact_248_dvd__triv__right,axiom,
% 5.17/5.35 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_right
% 5.17/5.35 thf(fact_249_dvd__triv__right,axiom,
% 5.17/5.35 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_right
% 5.17/5.35 thf(fact_250_dvd__triv__right,axiom,
% 5.17/5.35 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_right
% 5.17/5.35 thf(fact_251_dvd__triv__right,axiom,
% 5.17/5.35 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_triv_right
% 5.17/5.35 thf(fact_252_dvd__div__eq__iff,axiom,
% 5.17/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.35 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.17/5.35 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_iff
% 5.17/5.35 thf(fact_253_dvd__div__eq__iff,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( dvd_dvd_complex @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_complex @ C @ B )
% 5.17/5.35 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.17/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_iff
% 5.17/5.35 thf(fact_254_dvd__div__eq__iff,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_real @ C @ B )
% 5.17/5.35 => ( ( ( divide_divide_real @ A @ C )
% 5.17/5.35 = ( divide_divide_real @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_iff
% 5.17/5.35 thf(fact_255_dvd__div__eq__iff,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_rat @ C @ B )
% 5.17/5.35 => ( ( ( divide_divide_rat @ A @ C )
% 5.17/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_iff
% 5.17/5.35 thf(fact_256_dvd__div__eq__iff,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.35 => ( ( ( divide_divide_nat @ A @ C )
% 5.17/5.35 = ( divide_divide_nat @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_iff
% 5.17/5.35 thf(fact_257_dvd__div__eq__iff,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.17/5.35 => ( ( ( divide_divide_int @ A @ C )
% 5.17/5.35 = ( divide_divide_int @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_iff
% 5.17/5.35 thf(fact_258_dvd__div__eq__cancel,axiom,
% 5.17/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.35 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.17/5.35 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.35 => ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_cancel
% 5.17/5.35 thf(fact_259_dvd__div__eq__cancel,axiom,
% 5.17/5.35 ! [A: complex,C: complex,B: complex] :
% 5.17/5.35 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.17/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.35 => ( ( dvd_dvd_complex @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_complex @ C @ B )
% 5.17/5.35 => ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_cancel
% 5.17/5.35 thf(fact_260_dvd__div__eq__cancel,axiom,
% 5.17/5.35 ! [A: real,C: real,B: real] :
% 5.17/5.35 ( ( ( divide_divide_real @ A @ C )
% 5.17/5.35 = ( divide_divide_real @ B @ C ) )
% 5.17/5.35 => ( ( dvd_dvd_real @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_real @ C @ B )
% 5.17/5.35 => ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_cancel
% 5.17/5.35 thf(fact_261_dvd__div__eq__cancel,axiom,
% 5.17/5.35 ! [A: rat,C: rat,B: rat] :
% 5.17/5.35 ( ( ( divide_divide_rat @ A @ C )
% 5.17/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.35 => ( ( dvd_dvd_rat @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_rat @ C @ B )
% 5.17/5.35 => ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_cancel
% 5.17/5.35 thf(fact_262_dvd__div__eq__cancel,axiom,
% 5.17/5.35 ! [A: nat,C: nat,B: nat] :
% 5.17/5.35 ( ( ( divide_divide_nat @ A @ C )
% 5.17/5.35 = ( divide_divide_nat @ B @ C ) )
% 5.17/5.35 => ( ( dvd_dvd_nat @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.35 => ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_cancel
% 5.17/5.35 thf(fact_263_dvd__div__eq__cancel,axiom,
% 5.17/5.35 ! [A: int,C: int,B: int] :
% 5.17/5.35 ( ( ( divide_divide_int @ A @ C )
% 5.17/5.35 = ( divide_divide_int @ B @ C ) )
% 5.17/5.35 => ( ( dvd_dvd_int @ C @ A )
% 5.17/5.35 => ( ( dvd_dvd_int @ C @ B )
% 5.17/5.35 => ( A = B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_eq_cancel
% 5.17/5.35 thf(fact_264_div__div__div__same,axiom,
% 5.17/5.35 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.35 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.17/5.35 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_div_div_same
% 5.17/5.35 thf(fact_265_div__div__div__same,axiom,
% 5.17/5.35 ! [D: nat,B: nat,A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ D @ B )
% 5.17/5.35 => ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.35 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.17/5.35 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_div_div_same
% 5.17/5.35 thf(fact_266_div__div__div__same,axiom,
% 5.17/5.35 ! [D: int,B: int,A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ D @ B )
% 5.17/5.35 => ( ( dvd_dvd_int @ B @ A )
% 5.17/5.35 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.17/5.35 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_div_div_same
% 5.17/5.35 thf(fact_267_dvd__div__mult,axiom,
% 5.17/5.35 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.35 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.17/5.35 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_mult
% 5.17/5.35 thf(fact_268_dvd__div__mult,axiom,
% 5.17/5.35 ! [C: nat,B: nat,A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.35 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.17/5.35 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_mult
% 5.17/5.35 thf(fact_269_dvd__div__mult,axiom,
% 5.17/5.35 ! [C: int,B: int,A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ C @ B )
% 5.17/5.35 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.17/5.35 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_mult
% 5.17/5.35 thf(fact_270_div__mult__swap,axiom,
% 5.17/5.35 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.35 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.17/5.35 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_swap
% 5.17/5.35 thf(fact_271_div__mult__swap,axiom,
% 5.17/5.35 ! [C: nat,B: nat,A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.35 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_swap
% 5.17/5.35 thf(fact_272_div__mult__swap,axiom,
% 5.17/5.35 ! [C: int,B: int,A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ C @ B )
% 5.17/5.35 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.17/5.35 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_swap
% 5.17/5.35 thf(fact_273_div__div__eq__right,axiom,
% 5.17/5.35 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.35 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.17/5.35 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_div_eq_right
% 5.17/5.35 thf(fact_274_div__div__eq__right,axiom,
% 5.17/5.35 ! [C: nat,B: nat,A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.35 => ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.35 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.17/5.35 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_div_eq_right
% 5.17/5.35 thf(fact_275_div__div__eq__right,axiom,
% 5.17/5.35 ! [C: int,B: int,A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ C @ B )
% 5.17/5.35 => ( ( dvd_dvd_int @ B @ A )
% 5.17/5.35 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.17/5.35 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_div_eq_right
% 5.17/5.35 thf(fact_276_dvd__div__mult2__eq,axiom,
% 5.17/5.35 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.17/5.35 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.35 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_mult2_eq
% 5.17/5.35 thf(fact_277_dvd__div__mult2__eq,axiom,
% 5.17/5.35 ! [B: nat,C: nat,A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.17/5.35 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_mult2_eq
% 5.17/5.35 thf(fact_278_dvd__div__mult2__eq,axiom,
% 5.17/5.35 ! [B: int,C: int,A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.17/5.35 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.35 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_div_mult2_eq
% 5.17/5.35 thf(fact_279_dvd__mult__imp__div,axiom,
% 5.17/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.17/5.35 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_imp_div
% 5.17/5.35 thf(fact_280_dvd__mult__imp__div,axiom,
% 5.17/5.35 ! [A: nat,C: nat,B: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.17/5.35 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_imp_div
% 5.17/5.35 thf(fact_281_dvd__mult__imp__div,axiom,
% 5.17/5.35 ! [A: int,C: int,B: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.17/5.35 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_imp_div
% 5.17/5.35 thf(fact_282_div__mult__div__if__dvd,axiom,
% 5.17/5.35 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.17/5.35 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.17/5.35 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_div_if_dvd
% 5.17/5.35 thf(fact_283_div__mult__div__if__dvd,axiom,
% 5.17/5.35 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.35 => ( ( dvd_dvd_nat @ D @ C )
% 5.17/5.35 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.17/5.35 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_div_if_dvd
% 5.17/5.35 thf(fact_284_div__mult__div__if__dvd,axiom,
% 5.17/5.35 ! [B: int,A: int,D: int,C: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.35 => ( ( dvd_dvd_int @ D @ C )
% 5.17/5.35 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.17/5.35 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_div_if_dvd
% 5.17/5.35 thf(fact_285_real__of__nat__div4,axiom,
% 5.17/5.35 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % real_of_nat_div4
% 5.17/5.35 thf(fact_286_real__of__nat__div,axiom,
% 5.17/5.35 ! [D: nat,N: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ D @ N )
% 5.17/5.35 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.17/5.35 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % real_of_nat_div
% 5.17/5.35 thf(fact_287_even__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % even_numeral
% 5.17/5.35 thf(fact_288_even__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % even_numeral
% 5.17/5.35 thf(fact_289_even__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % even_numeral
% 5.17/5.35 thf(fact_290_evenE,axiom,
% 5.17/5.35 ! [A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.35 => ~ ! [B3: code_integer] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % evenE
% 5.17/5.35 thf(fact_291_evenE,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.35 => ~ ! [B3: nat] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % evenE
% 5.17/5.35 thf(fact_292_evenE,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.35 => ~ ! [B3: int] :
% 5.17/5.35 ( A
% 5.17/5.35 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % evenE
% 5.17/5.35 thf(fact_293_odd__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % odd_numeral
% 5.17/5.35 thf(fact_294_odd__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % odd_numeral
% 5.17/5.35 thf(fact_295_odd__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % odd_numeral
% 5.17/5.35 thf(fact_296_Suc__double__not__eq__double,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.35 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % Suc_double_not_eq_double
% 5.17/5.35 thf(fact_297_double__not__eq__Suc__double,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.17/5.35 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % double_not_eq_Suc_double
% 5.17/5.35 thf(fact_298_zdiv__numeral__Bit1,axiom,
% 5.17/5.35 ! [V: num,W: num] :
% 5.17/5.35 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.17/5.35 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zdiv_numeral_Bit1
% 5.17/5.35 thf(fact_299_bit__eq__rec,axiom,
% 5.17/5.35 ( ( ^ [Y5: code_integer,Z4: code_integer] : ( Y5 = Z4 ) )
% 5.17/5.35 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.17/5.35 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.17/5.35 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.17/5.35 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.35 = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % bit_eq_rec
% 5.17/5.35 thf(fact_300_bit__eq__rec,axiom,
% 5.17/5.35 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.35 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.35 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.17/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.17/5.35 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.35 = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % bit_eq_rec
% 5.17/5.35 thf(fact_301_bit__eq__rec,axiom,
% 5.17/5.35 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.35 = ( ^ [A3: int,B2: int] :
% 5.17/5.35 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.17/5.35 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.17/5.35 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.35 = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % bit_eq_rec
% 5.17/5.35 thf(fact_302_times__divide__eq__left,axiom,
% 5.17/5.35 ! [B: complex,C: complex,A: complex] :
% 5.17/5.35 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.17/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_eq_left
% 5.17/5.35 thf(fact_303_times__divide__eq__left,axiom,
% 5.17/5.35 ! [B: real,C: real,A: real] :
% 5.17/5.35 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.35 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_eq_left
% 5.17/5.35 thf(fact_304_times__divide__eq__left,axiom,
% 5.17/5.35 ! [B: rat,C: rat,A: rat] :
% 5.17/5.35 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.35 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_eq_left
% 5.17/5.35 thf(fact_305_divide__divide__eq__left,axiom,
% 5.17/5.35 ! [A: complex,B: complex,C: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_left
% 5.17/5.35 thf(fact_306_divide__divide__eq__left,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.17/5.35 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_left
% 5.17/5.35 thf(fact_307_divide__divide__eq__left,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.17/5.35 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_left
% 5.17/5.35 thf(fact_308_divide__divide__eq__right,axiom,
% 5.17/5.35 ! [A: complex,B: complex,C: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_right
% 5.17/5.35 thf(fact_309_divide__divide__eq__right,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.35 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_right
% 5.17/5.35 thf(fact_310_divide__divide__eq__right,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_right
% 5.17/5.35 thf(fact_311_times__divide__eq__right,axiom,
% 5.17/5.35 ! [A: complex,B: complex,C: complex] :
% 5.17/5.35 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_eq_right
% 5.17/5.35 thf(fact_312_times__divide__eq__right,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.35 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_eq_right
% 5.17/5.35 thf(fact_313_times__divide__eq__right,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_eq_right
% 5.17/5.35 thf(fact_314_buildup__nothing__in__leaf,axiom,
% 5.17/5.35 ! [N: nat,X: nat] :
% 5.17/5.35 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.17/5.35
% 5.17/5.35 % buildup_nothing_in_leaf
% 5.17/5.35 thf(fact_315_triangle__def,axiom,
% 5.17/5.35 ( nat_triangle
% 5.17/5.35 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % triangle_def
% 5.17/5.35 thf(fact_316_set__decode__Suc,axiom,
% 5.17/5.35 ! [N: nat,X: nat] :
% 5.17/5.35 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 5.17/5.35 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % set_decode_Suc
% 5.17/5.35 thf(fact_317_int__dvd__int__iff,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.35 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % int_dvd_int_iff
% 5.17/5.35 thf(fact_318_real__divide__square__eq,axiom,
% 5.17/5.35 ! [R2: real,A: real] :
% 5.17/5.35 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.17/5.35 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.17/5.35
% 5.17/5.35 % real_divide_square_eq
% 5.17/5.35 thf(fact_319_int__eq__iff__numeral,axiom,
% 5.17/5.35 ! [M: nat,V: num] :
% 5.17/5.35 ( ( ( semiri1314217659103216013at_int @ M )
% 5.17/5.35 = ( numeral_numeral_int @ V ) )
% 5.17/5.35 = ( M
% 5.17/5.35 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % int_eq_iff_numeral
% 5.17/5.35 thf(fact_320_zdiv__numeral__Bit0,axiom,
% 5.17/5.35 ! [V: num,W: num] :
% 5.17/5.35 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.17/5.35 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zdiv_numeral_Bit0
% 5.17/5.35 thf(fact_321_int__int__eq,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ( semiri1314217659103216013at_int @ M )
% 5.17/5.35 = ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.35 = ( M = N ) ) ).
% 5.17/5.35
% 5.17/5.35 % int_int_eq
% 5.17/5.35 thf(fact_322_subset__decode__imp__le,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.17/5.35 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % subset_decode_imp_le
% 5.17/5.35 thf(fact_323_zle__int,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.35 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zle_int
% 5.17/5.35 thf(fact_324_zdiv__int,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.17/5.35 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zdiv_int
% 5.17/5.35 thf(fact_325_divide__divide__eq__left_H,axiom,
% 5.17/5.35 ! [A: complex,B: complex,C: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_left'
% 5.17/5.35 thf(fact_326_divide__divide__eq__left_H,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.17/5.35 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_left'
% 5.17/5.35 thf(fact_327_divide__divide__eq__left_H,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.17/5.35 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_eq_left'
% 5.17/5.35 thf(fact_328_divide__divide__times__eq,axiom,
% 5.17/5.35 ! [X: complex,Y4: complex,Z: complex,W: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y4 @ Z ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_times_eq
% 5.17/5.35 thf(fact_329_divide__divide__times__eq,axiom,
% 5.17/5.35 ! [X: real,Y4: real,Z: real,W: real] :
% 5.17/5.35 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ Z @ W ) )
% 5.17/5.35 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y4 @ Z ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_times_eq
% 5.17/5.35 thf(fact_330_divide__divide__times__eq,axiom,
% 5.17/5.35 ! [X: rat,Y4: rat,Z: rat,W: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.17/5.35 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y4 @ Z ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_divide_times_eq
% 5.17/5.35 thf(fact_331_times__divide__times__eq,axiom,
% 5.17/5.35 ! [X: complex,Y4: complex,Z: complex,W: complex] :
% 5.17/5.35 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y4 @ W ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_times_eq
% 5.17/5.35 thf(fact_332_times__divide__times__eq,axiom,
% 5.17/5.35 ! [X: real,Y4: real,Z: real,W: real] :
% 5.17/5.35 ( ( times_times_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ Z @ W ) )
% 5.17/5.35 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y4 @ W ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_times_eq
% 5.17/5.35 thf(fact_333_times__divide__times__eq,axiom,
% 5.17/5.35 ! [X: rat,Y4: rat,Z: rat,W: rat] :
% 5.17/5.35 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.17/5.35 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y4 @ W ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % times_divide_times_eq
% 5.17/5.35 thf(fact_334_int__ops_I3_J,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.17/5.35 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % int_ops(3)
% 5.17/5.35 thf(fact_335_verit__eq__simplify_I9_J,axiom,
% 5.17/5.35 ! [X33: num,Y32: num] :
% 5.17/5.35 ( ( ( bit1 @ X33 )
% 5.17/5.35 = ( bit1 @ Y32 ) )
% 5.17/5.35 = ( X33 = Y32 ) ) ).
% 5.17/5.35
% 5.17/5.35 % verit_eq_simplify(9)
% 5.17/5.35 thf(fact_336_verit__eq__simplify_I8_J,axiom,
% 5.17/5.35 ! [X2: num,Y2: num] :
% 5.17/5.35 ( ( ( bit0 @ X2 )
% 5.17/5.35 = ( bit0 @ Y2 ) )
% 5.17/5.35 = ( X2 = Y2 ) ) ).
% 5.17/5.35
% 5.17/5.35 % verit_eq_simplify(8)
% 5.17/5.35 thf(fact_337_dual__order_Orefl,axiom,
% 5.17/5.35 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dual_order.refl
% 5.17/5.35 thf(fact_338_dual__order_Orefl,axiom,
% 5.17/5.35 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dual_order.refl
% 5.17/5.35 thf(fact_339_dual__order_Orefl,axiom,
% 5.17/5.35 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dual_order.refl
% 5.17/5.35 thf(fact_340_dual__order_Orefl,axiom,
% 5.17/5.35 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dual_order.refl
% 5.17/5.35 thf(fact_341_dual__order_Orefl,axiom,
% 5.17/5.35 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dual_order.refl
% 5.17/5.35 thf(fact_342_dual__order_Orefl,axiom,
% 5.17/5.35 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 5.17/5.35
% 5.17/5.35 % dual_order.refl
% 5.17/5.35 thf(fact_343_order__refl,axiom,
% 5.17/5.35 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 5.17/5.35
% 5.17/5.35 % order_refl
% 5.17/5.35 thf(fact_344_order__refl,axiom,
% 5.17/5.35 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.17/5.35
% 5.17/5.35 % order_refl
% 5.17/5.35 thf(fact_345_order__refl,axiom,
% 5.17/5.35 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.17/5.35
% 5.17/5.35 % order_refl
% 5.17/5.35 thf(fact_346_order__refl,axiom,
% 5.17/5.35 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.17/5.35
% 5.17/5.35 % order_refl
% 5.17/5.35 thf(fact_347_order__refl,axiom,
% 5.17/5.35 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.17/5.35
% 5.17/5.35 % order_refl
% 5.17/5.35 thf(fact_348_order__refl,axiom,
% 5.17/5.35 ! [X: real] : ( ord_less_eq_real @ X @ X ) ).
% 5.17/5.35
% 5.17/5.35 % order_refl
% 5.17/5.35 thf(fact_349_cnt__non__neg,axiom,
% 5.17/5.35 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ zero_zero_real @ ( vEBT_VEBT_cnt @ T ) ) ).
% 5.17/5.35
% 5.17/5.35 % cnt_non_neg
% 5.17/5.35 thf(fact_350_buildup__nothing__in__min__max,axiom,
% 5.17/5.35 ! [N: nat,X: nat] :
% 5.17/5.35 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.17/5.35
% 5.17/5.35 % buildup_nothing_in_min_max
% 5.17/5.35 thf(fact_351_set__decode__0,axiom,
% 5.17/5.35 ! [X: nat] :
% 5.17/5.35 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.17/5.35 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % set_decode_0
% 5.17/5.35 thf(fact_352_int__ops_I7_J,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.17/5.35 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % int_ops(7)
% 5.17/5.35 thf(fact_353_nat__int__comparison_I3_J,axiom,
% 5.17/5.35 ( ord_less_eq_nat
% 5.17/5.35 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat_int_comparison(3)
% 5.17/5.35 thf(fact_354_verit__eq__simplify_I12_J,axiom,
% 5.17/5.35 ! [X33: num] :
% 5.17/5.35 ( one
% 5.17/5.35 != ( bit1 @ X33 ) ) ).
% 5.17/5.35
% 5.17/5.35 % verit_eq_simplify(12)
% 5.17/5.35 thf(fact_355_verit__eq__simplify_I14_J,axiom,
% 5.17/5.35 ! [X2: num,X33: num] :
% 5.17/5.35 ( ( bit0 @ X2 )
% 5.17/5.35 != ( bit1 @ X33 ) ) ).
% 5.17/5.35
% 5.17/5.35 % verit_eq_simplify(14)
% 5.17/5.35 thf(fact_356_mult__zero__left,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.17/5.35 = zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_left
% 5.17/5.35 thf(fact_357_mult__zero__left,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( times_times_real @ zero_zero_real @ A )
% 5.17/5.35 = zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_left
% 5.17/5.35 thf(fact_358_mult__zero__left,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.17/5.35 = zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_left
% 5.17/5.35 thf(fact_359_mult__zero__left,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_left
% 5.17/5.35 thf(fact_360_mult__zero__left,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( times_times_int @ zero_zero_int @ A )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_left
% 5.17/5.35 thf(fact_361_mult__zero__right,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.17/5.35 = zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_right
% 5.17/5.35 thf(fact_362_mult__zero__right,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( times_times_real @ A @ zero_zero_real )
% 5.17/5.35 = zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_right
% 5.17/5.35 thf(fact_363_mult__zero__right,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.17/5.35 = zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_right
% 5.17/5.35 thf(fact_364_mult__zero__right,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_right
% 5.17/5.35 thf(fact_365_mult__zero__right,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( times_times_int @ A @ zero_zero_int )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % mult_zero_right
% 5.17/5.35 thf(fact_366_mult__eq__0__iff,axiom,
% 5.17/5.35 ! [A: complex,B: complex] :
% 5.17/5.35 ( ( ( times_times_complex @ A @ B )
% 5.17/5.35 = zero_zero_complex )
% 5.17/5.35 = ( ( A = zero_zero_complex )
% 5.17/5.35 | ( B = zero_zero_complex ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_eq_0_iff
% 5.17/5.35 thf(fact_367_mult__eq__0__iff,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ( times_times_real @ A @ B )
% 5.17/5.35 = zero_zero_real )
% 5.17/5.35 = ( ( A = zero_zero_real )
% 5.17/5.35 | ( B = zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_eq_0_iff
% 5.17/5.35 thf(fact_368_mult__eq__0__iff,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ( times_times_rat @ A @ B )
% 5.17/5.35 = zero_zero_rat )
% 5.17/5.35 = ( ( A = zero_zero_rat )
% 5.17/5.35 | ( B = zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_eq_0_iff
% 5.17/5.35 thf(fact_369_mult__eq__0__iff,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ A @ B )
% 5.17/5.35 = zero_zero_nat )
% 5.17/5.35 = ( ( A = zero_zero_nat )
% 5.17/5.35 | ( B = zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_eq_0_iff
% 5.17/5.35 thf(fact_370_mult__eq__0__iff,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ( times_times_int @ A @ B )
% 5.17/5.35 = zero_zero_int )
% 5.17/5.35 = ( ( A = zero_zero_int )
% 5.17/5.35 | ( B = zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_eq_0_iff
% 5.17/5.35 thf(fact_371_mult__cancel__left,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( ( times_times_complex @ C @ A )
% 5.17/5.35 = ( times_times_complex @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_complex )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_left
% 5.17/5.35 thf(fact_372_mult__cancel__left,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( ( times_times_real @ C @ A )
% 5.17/5.35 = ( times_times_real @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_real )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_left
% 5.17/5.35 thf(fact_373_mult__cancel__left,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( ( times_times_rat @ C @ A )
% 5.17/5.35 = ( times_times_rat @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_rat )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_left
% 5.17/5.35 thf(fact_374_mult__cancel__left,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ C @ A )
% 5.17/5.35 = ( times_times_nat @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_nat )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_left
% 5.17/5.35 thf(fact_375_mult__cancel__left,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( ( times_times_int @ C @ A )
% 5.17/5.35 = ( times_times_int @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_int )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_left
% 5.17/5.35 thf(fact_376_mult__cancel__right,axiom,
% 5.17/5.35 ! [A: complex,C: complex,B: complex] :
% 5.17/5.35 ( ( ( times_times_complex @ A @ C )
% 5.17/5.35 = ( times_times_complex @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_complex )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_right
% 5.17/5.35 thf(fact_377_mult__cancel__right,axiom,
% 5.17/5.35 ! [A: real,C: real,B: real] :
% 5.17/5.35 ( ( ( times_times_real @ A @ C )
% 5.17/5.35 = ( times_times_real @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_real )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_right
% 5.17/5.35 thf(fact_378_mult__cancel__right,axiom,
% 5.17/5.35 ! [A: rat,C: rat,B: rat] :
% 5.17/5.35 ( ( ( times_times_rat @ A @ C )
% 5.17/5.35 = ( times_times_rat @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_rat )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_right
% 5.17/5.35 thf(fact_379_mult__cancel__right,axiom,
% 5.17/5.35 ! [A: nat,C: nat,B: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ A @ C )
% 5.17/5.35 = ( times_times_nat @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_nat )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_right
% 5.17/5.35 thf(fact_380_mult__cancel__right,axiom,
% 5.17/5.35 ! [A: int,C: int,B: int] :
% 5.17/5.35 ( ( ( times_times_int @ A @ C )
% 5.17/5.35 = ( times_times_int @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_int )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel_right
% 5.17/5.35 thf(fact_381_div__0,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.17/5.35 = zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % div_0
% 5.17/5.35 thf(fact_382_div__0,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.17/5.35 = zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % div_0
% 5.17/5.35 thf(fact_383_div__0,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.17/5.35 = zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % div_0
% 5.17/5.35 thf(fact_384_div__0,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % div_0
% 5.17/5.35 thf(fact_385_div__0,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % div_0
% 5.17/5.35 thf(fact_386_div__by__0,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.17/5.35 = zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % div_by_0
% 5.17/5.35 thf(fact_387_div__by__0,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.17/5.35 = zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % div_by_0
% 5.17/5.35 thf(fact_388_div__by__0,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.17/5.35 = zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % div_by_0
% 5.17/5.35 thf(fact_389_div__by__0,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % div_by_0
% 5.17/5.35 thf(fact_390_div__by__0,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % div_by_0
% 5.17/5.35 thf(fact_391_divide__eq__0__iff,axiom,
% 5.17/5.35 ! [A: complex,B: complex] :
% 5.17/5.35 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.17/5.35 = zero_zero_complex )
% 5.17/5.35 = ( ( A = zero_zero_complex )
% 5.17/5.35 | ( B = zero_zero_complex ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_eq_0_iff
% 5.17/5.35 thf(fact_392_divide__eq__0__iff,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ( divide_divide_real @ A @ B )
% 5.17/5.35 = zero_zero_real )
% 5.17/5.35 = ( ( A = zero_zero_real )
% 5.17/5.35 | ( B = zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_eq_0_iff
% 5.17/5.35 thf(fact_393_divide__eq__0__iff,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ( divide_divide_rat @ A @ B )
% 5.17/5.35 = zero_zero_rat )
% 5.17/5.35 = ( ( A = zero_zero_rat )
% 5.17/5.35 | ( B = zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_eq_0_iff
% 5.17/5.35 thf(fact_394_divide__cancel__left,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.17/5.35 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_complex )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_cancel_left
% 5.17/5.35 thf(fact_395_divide__cancel__left,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( ( divide_divide_real @ C @ A )
% 5.17/5.35 = ( divide_divide_real @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_real )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_cancel_left
% 5.17/5.35 thf(fact_396_divide__cancel__left,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( ( divide_divide_rat @ C @ A )
% 5.17/5.35 = ( divide_divide_rat @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_rat )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_cancel_left
% 5.17/5.35 thf(fact_397_divide__cancel__right,axiom,
% 5.17/5.35 ! [A: complex,C: complex,B: complex] :
% 5.17/5.35 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.17/5.35 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_complex )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_cancel_right
% 5.17/5.35 thf(fact_398_divide__cancel__right,axiom,
% 5.17/5.35 ! [A: real,C: real,B: real] :
% 5.17/5.35 ( ( ( divide_divide_real @ A @ C )
% 5.17/5.35 = ( divide_divide_real @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_real )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_cancel_right
% 5.17/5.35 thf(fact_399_divide__cancel__right,axiom,
% 5.17/5.35 ! [A: rat,C: rat,B: rat] :
% 5.17/5.35 ( ( ( divide_divide_rat @ A @ C )
% 5.17/5.35 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_rat )
% 5.17/5.35 | ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_cancel_right
% 5.17/5.35 thf(fact_400_bits__div__0,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % bits_div_0
% 5.17/5.35 thf(fact_401_bits__div__0,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % bits_div_0
% 5.17/5.35 thf(fact_402_bits__div__by__0,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % bits_div_by_0
% 5.17/5.35 thf(fact_403_bits__div__by__0,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % bits_div_by_0
% 5.17/5.35 thf(fact_404_division__ring__divide__zero,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.17/5.35 = zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % division_ring_divide_zero
% 5.17/5.35 thf(fact_405_division__ring__divide__zero,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.17/5.35 = zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % division_ring_divide_zero
% 5.17/5.35 thf(fact_406_division__ring__divide__zero,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.17/5.35 = zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % division_ring_divide_zero
% 5.17/5.35 thf(fact_407_dvd__0__left__iff,axiom,
% 5.17/5.35 ! [A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.17/5.35 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left_iff
% 5.17/5.35 thf(fact_408_dvd__0__left__iff,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.17/5.35 = ( A = zero_zero_complex ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left_iff
% 5.17/5.35 thf(fact_409_dvd__0__left__iff,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.17/5.35 = ( A = zero_zero_real ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left_iff
% 5.17/5.35 thf(fact_410_dvd__0__left__iff,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.17/5.35 = ( A = zero_zero_rat ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left_iff
% 5.17/5.35 thf(fact_411_dvd__0__left__iff,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.17/5.35 = ( A = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left_iff
% 5.17/5.35 thf(fact_412_dvd__0__left__iff,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.17/5.35 = ( A = zero_zero_int ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left_iff
% 5.17/5.35 thf(fact_413_dvd__0__right,axiom,
% 5.17/5.35 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_right
% 5.17/5.35 thf(fact_414_dvd__0__right,axiom,
% 5.17/5.35 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_right
% 5.17/5.35 thf(fact_415_dvd__0__right,axiom,
% 5.17/5.35 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_right
% 5.17/5.35 thf(fact_416_dvd__0__right,axiom,
% 5.17/5.35 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_right
% 5.17/5.35 thf(fact_417_dvd__0__right,axiom,
% 5.17/5.35 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_right
% 5.17/5.35 thf(fact_418_dvd__0__right,axiom,
% 5.17/5.35 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_right
% 5.17/5.35 thf(fact_419_le0,axiom,
% 5.17/5.35 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.17/5.35
% 5.17/5.35 % le0
% 5.17/5.35 thf(fact_420_bot__nat__0_Oextremum,axiom,
% 5.17/5.35 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.17/5.35
% 5.17/5.35 % bot_nat_0.extremum
% 5.17/5.35 thf(fact_421_mult__cancel2,axiom,
% 5.17/5.35 ! [M: nat,K: nat,N: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ M @ K )
% 5.17/5.35 = ( times_times_nat @ N @ K ) )
% 5.17/5.35 = ( ( M = N )
% 5.17/5.35 | ( K = zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel2
% 5.17/5.35 thf(fact_422_mult__cancel1,axiom,
% 5.17/5.35 ! [K: nat,M: nat,N: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ K @ M )
% 5.17/5.35 = ( times_times_nat @ K @ N ) )
% 5.17/5.35 = ( ( M = N )
% 5.17/5.35 | ( K = zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_cancel1
% 5.17/5.35 thf(fact_423_mult__0__right,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % mult_0_right
% 5.17/5.35 thf(fact_424_mult__is__0,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ M @ N )
% 5.17/5.35 = zero_zero_nat )
% 5.17/5.35 = ( ( M = zero_zero_nat )
% 5.17/5.35 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_is_0
% 5.17/5.35 thf(fact_425_triangle__0,axiom,
% 5.17/5.35 ( ( nat_triangle @ zero_zero_nat )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % triangle_0
% 5.17/5.35 thf(fact_426_nonzero__mult__div__cancel__left,axiom,
% 5.17/5.35 ! [A: complex,B: complex] :
% 5.17/5.35 ( ( A != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.17/5.35 = B ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_left
% 5.17/5.35 thf(fact_427_nonzero__mult__div__cancel__left,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( A != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.17/5.35 = B ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_left
% 5.17/5.35 thf(fact_428_nonzero__mult__div__cancel__left,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( A != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.17/5.35 = B ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_left
% 5.17/5.35 thf(fact_429_nonzero__mult__div__cancel__left,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( A != zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.17/5.35 = B ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_left
% 5.17/5.35 thf(fact_430_nonzero__mult__div__cancel__left,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( A != zero_zero_int )
% 5.17/5.35 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.17/5.35 = B ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_left
% 5.17/5.35 thf(fact_431_nonzero__mult__div__cancel__right,axiom,
% 5.17/5.35 ! [B: complex,A: complex] :
% 5.17/5.35 ( ( B != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.17/5.35 = A ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_right
% 5.17/5.35 thf(fact_432_nonzero__mult__div__cancel__right,axiom,
% 5.17/5.35 ! [B: real,A: real] :
% 5.17/5.35 ( ( B != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.17/5.35 = A ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_right
% 5.17/5.35 thf(fact_433_nonzero__mult__div__cancel__right,axiom,
% 5.17/5.35 ! [B: rat,A: rat] :
% 5.17/5.35 ( ( B != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.17/5.35 = A ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_right
% 5.17/5.35 thf(fact_434_nonzero__mult__div__cancel__right,axiom,
% 5.17/5.35 ! [B: nat,A: nat] :
% 5.17/5.35 ( ( B != zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.17/5.35 = A ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_right
% 5.17/5.35 thf(fact_435_nonzero__mult__div__cancel__right,axiom,
% 5.17/5.35 ! [B: int,A: int] :
% 5.17/5.35 ( ( B != zero_zero_int )
% 5.17/5.35 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.17/5.35 = A ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_div_cancel_right
% 5.17/5.35 thf(fact_436_div__mult__mult1,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( C != zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.17/5.35 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_mult1
% 5.17/5.35 thf(fact_437_div__mult__mult1,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( C != zero_zero_int )
% 5.17/5.35 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.35 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_mult1
% 5.17/5.35 thf(fact_438_div__mult__mult2,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( C != zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_mult2
% 5.17/5.35 thf(fact_439_div__mult__mult2,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( C != zero_zero_int )
% 5.17/5.35 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.35 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_mult2
% 5.17/5.35 thf(fact_440_div__mult__mult1__if,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( ( C = zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.17/5.35 = zero_zero_nat ) )
% 5.17/5.35 & ( ( C != zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.17/5.35 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_mult1_if
% 5.17/5.35 thf(fact_441_div__mult__mult1__if,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( ( C = zero_zero_int )
% 5.17/5.35 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.35 = zero_zero_int ) )
% 5.17/5.35 & ( ( C != zero_zero_int )
% 5.17/5.35 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.35 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % div_mult_mult1_if
% 5.17/5.35 thf(fact_442_mult__divide__mult__cancel__left__if,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( ( C = zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.17/5.35 = zero_zero_complex ) )
% 5.17/5.35 & ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_divide_mult_cancel_left_if
% 5.17/5.35 thf(fact_443_mult__divide__mult__cancel__left__if,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( ( C = zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.35 = zero_zero_real ) )
% 5.17/5.35 & ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.35 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_divide_mult_cancel_left_if
% 5.17/5.35 thf(fact_444_mult__divide__mult__cancel__left__if,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( ( C = zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.35 = zero_zero_rat ) )
% 5.17/5.35 & ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.35 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_divide_mult_cancel_left_if
% 5.17/5.35 thf(fact_445_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_left
% 5.17/5.35 thf(fact_446_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.35 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_left
% 5.17/5.35 thf(fact_447_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.35 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_left
% 5.17/5.35 thf(fact_448_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_left2
% 5.17/5.35 thf(fact_449_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.17/5.35 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_left2
% 5.17/5.35 thf(fact_450_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_left2
% 5.17/5.35 thf(fact_451_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_right
% 5.17/5.35 thf(fact_452_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.35 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_right
% 5.17/5.35 thf(fact_453_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.35 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_right
% 5.17/5.35 thf(fact_454_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.17/5.35 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_right2
% 5.17/5.35 thf(fact_455_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.17/5.35 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_right2
% 5.17/5.35 thf(fact_456_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.35 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nonzero_mult_divide_mult_cancel_right2
% 5.17/5.35 thf(fact_457_dvd__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_z3403309356797280102nteger )
% 5.17/5.35 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_left
% 5.17/5.35 thf(fact_458_dvd__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_complex )
% 5.17/5.35 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_left
% 5.17/5.35 thf(fact_459_dvd__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_real )
% 5.17/5.35 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_left
% 5.17/5.35 thf(fact_460_dvd__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_rat )
% 5.17/5.35 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_left
% 5.17/5.35 thf(fact_461_dvd__mult__cancel__left,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.35 = ( ( C = zero_zero_int )
% 5.17/5.35 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_left
% 5.17/5.35 thf(fact_462_dvd__mult__cancel__right,axiom,
% 5.17/5.35 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_z3403309356797280102nteger )
% 5.17/5.35 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_right
% 5.17/5.35 thf(fact_463_dvd__mult__cancel__right,axiom,
% 5.17/5.35 ! [A: complex,C: complex,B: complex] :
% 5.17/5.35 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_complex )
% 5.17/5.35 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_right
% 5.17/5.35 thf(fact_464_dvd__mult__cancel__right,axiom,
% 5.17/5.35 ! [A: real,C: real,B: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_real )
% 5.17/5.35 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_right
% 5.17/5.35 thf(fact_465_dvd__mult__cancel__right,axiom,
% 5.17/5.35 ! [A: rat,C: rat,B: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_rat )
% 5.17/5.35 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_right
% 5.17/5.35 thf(fact_466_dvd__mult__cancel__right,axiom,
% 5.17/5.35 ! [A: int,C: int,B: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.35 = ( ( C = zero_zero_int )
% 5.17/5.35 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_mult_cancel_right
% 5.17/5.35 thf(fact_467_dvd__times__left__cancel__iff,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.35 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.17/5.35 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_times_left_cancel_iff
% 5.17/5.35 thf(fact_468_dvd__times__left__cancel__iff,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( A != zero_zero_nat )
% 5.17/5.35 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.17/5.35 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_times_left_cancel_iff
% 5.17/5.35 thf(fact_469_dvd__times__left__cancel__iff,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( A != zero_zero_int )
% 5.17/5.35 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.17/5.35 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_times_left_cancel_iff
% 5.17/5.35 thf(fact_470_dvd__times__right__cancel__iff,axiom,
% 5.17/5.35 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.35 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.35 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.17/5.35 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_times_right_cancel_iff
% 5.17/5.35 thf(fact_471_dvd__times__right__cancel__iff,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( A != zero_zero_nat )
% 5.17/5.35 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.17/5.35 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_times_right_cancel_iff
% 5.17/5.35 thf(fact_472_dvd__times__right__cancel__iff,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( A != zero_zero_int )
% 5.17/5.35 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.17/5.35 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_times_right_cancel_iff
% 5.17/5.35 thf(fact_473_of__nat__eq__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ( semiri8010041392384452111omplex @ M )
% 5.17/5.35 = zero_zero_complex )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_eq_0_iff
% 5.17/5.35 thf(fact_474_of__nat__eq__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ( semiri5074537144036343181t_real @ M )
% 5.17/5.35 = zero_zero_real )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_eq_0_iff
% 5.17/5.35 thf(fact_475_of__nat__eq__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ( semiri681578069525770553at_rat @ M )
% 5.17/5.35 = zero_zero_rat )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_eq_0_iff
% 5.17/5.35 thf(fact_476_of__nat__eq__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.17/5.35 = zero_zero_nat )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_eq_0_iff
% 5.17/5.35 thf(fact_477_of__nat__eq__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ( semiri1314217659103216013at_int @ M )
% 5.17/5.35 = zero_zero_int )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_eq_0_iff
% 5.17/5.35 thf(fact_478_of__nat__0__eq__iff,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( zero_zero_complex
% 5.17/5.35 = ( semiri8010041392384452111omplex @ N ) )
% 5.17/5.35 = ( zero_zero_nat = N ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0_eq_iff
% 5.17/5.35 thf(fact_479_of__nat__0__eq__iff,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( zero_zero_real
% 5.17/5.35 = ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.35 = ( zero_zero_nat = N ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0_eq_iff
% 5.17/5.35 thf(fact_480_of__nat__0__eq__iff,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( zero_zero_rat
% 5.17/5.35 = ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.35 = ( zero_zero_nat = N ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0_eq_iff
% 5.17/5.35 thf(fact_481_of__nat__0__eq__iff,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( zero_zero_nat
% 5.17/5.35 = ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.35 = ( zero_zero_nat = N ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0_eq_iff
% 5.17/5.35 thf(fact_482_of__nat__0__eq__iff,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( zero_zero_int
% 5.17/5.35 = ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.35 = ( zero_zero_nat = N ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0_eq_iff
% 5.17/5.35 thf(fact_483_of__nat__0,axiom,
% 5.17/5.35 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.17/5.35 = zero_zero_complex ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0
% 5.17/5.35 thf(fact_484_of__nat__0,axiom,
% 5.17/5.35 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.17/5.35 = zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0
% 5.17/5.35 thf(fact_485_of__nat__0,axiom,
% 5.17/5.35 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.17/5.35 = zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0
% 5.17/5.35 thf(fact_486_of__nat__0,axiom,
% 5.17/5.35 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0
% 5.17/5.35 thf(fact_487_of__nat__0,axiom,
% 5.17/5.35 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.17/5.35 = zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_0
% 5.17/5.35 thf(fact_488_one__eq__mult__iff,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ( suc @ zero_zero_nat )
% 5.17/5.35 = ( times_times_nat @ M @ N ) )
% 5.17/5.35 = ( ( M
% 5.17/5.35 = ( suc @ zero_zero_nat ) )
% 5.17/5.35 & ( N
% 5.17/5.35 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % one_eq_mult_iff
% 5.17/5.35 thf(fact_489_mult__eq__1__iff,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ M @ N )
% 5.17/5.35 = ( suc @ zero_zero_nat ) )
% 5.17/5.35 = ( ( M
% 5.17/5.35 = ( suc @ zero_zero_nat ) )
% 5.17/5.35 & ( N
% 5.17/5.35 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_eq_1_iff
% 5.17/5.35 thf(fact_490_dvd__1__left,axiom,
% 5.17/5.35 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_1_left
% 5.17/5.35 thf(fact_491_dvd__1__iff__1,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.17/5.35 = ( M
% 5.17/5.35 = ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_1_iff_1
% 5.17/5.35 thf(fact_492_div__by__Suc__0,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.17/5.35 = M ) ).
% 5.17/5.35
% 5.17/5.35 % div_by_Suc_0
% 5.17/5.35 thf(fact_493_nat__mult__dvd__cancel__disj,axiom,
% 5.17/5.35 ! [K: nat,M: nat,N: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.35 = ( ( K = zero_zero_nat )
% 5.17/5.35 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat_mult_dvd_cancel_disj
% 5.17/5.35 thf(fact_494_nat__mult__div__cancel__disj,axiom,
% 5.17/5.35 ! [K: nat,M: nat,N: nat] :
% 5.17/5.35 ( ( ( K = zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.35 = zero_zero_nat ) )
% 5.17/5.35 & ( ( K != zero_zero_nat )
% 5.17/5.35 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.35 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat_mult_div_cancel_disj
% 5.17/5.35 thf(fact_495_divide__eq__eq__numeral1_I1_J,axiom,
% 5.17/5.35 ! [B: complex,W: num,A: complex] :
% 5.17/5.35 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.35 = A )
% 5.17/5.35 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.17/5.35 != zero_zero_complex )
% 5.17/5.35 => ( B
% 5.17/5.35 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.17/5.35 & ( ( ( numera6690914467698888265omplex @ W )
% 5.17/5.35 = zero_zero_complex )
% 5.17/5.35 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_eq_eq_numeral1(1)
% 5.17/5.35 thf(fact_496_divide__eq__eq__numeral1_I1_J,axiom,
% 5.17/5.35 ! [B: real,W: num,A: real] :
% 5.17/5.35 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.17/5.35 = A )
% 5.17/5.35 = ( ( ( ( numeral_numeral_real @ W )
% 5.17/5.35 != zero_zero_real )
% 5.17/5.35 => ( B
% 5.17/5.35 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.17/5.35 & ( ( ( numeral_numeral_real @ W )
% 5.17/5.35 = zero_zero_real )
% 5.17/5.35 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_eq_eq_numeral1(1)
% 5.17/5.35 thf(fact_497_divide__eq__eq__numeral1_I1_J,axiom,
% 5.17/5.35 ! [B: rat,W: num,A: rat] :
% 5.17/5.35 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.17/5.35 = A )
% 5.17/5.35 = ( ( ( ( numeral_numeral_rat @ W )
% 5.17/5.35 != zero_zero_rat )
% 5.17/5.35 => ( B
% 5.17/5.35 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.17/5.35 & ( ( ( numeral_numeral_rat @ W )
% 5.17/5.35 = zero_zero_rat )
% 5.17/5.35 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_eq_eq_numeral1(1)
% 5.17/5.35 thf(fact_498_eq__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.35 ! [A: complex,B: complex,W: num] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.35 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.17/5.35 != zero_zero_complex )
% 5.17/5.35 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.35 = B ) )
% 5.17/5.35 & ( ( ( numera6690914467698888265omplex @ W )
% 5.17/5.35 = zero_zero_complex )
% 5.17/5.35 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % eq_divide_eq_numeral1(1)
% 5.17/5.35 thf(fact_499_eq__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.35 ! [A: real,B: real,W: num] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.35 = ( ( ( ( numeral_numeral_real @ W )
% 5.17/5.35 != zero_zero_real )
% 5.17/5.35 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.17/5.35 = B ) )
% 5.17/5.35 & ( ( ( numeral_numeral_real @ W )
% 5.17/5.35 = zero_zero_real )
% 5.17/5.35 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % eq_divide_eq_numeral1(1)
% 5.17/5.35 thf(fact_500_eq__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.35 ! [A: rat,B: rat,W: num] :
% 5.17/5.35 ( ( A
% 5.17/5.35 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.35 = ( ( ( ( numeral_numeral_rat @ W )
% 5.17/5.35 != zero_zero_rat )
% 5.17/5.35 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.17/5.35 = B ) )
% 5.17/5.35 & ( ( ( numeral_numeral_rat @ W )
% 5.17/5.35 = zero_zero_rat )
% 5.17/5.35 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % eq_divide_eq_numeral1(1)
% 5.17/5.35 thf(fact_501_of__nat__le__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_le_0_iff
% 5.17/5.35 thf(fact_502_of__nat__le__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_le_0_iff
% 5.17/5.35 thf(fact_503_of__nat__le__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_le_0_iff
% 5.17/5.35 thf(fact_504_of__nat__le__0__iff,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.17/5.35 = ( M = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % of_nat_le_0_iff
% 5.17/5.35 thf(fact_505_one__le__mult__iff,axiom,
% 5.17/5.35 ! [M: nat,N: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.17/5.35 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.17/5.35 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % one_le_mult_iff
% 5.17/5.35 thf(fact_506_verit__la__generic,axiom,
% 5.17/5.35 ! [A: int,X: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ X )
% 5.17/5.35 | ( A = X )
% 5.17/5.35 | ( ord_less_eq_int @ X @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % verit_la_generic
% 5.17/5.35 thf(fact_507_le__numeral__extra_I3_J,axiom,
% 5.17/5.35 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.17/5.35
% 5.17/5.35 % le_numeral_extra(3)
% 5.17/5.35 thf(fact_508_le__numeral__extra_I3_J,axiom,
% 5.17/5.35 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.17/5.35
% 5.17/5.35 % le_numeral_extra(3)
% 5.17/5.35 thf(fact_509_le__numeral__extra_I3_J,axiom,
% 5.17/5.35 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.17/5.35
% 5.17/5.35 % le_numeral_extra(3)
% 5.17/5.35 thf(fact_510_le__numeral__extra_I3_J,axiom,
% 5.17/5.35 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.17/5.35
% 5.17/5.35 % le_numeral_extra(3)
% 5.17/5.35 thf(fact_511_zero__neq__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ( zero_zero_complex
% 5.17/5.35 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_neq_numeral
% 5.17/5.35 thf(fact_512_zero__neq__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ( zero_zero_real
% 5.17/5.35 != ( numeral_numeral_real @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_neq_numeral
% 5.17/5.35 thf(fact_513_zero__neq__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ( zero_zero_rat
% 5.17/5.35 != ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_neq_numeral
% 5.17/5.35 thf(fact_514_zero__neq__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ( zero_zero_nat
% 5.17/5.35 != ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_neq_numeral
% 5.17/5.35 thf(fact_515_zero__neq__numeral,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ( zero_zero_int
% 5.17/5.35 != ( numeral_numeral_int @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_neq_numeral
% 5.17/5.35 thf(fact_516_mult__not__zero,axiom,
% 5.17/5.35 ! [A: complex,B: complex] :
% 5.17/5.35 ( ( ( times_times_complex @ A @ B )
% 5.17/5.35 != zero_zero_complex )
% 5.17/5.35 => ( ( A != zero_zero_complex )
% 5.17/5.35 & ( B != zero_zero_complex ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_not_zero
% 5.17/5.35 thf(fact_517_mult__not__zero,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ( times_times_real @ A @ B )
% 5.17/5.35 != zero_zero_real )
% 5.17/5.35 => ( ( A != zero_zero_real )
% 5.17/5.35 & ( B != zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_not_zero
% 5.17/5.35 thf(fact_518_mult__not__zero,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ( times_times_rat @ A @ B )
% 5.17/5.35 != zero_zero_rat )
% 5.17/5.35 => ( ( A != zero_zero_rat )
% 5.17/5.35 & ( B != zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_not_zero
% 5.17/5.35 thf(fact_519_mult__not__zero,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ A @ B )
% 5.17/5.35 != zero_zero_nat )
% 5.17/5.35 => ( ( A != zero_zero_nat )
% 5.17/5.35 & ( B != zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_not_zero
% 5.17/5.35 thf(fact_520_mult__not__zero,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ( times_times_int @ A @ B )
% 5.17/5.35 != zero_zero_int )
% 5.17/5.35 => ( ( A != zero_zero_int )
% 5.17/5.35 & ( B != zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_not_zero
% 5.17/5.35 thf(fact_521_divisors__zero,axiom,
% 5.17/5.35 ! [A: complex,B: complex] :
% 5.17/5.35 ( ( ( times_times_complex @ A @ B )
% 5.17/5.35 = zero_zero_complex )
% 5.17/5.35 => ( ( A = zero_zero_complex )
% 5.17/5.35 | ( B = zero_zero_complex ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divisors_zero
% 5.17/5.35 thf(fact_522_divisors__zero,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ( times_times_real @ A @ B )
% 5.17/5.35 = zero_zero_real )
% 5.17/5.35 => ( ( A = zero_zero_real )
% 5.17/5.35 | ( B = zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divisors_zero
% 5.17/5.35 thf(fact_523_divisors__zero,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ( times_times_rat @ A @ B )
% 5.17/5.35 = zero_zero_rat )
% 5.17/5.35 => ( ( A = zero_zero_rat )
% 5.17/5.35 | ( B = zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divisors_zero
% 5.17/5.35 thf(fact_524_divisors__zero,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ A @ B )
% 5.17/5.35 = zero_zero_nat )
% 5.17/5.35 => ( ( A = zero_zero_nat )
% 5.17/5.35 | ( B = zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divisors_zero
% 5.17/5.35 thf(fact_525_divisors__zero,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ( times_times_int @ A @ B )
% 5.17/5.35 = zero_zero_int )
% 5.17/5.35 => ( ( A = zero_zero_int )
% 5.17/5.35 | ( B = zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divisors_zero
% 5.17/5.35 thf(fact_526_no__zero__divisors,axiom,
% 5.17/5.35 ! [A: complex,B: complex] :
% 5.17/5.35 ( ( A != zero_zero_complex )
% 5.17/5.35 => ( ( B != zero_zero_complex )
% 5.17/5.35 => ( ( times_times_complex @ A @ B )
% 5.17/5.35 != zero_zero_complex ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % no_zero_divisors
% 5.17/5.35 thf(fact_527_no__zero__divisors,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( A != zero_zero_real )
% 5.17/5.35 => ( ( B != zero_zero_real )
% 5.17/5.35 => ( ( times_times_real @ A @ B )
% 5.17/5.35 != zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % no_zero_divisors
% 5.17/5.35 thf(fact_528_no__zero__divisors,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( A != zero_zero_rat )
% 5.17/5.35 => ( ( B != zero_zero_rat )
% 5.17/5.35 => ( ( times_times_rat @ A @ B )
% 5.17/5.35 != zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % no_zero_divisors
% 5.17/5.35 thf(fact_529_no__zero__divisors,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( A != zero_zero_nat )
% 5.17/5.35 => ( ( B != zero_zero_nat )
% 5.17/5.35 => ( ( times_times_nat @ A @ B )
% 5.17/5.35 != zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % no_zero_divisors
% 5.17/5.35 thf(fact_530_no__zero__divisors,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( A != zero_zero_int )
% 5.17/5.35 => ( ( B != zero_zero_int )
% 5.17/5.35 => ( ( times_times_int @ A @ B )
% 5.17/5.35 != zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % no_zero_divisors
% 5.17/5.35 thf(fact_531_mult__left__cancel,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( ( times_times_complex @ C @ A )
% 5.17/5.35 = ( times_times_complex @ C @ B ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_cancel
% 5.17/5.35 thf(fact_532_mult__left__cancel,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( ( times_times_real @ C @ A )
% 5.17/5.35 = ( times_times_real @ C @ B ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_cancel
% 5.17/5.35 thf(fact_533_mult__left__cancel,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( ( times_times_rat @ C @ A )
% 5.17/5.35 = ( times_times_rat @ C @ B ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_cancel
% 5.17/5.35 thf(fact_534_mult__left__cancel,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( C != zero_zero_nat )
% 5.17/5.35 => ( ( ( times_times_nat @ C @ A )
% 5.17/5.35 = ( times_times_nat @ C @ B ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_cancel
% 5.17/5.35 thf(fact_535_mult__left__cancel,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( C != zero_zero_int )
% 5.17/5.35 => ( ( ( times_times_int @ C @ A )
% 5.17/5.35 = ( times_times_int @ C @ B ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_cancel
% 5.17/5.35 thf(fact_536_mult__right__cancel,axiom,
% 5.17/5.35 ! [C: complex,A: complex,B: complex] :
% 5.17/5.35 ( ( C != zero_zero_complex )
% 5.17/5.35 => ( ( ( times_times_complex @ A @ C )
% 5.17/5.35 = ( times_times_complex @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_cancel
% 5.17/5.35 thf(fact_537_mult__right__cancel,axiom,
% 5.17/5.35 ! [C: real,A: real,B: real] :
% 5.17/5.35 ( ( C != zero_zero_real )
% 5.17/5.35 => ( ( ( times_times_real @ A @ C )
% 5.17/5.35 = ( times_times_real @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_cancel
% 5.17/5.35 thf(fact_538_mult__right__cancel,axiom,
% 5.17/5.35 ! [C: rat,A: rat,B: rat] :
% 5.17/5.35 ( ( C != zero_zero_rat )
% 5.17/5.35 => ( ( ( times_times_rat @ A @ C )
% 5.17/5.35 = ( times_times_rat @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_cancel
% 5.17/5.35 thf(fact_539_mult__right__cancel,axiom,
% 5.17/5.35 ! [C: nat,A: nat,B: nat] :
% 5.17/5.35 ( ( C != zero_zero_nat )
% 5.17/5.35 => ( ( ( times_times_nat @ A @ C )
% 5.17/5.35 = ( times_times_nat @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_cancel
% 5.17/5.35 thf(fact_540_mult__right__cancel,axiom,
% 5.17/5.35 ! [C: int,A: int,B: int] :
% 5.17/5.35 ( ( C != zero_zero_int )
% 5.17/5.35 => ( ( ( times_times_int @ A @ C )
% 5.17/5.35 = ( times_times_int @ B @ C ) )
% 5.17/5.35 = ( A = B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_cancel
% 5.17/5.35 thf(fact_541_dvd__0__left,axiom,
% 5.17/5.35 ! [A: code_integer] :
% 5.17/5.35 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.17/5.35 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left
% 5.17/5.35 thf(fact_542_dvd__0__left,axiom,
% 5.17/5.35 ! [A: complex] :
% 5.17/5.35 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.17/5.35 => ( A = zero_zero_complex ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left
% 5.17/5.35 thf(fact_543_dvd__0__left,axiom,
% 5.17/5.35 ! [A: real] :
% 5.17/5.35 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.17/5.35 => ( A = zero_zero_real ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left
% 5.17/5.35 thf(fact_544_dvd__0__left,axiom,
% 5.17/5.35 ! [A: rat] :
% 5.17/5.35 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.17/5.35 => ( A = zero_zero_rat ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left
% 5.17/5.35 thf(fact_545_dvd__0__left,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.17/5.35 => ( A = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left
% 5.17/5.35 thf(fact_546_dvd__0__left,axiom,
% 5.17/5.35 ! [A: int] :
% 5.17/5.35 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.17/5.35 => ( A = zero_zero_int ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_0_left
% 5.17/5.35 thf(fact_547_dvd__field__iff,axiom,
% 5.17/5.35 ( dvd_dvd_complex
% 5.17/5.35 = ( ^ [A3: complex,B2: complex] :
% 5.17/5.35 ( ( A3 = zero_zero_complex )
% 5.17/5.35 => ( B2 = zero_zero_complex ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_field_iff
% 5.17/5.35 thf(fact_548_dvd__field__iff,axiom,
% 5.17/5.35 ( dvd_dvd_real
% 5.17/5.35 = ( ^ [A3: real,B2: real] :
% 5.17/5.35 ( ( A3 = zero_zero_real )
% 5.17/5.35 => ( B2 = zero_zero_real ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_field_iff
% 5.17/5.35 thf(fact_549_dvd__field__iff,axiom,
% 5.17/5.35 ( dvd_dvd_rat
% 5.17/5.35 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.35 ( ( A3 = zero_zero_rat )
% 5.17/5.35 => ( B2 = zero_zero_rat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % dvd_field_iff
% 5.17/5.35 thf(fact_550_list__decode_Ocases,axiom,
% 5.17/5.35 ! [X: nat] :
% 5.17/5.35 ( ( X != zero_zero_nat )
% 5.17/5.35 => ~ ! [N2: nat] :
% 5.17/5.35 ( X
% 5.17/5.35 != ( suc @ N2 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % list_decode.cases
% 5.17/5.35 thf(fact_551_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Ocases,axiom,
% 5.17/5.35 ! [X: nat] :
% 5.17/5.35 ( ( X != zero_zero_nat )
% 5.17/5.35 => ( ( X
% 5.17/5.35 != ( suc @ zero_zero_nat ) )
% 5.17/5.35 => ~ ! [Va: nat] :
% 5.17/5.35 ( X
% 5.17/5.35 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.cases
% 5.17/5.35 thf(fact_552_nat_Odistinct_I1_J,axiom,
% 5.17/5.35 ! [X2: nat] :
% 5.17/5.35 ( zero_zero_nat
% 5.17/5.35 != ( suc @ X2 ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat.distinct(1)
% 5.17/5.35 thf(fact_553_old_Onat_Odistinct_I2_J,axiom,
% 5.17/5.35 ! [Nat2: nat] :
% 5.17/5.35 ( ( suc @ Nat2 )
% 5.17/5.35 != zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % old.nat.distinct(2)
% 5.17/5.35 thf(fact_554_old_Onat_Odistinct_I1_J,axiom,
% 5.17/5.35 ! [Nat2: nat] :
% 5.17/5.35 ( zero_zero_nat
% 5.17/5.35 != ( suc @ Nat2 ) ) ).
% 5.17/5.35
% 5.17/5.35 % old.nat.distinct(1)
% 5.17/5.35 thf(fact_555_nat_OdiscI,axiom,
% 5.17/5.35 ! [Nat: nat,X2: nat] :
% 5.17/5.35 ( ( Nat
% 5.17/5.35 = ( suc @ X2 ) )
% 5.17/5.35 => ( Nat != zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat.discI
% 5.17/5.35 thf(fact_556_old_Onat_Oexhaust,axiom,
% 5.17/5.35 ! [Y4: nat] :
% 5.17/5.35 ( ( Y4 != zero_zero_nat )
% 5.17/5.35 => ~ ! [Nat3: nat] :
% 5.17/5.35 ( Y4
% 5.17/5.35 != ( suc @ Nat3 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % old.nat.exhaust
% 5.17/5.35 thf(fact_557_nat__induct,axiom,
% 5.17/5.35 ! [P: nat > $o,N: nat] :
% 5.17/5.35 ( ( P @ zero_zero_nat )
% 5.17/5.35 => ( ! [N2: nat] :
% 5.17/5.35 ( ( P @ N2 )
% 5.17/5.35 => ( P @ ( suc @ N2 ) ) )
% 5.17/5.35 => ( P @ N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat_induct
% 5.17/5.35 thf(fact_558_diff__induct,axiom,
% 5.17/5.35 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.17/5.35 ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 5.17/5.35 => ( ! [Y: nat] : ( P @ zero_zero_nat @ ( suc @ Y ) )
% 5.17/5.35 => ( ! [X4: nat,Y: nat] :
% 5.17/5.35 ( ( P @ X4 @ Y )
% 5.17/5.35 => ( P @ ( suc @ X4 ) @ ( suc @ Y ) ) )
% 5.17/5.35 => ( P @ M @ N ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % diff_induct
% 5.17/5.35 thf(fact_559_zero__induct,axiom,
% 5.17/5.35 ! [P: nat > $o,K: nat] :
% 5.17/5.35 ( ( P @ K )
% 5.17/5.35 => ( ! [N2: nat] :
% 5.17/5.35 ( ( P @ ( suc @ N2 ) )
% 5.17/5.35 => ( P @ N2 ) )
% 5.17/5.35 => ( P @ zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_induct
% 5.17/5.35 thf(fact_560_Suc__neq__Zero,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( ( suc @ M )
% 5.17/5.35 != zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % Suc_neq_Zero
% 5.17/5.35 thf(fact_561_Zero__neq__Suc,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( zero_zero_nat
% 5.17/5.35 != ( suc @ M ) ) ).
% 5.17/5.35
% 5.17/5.35 % Zero_neq_Suc
% 5.17/5.35 thf(fact_562_Zero__not__Suc,axiom,
% 5.17/5.35 ! [M: nat] :
% 5.17/5.35 ( zero_zero_nat
% 5.17/5.35 != ( suc @ M ) ) ).
% 5.17/5.35
% 5.17/5.35 % Zero_not_Suc
% 5.17/5.35 thf(fact_563_not0__implies__Suc,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( N != zero_zero_nat )
% 5.17/5.35 => ? [M4: nat] :
% 5.17/5.35 ( N
% 5.17/5.35 = ( suc @ M4 ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % not0_implies_Suc
% 5.17/5.35 thf(fact_564_le__0__eq,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.17/5.35 = ( N = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % le_0_eq
% 5.17/5.35 thf(fact_565_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.35 => ( A = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % bot_nat_0.extremum_uniqueI
% 5.17/5.35 thf(fact_566_bot__nat__0_Oextremum__unique,axiom,
% 5.17/5.35 ! [A: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.35 = ( A = zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % bot_nat_0.extremum_unique
% 5.17/5.35 thf(fact_567_less__eq__nat_Osimps_I1_J,axiom,
% 5.17/5.35 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.17/5.35
% 5.17/5.35 % less_eq_nat.simps(1)
% 5.17/5.35 thf(fact_568_nat__mult__eq__cancel__disj,axiom,
% 5.17/5.35 ! [K: nat,M: nat,N: nat] :
% 5.17/5.35 ( ( ( times_times_nat @ K @ M )
% 5.17/5.35 = ( times_times_nat @ K @ N ) )
% 5.17/5.35 = ( ( K = zero_zero_nat )
% 5.17/5.35 | ( M = N ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % nat_mult_eq_cancel_disj
% 5.17/5.35 thf(fact_569_mult__0,axiom,
% 5.17/5.35 ! [N: nat] :
% 5.17/5.35 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.17/5.35 = zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % mult_0
% 5.17/5.35 thf(fact_570_zero__le__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_numeral
% 5.17/5.35 thf(fact_571_zero__le__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_numeral
% 5.17/5.35 thf(fact_572_zero__le__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_numeral
% 5.17/5.35 thf(fact_573_zero__le__numeral,axiom,
% 5.17/5.35 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_numeral
% 5.17/5.35 thf(fact_574_not__numeral__le__zero,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.17/5.35
% 5.17/5.35 % not_numeral_le_zero
% 5.17/5.35 thf(fact_575_not__numeral__le__zero,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.17/5.35
% 5.17/5.35 % not_numeral_le_zero
% 5.17/5.35 thf(fact_576_not__numeral__le__zero,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.17/5.35
% 5.17/5.35 % not_numeral_le_zero
% 5.17/5.35 thf(fact_577_not__numeral__le__zero,axiom,
% 5.17/5.35 ! [N: num] :
% 5.17/5.35 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.17/5.35
% 5.17/5.35 % not_numeral_le_zero
% 5.17/5.35 thf(fact_578_mult__mono,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono
% 5.17/5.35 thf(fact_579_mult__mono,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono
% 5.17/5.35 thf(fact_580_mult__mono,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono
% 5.17/5.35 thf(fact_581_mult__mono,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono
% 5.17/5.35 thf(fact_582_mult__mono_H,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono'
% 5.17/5.35 thf(fact_583_mult__mono_H,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_nat @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono'
% 5.17/5.35 thf(fact_584_mult__mono_H,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_int @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono'
% 5.17/5.35 thf(fact_585_mult__mono_H,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ C @ D )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_mono'
% 5.17/5.35 thf(fact_586_zero__le__square,axiom,
% 5.17/5.35 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_square
% 5.17/5.35 thf(fact_587_zero__le__square,axiom,
% 5.17/5.35 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_square
% 5.17/5.35 thf(fact_588_zero__le__square,axiom,
% 5.17/5.35 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_square
% 5.17/5.35 thf(fact_589_split__mult__pos__le,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.17/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_pos_le
% 5.17/5.35 thf(fact_590_split__mult__pos__le,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.17/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_pos_le
% 5.17/5.35 thf(fact_591_split__mult__pos__le,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.17/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_pos_le
% 5.17/5.35 thf(fact_592_mult__left__mono__neg,axiom,
% 5.17/5.35 ! [B: rat,A: rat,C: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.35 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono_neg
% 5.17/5.35 thf(fact_593_mult__left__mono__neg,axiom,
% 5.17/5.35 ! [B: int,A: int,C: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.35 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono_neg
% 5.17/5.35 thf(fact_594_mult__left__mono__neg,axiom,
% 5.17/5.35 ! [B: real,A: real,C: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.35 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono_neg
% 5.17/5.35 thf(fact_595_mult__nonpos__nonpos,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.17/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonpos
% 5.17/5.35 thf(fact_596_mult__nonpos__nonpos,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.35 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.17/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonpos
% 5.17/5.35 thf(fact_597_mult__nonpos__nonpos,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.17/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonpos
% 5.17/5.35 thf(fact_598_mult__left__mono,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono
% 5.17/5.35 thf(fact_599_mult__left__mono,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono
% 5.17/5.35 thf(fact_600_mult__left__mono,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono
% 5.17/5.35 thf(fact_601_mult__left__mono,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_left_mono
% 5.17/5.35 thf(fact_602_mult__right__mono__neg,axiom,
% 5.17/5.35 ! [B: rat,A: rat,C: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.35 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono_neg
% 5.17/5.35 thf(fact_603_mult__right__mono__neg,axiom,
% 5.17/5.35 ! [B: int,A: int,C: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.35 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono_neg
% 5.17/5.35 thf(fact_604_mult__right__mono__neg,axiom,
% 5.17/5.35 ! [B: real,A: real,C: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.35 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono_neg
% 5.17/5.35 thf(fact_605_mult__right__mono,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono
% 5.17/5.35 thf(fact_606_mult__right__mono,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono
% 5.17/5.35 thf(fact_607_mult__right__mono,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono
% 5.17/5.35 thf(fact_608_mult__right__mono,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_right_mono
% 5.17/5.35 thf(fact_609_mult__le__0__iff,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.17/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.17/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_le_0_iff
% 5.17/5.35 thf(fact_610_mult__le__0__iff,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.17/5.35 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.17/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_le_0_iff
% 5.17/5.35 thf(fact_611_mult__le__0__iff,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.17/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.17/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_le_0_iff
% 5.17/5.35 thf(fact_612_split__mult__neg__le,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.17/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_neg_le
% 5.17/5.35 thf(fact_613_split__mult__neg__le,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.35 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.17/5.35 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.35 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_neg_le
% 5.17/5.35 thf(fact_614_split__mult__neg__le,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.17/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_neg_le
% 5.17/5.35 thf(fact_615_split__mult__neg__le,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.17/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.17/5.35
% 5.17/5.35 % split_mult_neg_le
% 5.17/5.35 thf(fact_616_mult__nonneg__nonneg,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonneg
% 5.17/5.35 thf(fact_617_mult__nonneg__nonneg,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.35 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonneg
% 5.17/5.35 thf(fact_618_mult__nonneg__nonneg,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonneg
% 5.17/5.35 thf(fact_619_mult__nonneg__nonneg,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonneg
% 5.17/5.35 thf(fact_620_mult__nonneg__nonpos,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos
% 5.17/5.35 thf(fact_621_mult__nonneg__nonpos,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.35 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos
% 5.17/5.35 thf(fact_622_mult__nonneg__nonpos,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos
% 5.17/5.35 thf(fact_623_mult__nonneg__nonpos,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos
% 5.17/5.35 thf(fact_624_mult__nonpos__nonneg,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonneg
% 5.17/5.35 thf(fact_625_mult__nonpos__nonneg,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonneg
% 5.17/5.35 thf(fact_626_mult__nonpos__nonneg,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonneg
% 5.17/5.35 thf(fact_627_mult__nonpos__nonneg,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonpos_nonneg
% 5.17/5.35 thf(fact_628_mult__nonneg__nonpos2,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos2
% 5.17/5.35 thf(fact_629_mult__nonneg__nonpos2,axiom,
% 5.17/5.35 ! [A: nat,B: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.35 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos2
% 5.17/5.35 thf(fact_630_mult__nonneg__nonpos2,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos2
% 5.17/5.35 thf(fact_631_mult__nonneg__nonpos2,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % mult_nonneg_nonpos2
% 5.17/5.35 thf(fact_632_zero__le__mult__iff,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_mult_iff
% 5.17/5.35 thf(fact_633_zero__le__mult__iff,axiom,
% 5.17/5.35 ! [A: int,B: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.17/5.35 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.35 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.35 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_mult_iff
% 5.17/5.35 thf(fact_634_zero__le__mult__iff,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_mult_iff
% 5.17/5.35 thf(fact_635_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.35 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.17/5.35 thf(fact_636_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.17/5.35 ! [A: nat,B: nat,C: nat] :
% 5.17/5.35 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.35 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.17/5.35 thf(fact_637_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.17/5.35 ! [A: int,B: int,C: int] :
% 5.17/5.35 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.35 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.17/5.35 thf(fact_638_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.35 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.17/5.35 thf(fact_639_divide__le__0__iff,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.17/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.17/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_le_0_iff
% 5.17/5.35 thf(fact_640_divide__le__0__iff,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.17/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.17/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_le_0_iff
% 5.17/5.35 thf(fact_641_divide__right__mono,axiom,
% 5.17/5.35 ! [A: rat,B: rat,C: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.35 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_right_mono
% 5.17/5.35 thf(fact_642_divide__right__mono,axiom,
% 5.17/5.35 ! [A: real,B: real,C: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.35 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_right_mono
% 5.17/5.35 thf(fact_643_zero__le__divide__iff,axiom,
% 5.17/5.35 ! [A: rat,B: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.35 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.35 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.35 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_divide_iff
% 5.17/5.35 thf(fact_644_zero__le__divide__iff,axiom,
% 5.17/5.35 ! [A: real,B: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.35 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.35 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.17/5.35 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.35 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % zero_le_divide_iff
% 5.17/5.35 thf(fact_645_divide__nonneg__nonneg,axiom,
% 5.17/5.35 ! [X: rat,Y4: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.35 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_nonneg_nonneg
% 5.17/5.35 thf(fact_646_divide__nonneg__nonneg,axiom,
% 5.17/5.35 ! [X: real,Y4: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_nonneg_nonneg
% 5.17/5.35 thf(fact_647_divide__nonneg__nonpos,axiom,
% 5.17/5.35 ! [X: rat,Y4: rat] :
% 5.17/5.35 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.35 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.17/5.35 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.35
% 5.17/5.35 % divide_nonneg_nonpos
% 5.17/5.35 thf(fact_648_divide__nonneg__nonpos,axiom,
% 5.17/5.35 ! [X: real,Y4: real] :
% 5.17/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.35 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.17/5.35 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_nonneg_nonpos
% 5.17/5.36 thf(fact_649_divide__nonpos__nonneg,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.36 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_nonpos_nonneg
% 5.17/5.36 thf(fact_650_divide__nonpos__nonneg,axiom,
% 5.17/5.36 ! [X: real,Y4: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.36 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_nonpos_nonneg
% 5.17/5.36 thf(fact_651_divide__nonpos__nonpos,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.36 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.17/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_nonpos_nonpos
% 5.17/5.36 thf(fact_652_divide__nonpos__nonpos,axiom,
% 5.17/5.36 ! [X: real,Y4: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.36 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.17/5.36 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_nonpos_nonpos
% 5.17/5.36 thf(fact_653_divide__right__mono__neg,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.36 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_right_mono_neg
% 5.17/5.36 thf(fact_654_divide__right__mono__neg,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.36 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_right_mono_neg
% 5.17/5.36 thf(fact_655_frac__eq__eq,axiom,
% 5.17/5.36 ! [Y4: complex,Z: complex,X: complex,W: complex] :
% 5.17/5.36 ( ( Y4 != zero_zero_complex )
% 5.17/5.36 => ( ( Z != zero_zero_complex )
% 5.17/5.36 => ( ( ( divide1717551699836669952omplex @ X @ Y4 )
% 5.17/5.36 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.17/5.36 = ( ( times_times_complex @ X @ Z )
% 5.17/5.36 = ( times_times_complex @ W @ Y4 ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % frac_eq_eq
% 5.17/5.36 thf(fact_656_frac__eq__eq,axiom,
% 5.17/5.36 ! [Y4: real,Z: real,X: real,W: real] :
% 5.17/5.36 ( ( Y4 != zero_zero_real )
% 5.17/5.36 => ( ( Z != zero_zero_real )
% 5.17/5.36 => ( ( ( divide_divide_real @ X @ Y4 )
% 5.17/5.36 = ( divide_divide_real @ W @ Z ) )
% 5.17/5.36 = ( ( times_times_real @ X @ Z )
% 5.17/5.36 = ( times_times_real @ W @ Y4 ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % frac_eq_eq
% 5.17/5.36 thf(fact_657_frac__eq__eq,axiom,
% 5.17/5.36 ! [Y4: rat,Z: rat,X: rat,W: rat] :
% 5.17/5.36 ( ( Y4 != zero_zero_rat )
% 5.17/5.36 => ( ( Z != zero_zero_rat )
% 5.17/5.36 => ( ( ( divide_divide_rat @ X @ Y4 )
% 5.17/5.36 = ( divide_divide_rat @ W @ Z ) )
% 5.17/5.36 = ( ( times_times_rat @ X @ Z )
% 5.17/5.36 = ( times_times_rat @ W @ Y4 ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % frac_eq_eq
% 5.17/5.36 thf(fact_658_divide__eq__eq,axiom,
% 5.17/5.36 ! [B: complex,C: complex,A: complex] :
% 5.17/5.36 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.17/5.36 = A )
% 5.17/5.36 = ( ( ( C != zero_zero_complex )
% 5.17/5.36 => ( B
% 5.17/5.36 = ( times_times_complex @ A @ C ) ) )
% 5.17/5.36 & ( ( C = zero_zero_complex )
% 5.17/5.36 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_eq
% 5.17/5.36 thf(fact_659_divide__eq__eq,axiom,
% 5.17/5.36 ! [B: real,C: real,A: real] :
% 5.17/5.36 ( ( ( divide_divide_real @ B @ C )
% 5.17/5.36 = A )
% 5.17/5.36 = ( ( ( C != zero_zero_real )
% 5.17/5.36 => ( B
% 5.17/5.36 = ( times_times_real @ A @ C ) ) )
% 5.17/5.36 & ( ( C = zero_zero_real )
% 5.17/5.36 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_eq
% 5.17/5.36 thf(fact_660_divide__eq__eq,axiom,
% 5.17/5.36 ! [B: rat,C: rat,A: rat] :
% 5.17/5.36 ( ( ( divide_divide_rat @ B @ C )
% 5.17/5.36 = A )
% 5.17/5.36 = ( ( ( C != zero_zero_rat )
% 5.17/5.36 => ( B
% 5.17/5.36 = ( times_times_rat @ A @ C ) ) )
% 5.17/5.36 & ( ( C = zero_zero_rat )
% 5.17/5.36 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_eq
% 5.17/5.36 thf(fact_661_eq__divide__eq,axiom,
% 5.17/5.36 ! [A: complex,B: complex,C: complex] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.36 = ( ( ( C != zero_zero_complex )
% 5.17/5.36 => ( ( times_times_complex @ A @ C )
% 5.17/5.36 = B ) )
% 5.17/5.36 & ( ( C = zero_zero_complex )
% 5.17/5.36 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_eq
% 5.17/5.36 thf(fact_662_eq__divide__eq,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( divide_divide_real @ B @ C ) )
% 5.17/5.36 = ( ( ( C != zero_zero_real )
% 5.17/5.36 => ( ( times_times_real @ A @ C )
% 5.17/5.36 = B ) )
% 5.17/5.36 & ( ( C = zero_zero_real )
% 5.17/5.36 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_eq
% 5.17/5.36 thf(fact_663_eq__divide__eq,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.36 = ( ( ( C != zero_zero_rat )
% 5.17/5.36 => ( ( times_times_rat @ A @ C )
% 5.17/5.36 = B ) )
% 5.17/5.36 & ( ( C = zero_zero_rat )
% 5.17/5.36 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_eq
% 5.17/5.36 thf(fact_664_divide__eq__imp,axiom,
% 5.17/5.36 ! [C: complex,B: complex,A: complex] :
% 5.17/5.36 ( ( C != zero_zero_complex )
% 5.17/5.36 => ( ( B
% 5.17/5.36 = ( times_times_complex @ A @ C ) )
% 5.17/5.36 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.17/5.36 = A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_imp
% 5.17/5.36 thf(fact_665_divide__eq__imp,axiom,
% 5.17/5.36 ! [C: real,B: real,A: real] :
% 5.17/5.36 ( ( C != zero_zero_real )
% 5.17/5.36 => ( ( B
% 5.17/5.36 = ( times_times_real @ A @ C ) )
% 5.17/5.36 => ( ( divide_divide_real @ B @ C )
% 5.17/5.36 = A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_imp
% 5.17/5.36 thf(fact_666_divide__eq__imp,axiom,
% 5.17/5.36 ! [C: rat,B: rat,A: rat] :
% 5.17/5.36 ( ( C != zero_zero_rat )
% 5.17/5.36 => ( ( B
% 5.17/5.36 = ( times_times_rat @ A @ C ) )
% 5.17/5.36 => ( ( divide_divide_rat @ B @ C )
% 5.17/5.36 = A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_imp
% 5.17/5.36 thf(fact_667_eq__divide__imp,axiom,
% 5.17/5.36 ! [C: complex,A: complex,B: complex] :
% 5.17/5.36 ( ( C != zero_zero_complex )
% 5.17/5.36 => ( ( ( times_times_complex @ A @ C )
% 5.17/5.36 = B )
% 5.17/5.36 => ( A
% 5.17/5.36 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_imp
% 5.17/5.36 thf(fact_668_eq__divide__imp,axiom,
% 5.17/5.36 ! [C: real,A: real,B: real] :
% 5.17/5.36 ( ( C != zero_zero_real )
% 5.17/5.36 => ( ( ( times_times_real @ A @ C )
% 5.17/5.36 = B )
% 5.17/5.36 => ( A
% 5.17/5.36 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_imp
% 5.17/5.36 thf(fact_669_eq__divide__imp,axiom,
% 5.17/5.36 ! [C: rat,A: rat,B: rat] :
% 5.17/5.36 ( ( C != zero_zero_rat )
% 5.17/5.36 => ( ( ( times_times_rat @ A @ C )
% 5.17/5.36 = B )
% 5.17/5.36 => ( A
% 5.17/5.36 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_imp
% 5.17/5.36 thf(fact_670_nonzero__divide__eq__eq,axiom,
% 5.17/5.36 ! [C: complex,B: complex,A: complex] :
% 5.17/5.36 ( ( C != zero_zero_complex )
% 5.17/5.36 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.17/5.36 = A )
% 5.17/5.36 = ( B
% 5.17/5.36 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonzero_divide_eq_eq
% 5.17/5.36 thf(fact_671_nonzero__divide__eq__eq,axiom,
% 5.17/5.36 ! [C: real,B: real,A: real] :
% 5.17/5.36 ( ( C != zero_zero_real )
% 5.17/5.36 => ( ( ( divide_divide_real @ B @ C )
% 5.17/5.36 = A )
% 5.17/5.36 = ( B
% 5.17/5.36 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonzero_divide_eq_eq
% 5.17/5.36 thf(fact_672_nonzero__divide__eq__eq,axiom,
% 5.17/5.36 ! [C: rat,B: rat,A: rat] :
% 5.17/5.36 ( ( C != zero_zero_rat )
% 5.17/5.36 => ( ( ( divide_divide_rat @ B @ C )
% 5.17/5.36 = A )
% 5.17/5.36 = ( B
% 5.17/5.36 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonzero_divide_eq_eq
% 5.17/5.36 thf(fact_673_nonzero__eq__divide__eq,axiom,
% 5.17/5.36 ! [C: complex,A: complex,B: complex] :
% 5.17/5.36 ( ( C != zero_zero_complex )
% 5.17/5.36 => ( ( A
% 5.17/5.36 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.36 = ( ( times_times_complex @ A @ C )
% 5.17/5.36 = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonzero_eq_divide_eq
% 5.17/5.36 thf(fact_674_nonzero__eq__divide__eq,axiom,
% 5.17/5.36 ! [C: real,A: real,B: real] :
% 5.17/5.36 ( ( C != zero_zero_real )
% 5.17/5.36 => ( ( A
% 5.17/5.36 = ( divide_divide_real @ B @ C ) )
% 5.17/5.36 = ( ( times_times_real @ A @ C )
% 5.17/5.36 = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonzero_eq_divide_eq
% 5.17/5.36 thf(fact_675_nonzero__eq__divide__eq,axiom,
% 5.17/5.36 ! [C: rat,A: rat,B: rat] :
% 5.17/5.36 ( ( C != zero_zero_rat )
% 5.17/5.36 => ( ( A
% 5.17/5.36 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.36 = ( ( times_times_rat @ A @ C )
% 5.17/5.36 = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonzero_eq_divide_eq
% 5.17/5.36 thf(fact_676_of__nat__0__le__iff,axiom,
% 5.17/5.36 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_0_le_iff
% 5.17/5.36 thf(fact_677_of__nat__0__le__iff,axiom,
% 5.17/5.36 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_0_le_iff
% 5.17/5.36 thf(fact_678_of__nat__0__le__iff,axiom,
% 5.17/5.36 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_0_le_iff
% 5.17/5.36 thf(fact_679_of__nat__0__le__iff,axiom,
% 5.17/5.36 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_0_le_iff
% 5.17/5.36 thf(fact_680_dvd__div__eq__0__iff,axiom,
% 5.17/5.36 ! [B: code_integer,A: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.36 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.17/5.36 = zero_z3403309356797280102nteger )
% 5.17/5.36 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_0_iff
% 5.17/5.36 thf(fact_681_dvd__div__eq__0__iff,axiom,
% 5.17/5.36 ! [B: complex,A: complex] :
% 5.17/5.36 ( ( dvd_dvd_complex @ B @ A )
% 5.17/5.36 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.17/5.36 = zero_zero_complex )
% 5.17/5.36 = ( A = zero_zero_complex ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_0_iff
% 5.17/5.36 thf(fact_682_dvd__div__eq__0__iff,axiom,
% 5.17/5.36 ! [B: real,A: real] :
% 5.17/5.36 ( ( dvd_dvd_real @ B @ A )
% 5.17/5.36 => ( ( ( divide_divide_real @ A @ B )
% 5.17/5.36 = zero_zero_real )
% 5.17/5.36 = ( A = zero_zero_real ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_0_iff
% 5.17/5.36 thf(fact_683_dvd__div__eq__0__iff,axiom,
% 5.17/5.36 ! [B: rat,A: rat] :
% 5.17/5.36 ( ( dvd_dvd_rat @ B @ A )
% 5.17/5.36 => ( ( ( divide_divide_rat @ A @ B )
% 5.17/5.36 = zero_zero_rat )
% 5.17/5.36 = ( A = zero_zero_rat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_0_iff
% 5.17/5.36 thf(fact_684_dvd__div__eq__0__iff,axiom,
% 5.17/5.36 ! [B: nat,A: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.36 => ( ( ( divide_divide_nat @ A @ B )
% 5.17/5.36 = zero_zero_nat )
% 5.17/5.36 = ( A = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_0_iff
% 5.17/5.36 thf(fact_685_dvd__div__eq__0__iff,axiom,
% 5.17/5.36 ! [B: int,A: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.36 => ( ( ( divide_divide_int @ A @ B )
% 5.17/5.36 = zero_zero_int )
% 5.17/5.36 = ( A = zero_zero_int ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_0_iff
% 5.17/5.36 thf(fact_686_of__nat__neq__0,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.17/5.36 != zero_zero_complex ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_neq_0
% 5.17/5.36 thf(fact_687_of__nat__neq__0,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.17/5.36 != zero_zero_real ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_neq_0
% 5.17/5.36 thf(fact_688_of__nat__neq__0,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.17/5.36 != zero_zero_rat ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_neq_0
% 5.17/5.36 thf(fact_689_of__nat__neq__0,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.17/5.36 != zero_zero_nat ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_neq_0
% 5.17/5.36 thf(fact_690_of__nat__neq__0,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.17/5.36 != zero_zero_int ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_neq_0
% 5.17/5.36 thf(fact_691_verit__comp__simplify1_I2_J,axiom,
% 5.17/5.36 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.17/5.36
% 5.17/5.36 % verit_comp_simplify1(2)
% 5.17/5.36 thf(fact_692_verit__comp__simplify1_I2_J,axiom,
% 5.17/5.36 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.17/5.36
% 5.17/5.36 % verit_comp_simplify1(2)
% 5.17/5.36 thf(fact_693_verit__comp__simplify1_I2_J,axiom,
% 5.17/5.36 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.17/5.36
% 5.17/5.36 % verit_comp_simplify1(2)
% 5.17/5.36 thf(fact_694_verit__comp__simplify1_I2_J,axiom,
% 5.17/5.36 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.17/5.36
% 5.17/5.36 % verit_comp_simplify1(2)
% 5.17/5.36 thf(fact_695_verit__comp__simplify1_I2_J,axiom,
% 5.17/5.36 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.17/5.36
% 5.17/5.36 % verit_comp_simplify1(2)
% 5.17/5.36 thf(fact_696_verit__comp__simplify1_I2_J,axiom,
% 5.17/5.36 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 5.17/5.36
% 5.17/5.36 % verit_comp_simplify1(2)
% 5.17/5.36 thf(fact_697_nle__le,axiom,
% 5.17/5.36 ! [A: rat,B: rat] :
% 5.17/5.36 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.17/5.36 = ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.36 & ( B != A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nle_le
% 5.17/5.36 thf(fact_698_nle__le,axiom,
% 5.17/5.36 ! [A: num,B: num] :
% 5.17/5.36 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.17/5.36 = ( ( ord_less_eq_num @ B @ A )
% 5.17/5.36 & ( B != A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nle_le
% 5.17/5.36 thf(fact_699_nle__le,axiom,
% 5.17/5.36 ! [A: nat,B: nat] :
% 5.17/5.36 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.17/5.36 = ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.36 & ( B != A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nle_le
% 5.17/5.36 thf(fact_700_nle__le,axiom,
% 5.17/5.36 ! [A: int,B: int] :
% 5.17/5.36 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.17/5.36 = ( ( ord_less_eq_int @ B @ A )
% 5.17/5.36 & ( B != A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nle_le
% 5.17/5.36 thf(fact_701_nle__le,axiom,
% 5.17/5.36 ! [A: real,B: real] :
% 5.17/5.36 ( ( ~ ( ord_less_eq_real @ A @ B ) )
% 5.17/5.36 = ( ( ord_less_eq_real @ B @ A )
% 5.17/5.36 & ( B != A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nle_le
% 5.17/5.36 thf(fact_702_le__cases3,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.36 ( ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_rat @ Y4 @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.36 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_rat @ X @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_rat @ Z @ Y4 ) )
% 5.17/5.36 => ( ( ( ord_less_eq_rat @ Z @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_rat @ Y4 @ X ) )
% 5.17/5.36 => ( ( ( ord_less_eq_rat @ Y4 @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 5.17/5.36 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 5.17/5.36 => ~ ( ord_less_eq_rat @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_cases3
% 5.17/5.36 thf(fact_703_le__cases3,axiom,
% 5.17/5.36 ! [X: num,Y4: num,Z: num] :
% 5.17/5.36 ( ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_num @ Y4 @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_num @ Y4 @ X )
% 5.17/5.36 => ~ ( ord_less_eq_num @ X @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_num @ X @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_num @ Z @ Y4 ) )
% 5.17/5.36 => ( ( ( ord_less_eq_num @ Z @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_num @ Y4 @ X ) )
% 5.17/5.36 => ( ( ( ord_less_eq_num @ Y4 @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_num @ Z @ X ) )
% 5.17/5.36 => ~ ( ( ord_less_eq_num @ Z @ X )
% 5.17/5.36 => ~ ( ord_less_eq_num @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_cases3
% 5.17/5.36 thf(fact_704_le__cases3,axiom,
% 5.17/5.36 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.36 ( ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_nat @ Y4 @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.36 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_nat @ X @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_nat @ Z @ Y4 ) )
% 5.17/5.36 => ( ( ( ord_less_eq_nat @ Z @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_nat @ Y4 @ X ) )
% 5.17/5.36 => ( ( ( ord_less_eq_nat @ Y4 @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 5.17/5.36 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 5.17/5.36 => ~ ( ord_less_eq_nat @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_cases3
% 5.17/5.36 thf(fact_705_le__cases3,axiom,
% 5.17/5.36 ! [X: int,Y4: int,Z: int] :
% 5.17/5.36 ( ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_int @ Y4 @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_int @ Y4 @ X )
% 5.17/5.36 => ~ ( ord_less_eq_int @ X @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_int @ X @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_int @ Z @ Y4 ) )
% 5.17/5.36 => ( ( ( ord_less_eq_int @ Z @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_int @ Y4 @ X ) )
% 5.17/5.36 => ( ( ( ord_less_eq_int @ Y4 @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_int @ Z @ X ) )
% 5.17/5.36 => ~ ( ( ord_less_eq_int @ Z @ X )
% 5.17/5.36 => ~ ( ord_less_eq_int @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_cases3
% 5.17/5.36 thf(fact_706_le__cases3,axiom,
% 5.17/5.36 ! [X: real,Y4: real,Z: real] :
% 5.17/5.36 ( ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_real @ Y4 @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.36 => ~ ( ord_less_eq_real @ X @ Z ) )
% 5.17/5.36 => ( ( ( ord_less_eq_real @ X @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_real @ Z @ Y4 ) )
% 5.17/5.36 => ( ( ( ord_less_eq_real @ Z @ Y4 )
% 5.17/5.36 => ~ ( ord_less_eq_real @ Y4 @ X ) )
% 5.17/5.36 => ( ( ( ord_less_eq_real @ Y4 @ Z )
% 5.17/5.36 => ~ ( ord_less_eq_real @ Z @ X ) )
% 5.17/5.36 => ~ ( ( ord_less_eq_real @ Z @ X )
% 5.17/5.36 => ~ ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_cases3
% 5.17/5.36 thf(fact_707_order__class_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [X3: set_int,Y6: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ X3 @ Y6 )
% 5.17/5.36 & ( ord_less_eq_set_int @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_class.order_eq_iff
% 5.17/5.36 thf(fact_708_order__class_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [X3: rat,Y6: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X3 @ Y6 )
% 5.17/5.36 & ( ord_less_eq_rat @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_class.order_eq_iff
% 5.17/5.36 thf(fact_709_order__class_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [X3: num,Y6: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X3 @ Y6 )
% 5.17/5.36 & ( ord_less_eq_num @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_class.order_eq_iff
% 5.17/5.36 thf(fact_710_order__class_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [X3: nat,Y6: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 5.17/5.36 & ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_class.order_eq_iff
% 5.17/5.36 thf(fact_711_order__class_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [X3: int,Y6: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ X3 @ Y6 )
% 5.17/5.36 & ( ord_less_eq_int @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_class.order_eq_iff
% 5.17/5.36 thf(fact_712_order__class_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [X3: real,Y6: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X3 @ Y6 )
% 5.17/5.36 & ( ord_less_eq_real @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_class.order_eq_iff
% 5.17/5.36 thf(fact_713_ord__eq__le__trans,axiom,
% 5.17/5.36 ! [A: set_int,B: set_int,C: set_int] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ B @ C )
% 5.17/5.36 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_trans
% 5.17/5.36 thf(fact_714_ord__eq__le__trans,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_trans
% 5.17/5.36 thf(fact_715_ord__eq__le__trans,axiom,
% 5.17/5.36 ! [A: num,B: num,C: num] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_trans
% 5.17/5.36 thf(fact_716_ord__eq__le__trans,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.36 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_trans
% 5.17/5.36 thf(fact_717_ord__eq__le__trans,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.36 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_trans
% 5.17/5.36 thf(fact_718_ord__eq__le__trans,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.36 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_trans
% 5.17/5.36 thf(fact_719_ord__le__eq__trans,axiom,
% 5.17/5.36 ! [A: set_int,B: set_int,C: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.36 => ( ( B = C )
% 5.17/5.36 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_trans
% 5.17/5.36 thf(fact_720_ord__le__eq__trans,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( B = C )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_trans
% 5.17/5.36 thf(fact_721_ord__le__eq__trans,axiom,
% 5.17/5.36 ! [A: num,B: num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( B = C )
% 5.17/5.36 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_trans
% 5.17/5.36 thf(fact_722_ord__le__eq__trans,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.36 => ( ( B = C )
% 5.17/5.36 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_trans
% 5.17/5.36 thf(fact_723_ord__le__eq__trans,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 => ( ( B = C )
% 5.17/5.36 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_trans
% 5.17/5.36 thf(fact_724_ord__le__eq__trans,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( ( B = C )
% 5.17/5.36 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_trans
% 5.17/5.36 thf(fact_725_order__antisym,axiom,
% 5.17/5.36 ! [X: set_int,Y4: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ Y4 @ X )
% 5.17/5.36 => ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym
% 5.17/5.36 thf(fact_726_order__antisym,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.36 => ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym
% 5.17/5.36 thf(fact_727_order__antisym,axiom,
% 5.17/5.36 ! [X: num,Y4: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_num @ Y4 @ X )
% 5.17/5.36 => ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym
% 5.17/5.36 thf(fact_728_order__antisym,axiom,
% 5.17/5.36 ! [X: nat,Y4: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.36 => ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym
% 5.17/5.36 thf(fact_729_order__antisym,axiom,
% 5.17/5.36 ! [X: int,Y4: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_int @ Y4 @ X )
% 5.17/5.36 => ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym
% 5.17/5.36 thf(fact_730_order__antisym,axiom,
% 5.17/5.36 ! [X: real,Y4: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.36 => ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym
% 5.17/5.36 thf(fact_731_order_Otrans,axiom,
% 5.17/5.36 ! [A: set_int,B: set_int,C: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ B @ C )
% 5.17/5.36 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order.trans
% 5.17/5.36 thf(fact_732_order_Otrans,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order.trans
% 5.17/5.36 thf(fact_733_order_Otrans,axiom,
% 5.17/5.36 ! [A: num,B: num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order.trans
% 5.17/5.36 thf(fact_734_order_Otrans,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.36 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order.trans
% 5.17/5.36 thf(fact_735_order_Otrans,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.36 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order.trans
% 5.17/5.36 thf(fact_736_order_Otrans,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.36 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order.trans
% 5.17/5.36 thf(fact_737_order__trans,axiom,
% 5.17/5.36 ! [X: set_int,Y4: set_int,Z: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ Y4 @ Z )
% 5.17/5.36 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_trans
% 5.17/5.36 thf(fact_738_order__trans,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_rat @ Y4 @ Z )
% 5.17/5.36 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_trans
% 5.17/5.36 thf(fact_739_order__trans,axiom,
% 5.17/5.36 ! [X: num,Y4: num,Z: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_num @ Y4 @ Z )
% 5.17/5.36 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_trans
% 5.17/5.36 thf(fact_740_order__trans,axiom,
% 5.17/5.36 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_nat @ Y4 @ Z )
% 5.17/5.36 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_trans
% 5.17/5.36 thf(fact_741_order__trans,axiom,
% 5.17/5.36 ! [X: int,Y4: int,Z: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_int @ Y4 @ Z )
% 5.17/5.36 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_trans
% 5.17/5.36 thf(fact_742_order__trans,axiom,
% 5.17/5.36 ! [X: real,Y4: real,Z: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.36 => ( ( ord_less_eq_real @ Y4 @ Z )
% 5.17/5.36 => ( ord_less_eq_real @ X @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_trans
% 5.17/5.36 thf(fact_743_linorder__wlog,axiom,
% 5.17/5.36 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.17/5.36 ( ! [A4: rat,B3: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( ! [A4: rat,B3: rat] :
% 5.17/5.36 ( ( P @ B3 @ A4 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( P @ A @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_wlog
% 5.17/5.36 thf(fact_744_linorder__wlog,axiom,
% 5.17/5.36 ! [P: num > num > $o,A: num,B: num] :
% 5.17/5.36 ( ! [A4: num,B3: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( ! [A4: num,B3: num] :
% 5.17/5.36 ( ( P @ B3 @ A4 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( P @ A @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_wlog
% 5.17/5.36 thf(fact_745_linorder__wlog,axiom,
% 5.17/5.36 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.17/5.36 ( ! [A4: nat,B3: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( ! [A4: nat,B3: nat] :
% 5.17/5.36 ( ( P @ B3 @ A4 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( P @ A @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_wlog
% 5.17/5.36 thf(fact_746_linorder__wlog,axiom,
% 5.17/5.36 ! [P: int > int > $o,A: int,B: int] :
% 5.17/5.36 ( ! [A4: int,B3: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( ! [A4: int,B3: int] :
% 5.17/5.36 ( ( P @ B3 @ A4 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( P @ A @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_wlog
% 5.17/5.36 thf(fact_747_linorder__wlog,axiom,
% 5.17/5.36 ! [P: real > real > $o,A: real,B: real] :
% 5.17/5.36 ( ! [A4: real,B3: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A4 @ B3 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( ! [A4: real,B3: real] :
% 5.17/5.36 ( ( P @ B3 @ A4 )
% 5.17/5.36 => ( P @ A4 @ B3 ) )
% 5.17/5.36 => ( P @ A @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_wlog
% 5.17/5.36 thf(fact_748_dual__order_Oeq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: set_int,B2: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.17/5.36 & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.eq_iff
% 5.17/5.36 thf(fact_749_dual__order_Oeq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.17/5.36 & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.eq_iff
% 5.17/5.36 thf(fact_750_dual__order_Oeq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: num,B2: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.17/5.36 & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.eq_iff
% 5.17/5.36 thf(fact_751_dual__order_Oeq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.17/5.36 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.eq_iff
% 5.17/5.36 thf(fact_752_dual__order_Oeq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: int,B2: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.17/5.36 & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.eq_iff
% 5.17/5.36 thf(fact_753_dual__order_Oeq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: real,B2: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.17/5.36 & ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.eq_iff
% 5.17/5.36 thf(fact_754_dual__order_Oantisym,axiom,
% 5.17/5.36 ! [B: set_int,A: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.antisym
% 5.17/5.36 thf(fact_755_dual__order_Oantisym,axiom,
% 5.17/5.36 ! [B: rat,A: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.antisym
% 5.17/5.36 thf(fact_756_dual__order_Oantisym,axiom,
% 5.17/5.36 ! [B: num,A: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.antisym
% 5.17/5.36 thf(fact_757_dual__order_Oantisym,axiom,
% 5.17/5.36 ! [B: nat,A: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.antisym
% 5.17/5.36 thf(fact_758_dual__order_Oantisym,axiom,
% 5.17/5.36 ! [B: int,A: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.antisym
% 5.17/5.36 thf(fact_759_dual__order_Oantisym,axiom,
% 5.17/5.36 ! [B: real,A: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.antisym
% 5.17/5.36 thf(fact_760_dual__order_Otrans,axiom,
% 5.17/5.36 ! [B: set_int,A: set_int,C: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ C @ B )
% 5.17/5.36 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.trans
% 5.17/5.36 thf(fact_761_dual__order_Otrans,axiom,
% 5.17/5.36 ! [B: rat,A: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_rat @ C @ B )
% 5.17/5.36 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.trans
% 5.17/5.36 thf(fact_762_dual__order_Otrans,axiom,
% 5.17/5.36 ! [B: num,A: num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_num @ C @ B )
% 5.17/5.36 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.trans
% 5.17/5.36 thf(fact_763_dual__order_Otrans,axiom,
% 5.17/5.36 ! [B: nat,A: nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_nat @ C @ B )
% 5.17/5.36 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.trans
% 5.17/5.36 thf(fact_764_dual__order_Otrans,axiom,
% 5.17/5.36 ! [B: int,A: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_int @ C @ B )
% 5.17/5.36 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.trans
% 5.17/5.36 thf(fact_765_dual__order_Otrans,axiom,
% 5.17/5.36 ! [B: real,A: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.36 => ( ( ord_less_eq_real @ C @ B )
% 5.17/5.36 => ( ord_less_eq_real @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dual_order.trans
% 5.17/5.36 thf(fact_766_antisym,axiom,
% 5.17/5.36 ! [A: set_int,B: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ B @ A )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % antisym
% 5.17/5.36 thf(fact_767_antisym,axiom,
% 5.17/5.36 ! [A: rat,B: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % antisym
% 5.17/5.36 thf(fact_768_antisym,axiom,
% 5.17/5.36 ! [A: num,B: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ A )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % antisym
% 5.17/5.36 thf(fact_769_antisym,axiom,
% 5.17/5.36 ! [A: nat,B: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % antisym
% 5.17/5.36 thf(fact_770_antisym,axiom,
% 5.17/5.36 ! [A: int,B: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_int @ B @ A )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % antisym
% 5.17/5.36 thf(fact_771_antisym,axiom,
% 5.17/5.36 ! [A: real,B: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_real @ B @ A )
% 5.17/5.36 => ( A = B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % antisym
% 5.17/5.36 thf(fact_772_Orderings_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: set_int,B2: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.17/5.36 & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Orderings.order_eq_iff
% 5.17/5.36 thf(fact_773_Orderings_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.17/5.36 & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Orderings.order_eq_iff
% 5.17/5.36 thf(fact_774_Orderings_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: num,Z4: num] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: num,B2: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.17/5.36 & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Orderings.order_eq_iff
% 5.17/5.36 thf(fact_775_Orderings_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.17/5.36 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Orderings.order_eq_iff
% 5.17/5.36 thf(fact_776_Orderings_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: int,B2: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.17/5.36 & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Orderings.order_eq_iff
% 5.17/5.36 thf(fact_777_Orderings_Oorder__eq__iff,axiom,
% 5.17/5.36 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: real,B2: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.17/5.36 & ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Orderings.order_eq_iff
% 5.17/5.36 thf(fact_778_order__subst1,axiom,
% 5.17/5.36 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_779_order__subst1,axiom,
% 5.17/5.36 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_780_order__subst1,axiom,
% 5.17/5.36 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.36 => ( ! [X4: nat,Y: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_781_order__subst1,axiom,
% 5.17/5.36 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.36 => ( ! [X4: int,Y: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_782_order__subst1,axiom,
% 5.17/5.36 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.36 => ( ! [X4: real,Y: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_783_order__subst1,axiom,
% 5.17/5.36 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_784_order__subst1,axiom,
% 5.17/5.36 ! [A: num,F: num > num,B: num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_785_order__subst1,axiom,
% 5.17/5.36 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.36 => ( ! [X4: nat,Y: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_786_order__subst1,axiom,
% 5.17/5.36 ! [A: num,F: int > num,B: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.36 => ( ! [X4: int,Y: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_787_order__subst1,axiom,
% 5.17/5.36 ! [A: num,F: real > num,B: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.36 => ( ! [X4: real,Y: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst1
% 5.17/5.36 thf(fact_788_order__subst2,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_789_order__subst2,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_790_order__subst2,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_791_order__subst2,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_792_order__subst2,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_793_order__subst2,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_794_order__subst2,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_795_order__subst2,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_796_order__subst2,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_797_order__subst2,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_subst2
% 5.17/5.36 thf(fact_798_order__eq__refl,axiom,
% 5.17/5.36 ! [X: set_int,Y4: set_int] :
% 5.17/5.36 ( ( X = Y4 )
% 5.17/5.36 => ( ord_less_eq_set_int @ X @ Y4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_eq_refl
% 5.17/5.36 thf(fact_799_order__eq__refl,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat] :
% 5.17/5.36 ( ( X = Y4 )
% 5.17/5.36 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_eq_refl
% 5.17/5.36 thf(fact_800_order__eq__refl,axiom,
% 5.17/5.36 ! [X: num,Y4: num] :
% 5.17/5.36 ( ( X = Y4 )
% 5.17/5.36 => ( ord_less_eq_num @ X @ Y4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_eq_refl
% 5.17/5.36 thf(fact_801_order__eq__refl,axiom,
% 5.17/5.36 ! [X: nat,Y4: nat] :
% 5.17/5.36 ( ( X = Y4 )
% 5.17/5.36 => ( ord_less_eq_nat @ X @ Y4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_eq_refl
% 5.17/5.36 thf(fact_802_order__eq__refl,axiom,
% 5.17/5.36 ! [X: int,Y4: int] :
% 5.17/5.36 ( ( X = Y4 )
% 5.17/5.36 => ( ord_less_eq_int @ X @ Y4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_eq_refl
% 5.17/5.36 thf(fact_803_order__eq__refl,axiom,
% 5.17/5.36 ! [X: real,Y4: real] :
% 5.17/5.36 ( ( X = Y4 )
% 5.17/5.36 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_eq_refl
% 5.17/5.36 thf(fact_804_verit__la__disequality,axiom,
% 5.17/5.36 ! [A: rat,B: rat] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 | ~ ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % verit_la_disequality
% 5.17/5.36 thf(fact_805_verit__la__disequality,axiom,
% 5.17/5.36 ! [A: num,B: num] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 | ~ ( ord_less_eq_num @ A @ B )
% 5.17/5.36 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % verit_la_disequality
% 5.17/5.36 thf(fact_806_verit__la__disequality,axiom,
% 5.17/5.36 ! [A: nat,B: nat] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 | ~ ( ord_less_eq_nat @ A @ B )
% 5.17/5.36 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % verit_la_disequality
% 5.17/5.36 thf(fact_807_verit__la__disequality,axiom,
% 5.17/5.36 ! [A: int,B: int] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 | ~ ( ord_less_eq_int @ A @ B )
% 5.17/5.36 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % verit_la_disequality
% 5.17/5.36 thf(fact_808_verit__la__disequality,axiom,
% 5.17/5.36 ! [A: real,B: real] :
% 5.17/5.36 ( ( A = B )
% 5.17/5.36 | ~ ( ord_less_eq_real @ A @ B )
% 5.17/5.36 | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % verit_la_disequality
% 5.17/5.36 thf(fact_809_linorder__linear,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.36 | ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_linear
% 5.17/5.36 thf(fact_810_linorder__linear,axiom,
% 5.17/5.36 ! [X: num,Y4: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.36 | ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_linear
% 5.17/5.36 thf(fact_811_linorder__linear,axiom,
% 5.17/5.36 ! [X: nat,Y4: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.36 | ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_linear
% 5.17/5.36 thf(fact_812_linorder__linear,axiom,
% 5.17/5.36 ! [X: int,Y4: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.36 | ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_linear
% 5.17/5.36 thf(fact_813_linorder__linear,axiom,
% 5.17/5.36 ! [X: real,Y4: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.36 | ( ord_less_eq_real @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_linear
% 5.17/5.36 thf(fact_814_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_815_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_816_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_817_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_818_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_819_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_820_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: num,F: num > num,B: num,C: num] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_821_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_822_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: int,F: num > int,B: num,C: num] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_823_ord__eq__le__subst,axiom,
% 5.17/5.36 ! [A: real,F: num > real,B: num,C: num] :
% 5.17/5.36 ( ( A
% 5.17/5.36 = ( F @ B ) )
% 5.17/5.36 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_eq_le_subst
% 5.17/5.36 thf(fact_824_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_825_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_826_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_827_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_828_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: rat,Y: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_829_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_830_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > num,C: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_831_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_832_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_833_ord__le__eq__subst,axiom,
% 5.17/5.36 ! [A: num,B: num,F: num > real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.36 => ( ( ( F @ B )
% 5.17/5.36 = C )
% 5.17/5.36 => ( ! [X4: num,Y: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.36 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ord_le_eq_subst
% 5.17/5.36 thf(fact_834_linorder__le__cases,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat] :
% 5.17/5.36 ( ~ ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.36 => ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_le_cases
% 5.17/5.36 thf(fact_835_linorder__le__cases,axiom,
% 5.17/5.36 ! [X: num,Y4: num] :
% 5.17/5.36 ( ~ ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.36 => ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_le_cases
% 5.17/5.36 thf(fact_836_linorder__le__cases,axiom,
% 5.17/5.36 ! [X: nat,Y4: nat] :
% 5.17/5.36 ( ~ ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.36 => ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_le_cases
% 5.17/5.36 thf(fact_837_linorder__le__cases,axiom,
% 5.17/5.36 ! [X: int,Y4: int] :
% 5.17/5.36 ( ~ ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.36 => ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_le_cases
% 5.17/5.36 thf(fact_838_linorder__le__cases,axiom,
% 5.17/5.36 ! [X: real,Y4: real] :
% 5.17/5.36 ( ~ ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.36 => ( ord_less_eq_real @ Y4 @ X ) ) ).
% 5.17/5.36
% 5.17/5.36 % linorder_le_cases
% 5.17/5.36 thf(fact_839_order__antisym__conv,axiom,
% 5.17/5.36 ! [Y4: set_int,X: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ Y4 @ X )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.36 = ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym_conv
% 5.17/5.36 thf(fact_840_order__antisym__conv,axiom,
% 5.17/5.36 ! [Y4: rat,X: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.36 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.36 = ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym_conv
% 5.17/5.36 thf(fact_841_order__antisym__conv,axiom,
% 5.17/5.36 ! [Y4: num,X: num] :
% 5.17/5.36 ( ( ord_less_eq_num @ Y4 @ X )
% 5.17/5.36 => ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.36 = ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym_conv
% 5.17/5.36 thf(fact_842_order__antisym__conv,axiom,
% 5.17/5.36 ! [Y4: nat,X: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.36 => ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.36 = ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym_conv
% 5.17/5.36 thf(fact_843_order__antisym__conv,axiom,
% 5.17/5.36 ! [Y4: int,X: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ Y4 @ X )
% 5.17/5.36 => ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.36 = ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym_conv
% 5.17/5.36 thf(fact_844_order__antisym__conv,axiom,
% 5.17/5.36 ! [Y4: real,X: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.36 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.36 = ( X = Y4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % order_antisym_conv
% 5.17/5.36 thf(fact_845_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.17/5.36 ! [C: nat,A: nat,B: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.36 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.36 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.17/5.36 thf(fact_846_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.17/5.36 ! [C: int,A: int,B: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.36 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.36 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.17/5.36 thf(fact_847_divide__eq__eq__numeral_I1_J,axiom,
% 5.17/5.36 ! [B: complex,C: complex,W: num] :
% 5.17/5.36 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.17/5.36 = ( numera6690914467698888265omplex @ W ) )
% 5.17/5.36 = ( ( ( C != zero_zero_complex )
% 5.17/5.36 => ( B
% 5.17/5.36 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.17/5.36 & ( ( C = zero_zero_complex )
% 5.17/5.36 => ( ( numera6690914467698888265omplex @ W )
% 5.17/5.36 = zero_zero_complex ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_eq_numeral(1)
% 5.17/5.36 thf(fact_848_divide__eq__eq__numeral_I1_J,axiom,
% 5.17/5.36 ! [B: real,C: real,W: num] :
% 5.17/5.36 ( ( ( divide_divide_real @ B @ C )
% 5.17/5.36 = ( numeral_numeral_real @ W ) )
% 5.17/5.36 = ( ( ( C != zero_zero_real )
% 5.17/5.36 => ( B
% 5.17/5.36 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.17/5.36 & ( ( C = zero_zero_real )
% 5.17/5.36 => ( ( numeral_numeral_real @ W )
% 5.17/5.36 = zero_zero_real ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_eq_numeral(1)
% 5.17/5.36 thf(fact_849_divide__eq__eq__numeral_I1_J,axiom,
% 5.17/5.36 ! [B: rat,C: rat,W: num] :
% 5.17/5.36 ( ( ( divide_divide_rat @ B @ C )
% 5.17/5.36 = ( numeral_numeral_rat @ W ) )
% 5.17/5.36 = ( ( ( C != zero_zero_rat )
% 5.17/5.36 => ( B
% 5.17/5.36 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.17/5.36 & ( ( C = zero_zero_rat )
% 5.17/5.36 => ( ( numeral_numeral_rat @ W )
% 5.17/5.36 = zero_zero_rat ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_eq_eq_numeral(1)
% 5.17/5.36 thf(fact_850_eq__divide__eq__numeral_I1_J,axiom,
% 5.17/5.36 ! [W: num,B: complex,C: complex] :
% 5.17/5.36 ( ( ( numera6690914467698888265omplex @ W )
% 5.17/5.36 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.36 = ( ( ( C != zero_zero_complex )
% 5.17/5.36 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.17/5.36 = B ) )
% 5.17/5.36 & ( ( C = zero_zero_complex )
% 5.17/5.36 => ( ( numera6690914467698888265omplex @ W )
% 5.17/5.36 = zero_zero_complex ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_eq_numeral(1)
% 5.17/5.36 thf(fact_851_eq__divide__eq__numeral_I1_J,axiom,
% 5.17/5.36 ! [W: num,B: real,C: real] :
% 5.17/5.36 ( ( ( numeral_numeral_real @ W )
% 5.17/5.36 = ( divide_divide_real @ B @ C ) )
% 5.17/5.36 = ( ( ( C != zero_zero_real )
% 5.17/5.36 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.17/5.36 = B ) )
% 5.17/5.36 & ( ( C = zero_zero_real )
% 5.17/5.36 => ( ( numeral_numeral_real @ W )
% 5.17/5.36 = zero_zero_real ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_eq_numeral(1)
% 5.17/5.36 thf(fact_852_eq__divide__eq__numeral_I1_J,axiom,
% 5.17/5.36 ! [W: num,B: rat,C: rat] :
% 5.17/5.36 ( ( ( numeral_numeral_rat @ W )
% 5.17/5.36 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.36 = ( ( ( C != zero_zero_rat )
% 5.17/5.36 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.17/5.36 = B ) )
% 5.17/5.36 & ( ( C = zero_zero_rat )
% 5.17/5.36 => ( ( numeral_numeral_rat @ W )
% 5.17/5.36 = zero_zero_rat ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_divide_eq_numeral(1)
% 5.17/5.36 thf(fact_853_dvd__div__eq__mult,axiom,
% 5.17/5.36 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.36 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.36 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.17/5.36 = C )
% 5.17/5.36 = ( B
% 5.17/5.36 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_mult
% 5.17/5.36 thf(fact_854_dvd__div__eq__mult,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( A != zero_zero_nat )
% 5.17/5.36 => ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.36 => ( ( ( divide_divide_nat @ B @ A )
% 5.17/5.36 = C )
% 5.17/5.36 = ( B
% 5.17/5.36 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_mult
% 5.17/5.36 thf(fact_855_dvd__div__eq__mult,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( A != zero_zero_int )
% 5.17/5.36 => ( ( dvd_dvd_int @ A @ B )
% 5.17/5.36 => ( ( ( divide_divide_int @ B @ A )
% 5.17/5.36 = C )
% 5.17/5.36 = ( B
% 5.17/5.36 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_eq_mult
% 5.17/5.36 thf(fact_856_div__dvd__iff__mult,axiom,
% 5.17/5.36 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.36 ( ( B != zero_z3403309356797280102nteger )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.17/5.36 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % div_dvd_iff_mult
% 5.17/5.36 thf(fact_857_div__dvd__iff__mult,axiom,
% 5.17/5.36 ! [B: nat,A: nat,C: nat] :
% 5.17/5.36 ( ( B != zero_zero_nat )
% 5.17/5.36 => ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.36 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.17/5.36 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % div_dvd_iff_mult
% 5.17/5.36 thf(fact_858_div__dvd__iff__mult,axiom,
% 5.17/5.36 ! [B: int,A: int,C: int] :
% 5.17/5.36 ( ( B != zero_zero_int )
% 5.17/5.36 => ( ( dvd_dvd_int @ B @ A )
% 5.17/5.36 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.17/5.36 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % div_dvd_iff_mult
% 5.17/5.36 thf(fact_859_dvd__div__iff__mult,axiom,
% 5.17/5.36 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.36 ( ( C != zero_z3403309356797280102nteger )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.17/5.36 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_iff_mult
% 5.17/5.36 thf(fact_860_dvd__div__iff__mult,axiom,
% 5.17/5.36 ! [C: nat,B: nat,A: nat] :
% 5.17/5.36 ( ( C != zero_zero_nat )
% 5.17/5.36 => ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.36 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.17/5.36 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_iff_mult
% 5.17/5.36 thf(fact_861_dvd__div__iff__mult,axiom,
% 5.17/5.36 ! [C: int,B: int,A: int] :
% 5.17/5.36 ( ( C != zero_zero_int )
% 5.17/5.36 => ( ( dvd_dvd_int @ C @ B )
% 5.17/5.36 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.17/5.36 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_iff_mult
% 5.17/5.36 thf(fact_862_dvd__div__div__eq__mult,axiom,
% 5.17/5.36 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.17/5.36 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.36 => ( ( C != zero_z3403309356797280102nteger )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.17/5.36 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.17/5.36 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.17/5.36 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.17/5.36 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_div_eq_mult
% 5.17/5.36 thf(fact_863_dvd__div__div__eq__mult,axiom,
% 5.17/5.36 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.17/5.36 ( ( A != zero_zero_nat )
% 5.17/5.36 => ( ( C != zero_zero_nat )
% 5.17/5.36 => ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.36 => ( ( dvd_dvd_nat @ C @ D )
% 5.17/5.36 => ( ( ( divide_divide_nat @ B @ A )
% 5.17/5.36 = ( divide_divide_nat @ D @ C ) )
% 5.17/5.36 = ( ( times_times_nat @ B @ C )
% 5.17/5.36 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_div_eq_mult
% 5.17/5.36 thf(fact_864_dvd__div__div__eq__mult,axiom,
% 5.17/5.36 ! [A: int,C: int,B: int,D: int] :
% 5.17/5.36 ( ( A != zero_zero_int )
% 5.17/5.36 => ( ( C != zero_zero_int )
% 5.17/5.36 => ( ( dvd_dvd_int @ A @ B )
% 5.17/5.36 => ( ( dvd_dvd_int @ C @ D )
% 5.17/5.36 => ( ( ( divide_divide_int @ B @ A )
% 5.17/5.36 = ( divide_divide_int @ D @ C ) )
% 5.17/5.36 = ( ( times_times_int @ B @ C )
% 5.17/5.36 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_div_div_eq_mult
% 5.17/5.36 thf(fact_865_numeral__1__eq__Suc__0,axiom,
% 5.17/5.36 ( ( numeral_numeral_nat @ one )
% 5.17/5.36 = ( suc @ zero_zero_nat ) ) ).
% 5.17/5.36
% 5.17/5.36 % numeral_1_eq_Suc_0
% 5.17/5.36 thf(fact_866_nat__int__comparison_I1_J,axiom,
% 5.17/5.36 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.36 ( ( semiri1314217659103216013at_int @ A3 )
% 5.17/5.36 = ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nat_int_comparison(1)
% 5.17/5.36 thf(fact_867_int__if,axiom,
% 5.17/5.36 ! [P: $o,A: nat,B: nat] :
% 5.17/5.36 ( ( P
% 5.17/5.36 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.17/5.36 = ( semiri1314217659103216013at_int @ A ) ) )
% 5.17/5.36 & ( ~ P
% 5.17/5.36 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.17/5.36 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % int_if
% 5.17/5.36 thf(fact_868_even__zero,axiom,
% 5.17/5.36 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.17/5.36
% 5.17/5.36 % even_zero
% 5.17/5.36 thf(fact_869_even__zero,axiom,
% 5.17/5.36 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.17/5.36
% 5.17/5.36 % even_zero
% 5.17/5.36 thf(fact_870_even__zero,axiom,
% 5.17/5.36 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.17/5.36
% 5.17/5.36 % even_zero
% 5.17/5.36 thf(fact_871_numeral__2__eq__2,axiom,
% 5.17/5.36 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.17/5.36 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % numeral_2_eq_2
% 5.17/5.36 thf(fact_872_numeral__3__eq__3,axiom,
% 5.17/5.36 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.17/5.36 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % numeral_3_eq_3
% 5.17/5.36 thf(fact_873_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I1_J,axiom,
% 5.17/5.36 ( ( vEBT_V8646137997579335489_i_l_d @ zero_zero_nat )
% 5.17/5.36 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(1)
% 5.17/5.36 thf(fact_874_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I2_J,axiom,
% 5.17/5.36 ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ zero_zero_nat ) )
% 5.17/5.36 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(2)
% 5.17/5.36 thf(fact_875_verit__eq__simplify_I10_J,axiom,
% 5.17/5.36 ! [X2: num] :
% 5.17/5.36 ( one
% 5.17/5.36 != ( bit0 @ X2 ) ) ).
% 5.17/5.36
% 5.17/5.36 % verit_eq_simplify(10)
% 5.17/5.36 thf(fact_876_le__zero__eq,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.17/5.36 = ( N = zero_zero_nat ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_zero_eq
% 5.17/5.36 thf(fact_877_unset__bit__0,axiom,
% 5.17/5.36 ! [A: int] :
% 5.17/5.36 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.17/5.36 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % unset_bit_0
% 5.17/5.36 thf(fact_878_unset__bit__0,axiom,
% 5.17/5.36 ! [A: nat] :
% 5.17/5.36 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.17/5.36 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % unset_bit_0
% 5.17/5.36 thf(fact_879_unset__bit__0,axiom,
% 5.17/5.36 ! [A: code_integer] :
% 5.17/5.36 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 5.17/5.36 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % unset_bit_0
% 5.17/5.36 thf(fact_880_even__set__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 & ( M != zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_set_bit_iff
% 5.17/5.36 thf(fact_881_even__set__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 & ( M != zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_set_bit_iff
% 5.17/5.36 thf(fact_882_even__set__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 & ( M != zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_set_bit_iff
% 5.17/5.36 thf(fact_883_even__flip__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 != ( M = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_flip_bit_iff
% 5.17/5.36 thf(fact_884_even__flip__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 != ( M = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_flip_bit_iff
% 5.17/5.36 thf(fact_885_even__flip__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 != ( M = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_flip_bit_iff
% 5.17/5.36 thf(fact_886_even__unset__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 | ( M = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_unset_bit_iff
% 5.17/5.36 thf(fact_887_even__unset__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 | ( M = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_unset_bit_iff
% 5.17/5.36 thf(fact_888_even__unset__bit__iff,axiom,
% 5.17/5.36 ! [M: nat,A: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.17/5.36 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.36 | ( M = zero_zero_nat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % even_unset_bit_iff
% 5.17/5.36 thf(fact_889_subset__antisym,axiom,
% 5.17/5.36 ! [A2: set_int,B4: set_int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.36 => ( ( ord_less_eq_set_int @ B4 @ A2 )
% 5.17/5.36 => ( A2 = B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % subset_antisym
% 5.17/5.36 thf(fact_890_subsetI,axiom,
% 5.17/5.36 ! [A2: set_complex,B4: set_complex] :
% 5.17/5.36 ( ! [X4: complex] :
% 5.17/5.36 ( ( member_complex @ X4 @ A2 )
% 5.17/5.36 => ( member_complex @ X4 @ B4 ) )
% 5.17/5.36 => ( ord_le211207098394363844omplex @ A2 @ B4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetI
% 5.17/5.36 thf(fact_891_subsetI,axiom,
% 5.17/5.36 ! [A2: set_real,B4: set_real] :
% 5.17/5.36 ( ! [X4: real] :
% 5.17/5.36 ( ( member_real @ X4 @ A2 )
% 5.17/5.36 => ( member_real @ X4 @ B4 ) )
% 5.17/5.36 => ( ord_less_eq_set_real @ A2 @ B4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetI
% 5.17/5.36 thf(fact_892_subsetI,axiom,
% 5.17/5.36 ! [A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.36 ( ! [X4: set_nat] :
% 5.17/5.36 ( ( member_set_nat @ X4 @ A2 )
% 5.17/5.36 => ( member_set_nat @ X4 @ B4 ) )
% 5.17/5.36 => ( ord_le6893508408891458716et_nat @ A2 @ B4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetI
% 5.17/5.36 thf(fact_893_subsetI,axiom,
% 5.17/5.36 ! [A2: set_nat,B4: set_nat] :
% 5.17/5.36 ( ! [X4: nat] :
% 5.17/5.36 ( ( member_nat @ X4 @ A2 )
% 5.17/5.36 => ( member_nat @ X4 @ B4 ) )
% 5.17/5.36 => ( ord_less_eq_set_nat @ A2 @ B4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetI
% 5.17/5.36 thf(fact_894_subsetI,axiom,
% 5.17/5.36 ! [A2: set_int,B4: set_int] :
% 5.17/5.36 ( ! [X4: int] :
% 5.17/5.36 ( ( member_int @ X4 @ A2 )
% 5.17/5.36 => ( member_int @ X4 @ B4 ) )
% 5.17/5.36 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetI
% 5.17/5.36 thf(fact_895_odd__Suc__minus__one,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.36 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.17/5.36 = N ) ) ).
% 5.17/5.36
% 5.17/5.36 % odd_Suc_minus_one
% 5.17/5.36 thf(fact_896_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I2_J,axiom,
% 5.17/5.36 ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ zero_zero_nat ) )
% 5.17/5.36 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(2)
% 5.17/5.36 thf(fact_897_unset__bit__nonnegative__int__iff,axiom,
% 5.17/5.36 ! [N: nat,K: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.17/5.36 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.36
% 5.17/5.36 % unset_bit_nonnegative_int_iff
% 5.17/5.36 thf(fact_898_set__bit__nonnegative__int__iff,axiom,
% 5.17/5.36 ! [N: nat,K: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.17/5.36 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.36
% 5.17/5.36 % set_bit_nonnegative_int_iff
% 5.17/5.36 thf(fact_899_flip__bit__nonnegative__int__iff,axiom,
% 5.17/5.36 ! [N: nat,K: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.17/5.36 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.36
% 5.17/5.36 % flip_bit_nonnegative_int_iff
% 5.17/5.36 thf(fact_900_diff__self,axiom,
% 5.17/5.36 ! [A: complex] :
% 5.17/5.36 ( ( minus_minus_complex @ A @ A )
% 5.17/5.36 = zero_zero_complex ) ).
% 5.17/5.36
% 5.17/5.36 % diff_self
% 5.17/5.36 thf(fact_901_diff__self,axiom,
% 5.17/5.36 ! [A: real] :
% 5.17/5.36 ( ( minus_minus_real @ A @ A )
% 5.17/5.36 = zero_zero_real ) ).
% 5.17/5.36
% 5.17/5.36 % diff_self
% 5.17/5.36 thf(fact_902_diff__self,axiom,
% 5.17/5.36 ! [A: rat] :
% 5.17/5.36 ( ( minus_minus_rat @ A @ A )
% 5.17/5.36 = zero_zero_rat ) ).
% 5.17/5.36
% 5.17/5.36 % diff_self
% 5.17/5.36 thf(fact_903_diff__self,axiom,
% 5.17/5.36 ! [A: int] :
% 5.17/5.36 ( ( minus_minus_int @ A @ A )
% 5.17/5.36 = zero_zero_int ) ).
% 5.17/5.36
% 5.17/5.36 % diff_self
% 5.17/5.36 thf(fact_904_diff__0__right,axiom,
% 5.17/5.36 ! [A: complex] :
% 5.17/5.36 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_0_right
% 5.17/5.36 thf(fact_905_diff__0__right,axiom,
% 5.17/5.36 ! [A: real] :
% 5.17/5.36 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_0_right
% 5.17/5.36 thf(fact_906_diff__0__right,axiom,
% 5.17/5.36 ! [A: rat] :
% 5.17/5.36 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_0_right
% 5.17/5.36 thf(fact_907_diff__0__right,axiom,
% 5.17/5.36 ! [A: int] :
% 5.17/5.36 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_0_right
% 5.17/5.36 thf(fact_908_zero__diff,axiom,
% 5.17/5.36 ! [A: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.17/5.36 = zero_zero_nat ) ).
% 5.17/5.36
% 5.17/5.36 % zero_diff
% 5.17/5.36 thf(fact_909_diff__zero,axiom,
% 5.17/5.36 ! [A: complex] :
% 5.17/5.36 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_zero
% 5.17/5.36 thf(fact_910_diff__zero,axiom,
% 5.17/5.36 ! [A: real] :
% 5.17/5.36 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_zero
% 5.17/5.36 thf(fact_911_diff__zero,axiom,
% 5.17/5.36 ! [A: rat] :
% 5.17/5.36 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_zero
% 5.17/5.36 thf(fact_912_diff__zero,axiom,
% 5.17/5.36 ! [A: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_zero
% 5.17/5.36 thf(fact_913_diff__zero,axiom,
% 5.17/5.36 ! [A: int] :
% 5.17/5.36 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.17/5.36 = A ) ).
% 5.17/5.36
% 5.17/5.36 % diff_zero
% 5.17/5.36 thf(fact_914_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.17/5.36 ! [A: complex] :
% 5.17/5.36 ( ( minus_minus_complex @ A @ A )
% 5.17/5.36 = zero_zero_complex ) ).
% 5.17/5.36
% 5.17/5.36 % cancel_comm_monoid_add_class.diff_cancel
% 5.17/5.36 thf(fact_915_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.17/5.36 ! [A: real] :
% 5.17/5.36 ( ( minus_minus_real @ A @ A )
% 5.17/5.36 = zero_zero_real ) ).
% 5.17/5.36
% 5.17/5.36 % cancel_comm_monoid_add_class.diff_cancel
% 5.17/5.36 thf(fact_916_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.17/5.36 ! [A: rat] :
% 5.17/5.36 ( ( minus_minus_rat @ A @ A )
% 5.17/5.36 = zero_zero_rat ) ).
% 5.17/5.36
% 5.17/5.36 % cancel_comm_monoid_add_class.diff_cancel
% 5.17/5.36 thf(fact_917_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.17/5.36 ! [A: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ A @ A )
% 5.17/5.36 = zero_zero_nat ) ).
% 5.17/5.36
% 5.17/5.36 % cancel_comm_monoid_add_class.diff_cancel
% 5.17/5.36 thf(fact_918_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.17/5.36 ! [A: int] :
% 5.17/5.36 ( ( minus_minus_int @ A @ A )
% 5.17/5.36 = zero_zero_int ) ).
% 5.17/5.36
% 5.17/5.36 % cancel_comm_monoid_add_class.diff_cancel
% 5.17/5.36 thf(fact_919_Suc__diff__diff,axiom,
% 5.17/5.36 ! [M: nat,N: nat,K: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.17/5.36 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.17/5.36
% 5.17/5.36 % Suc_diff_diff
% 5.17/5.36 thf(fact_920_diff__Suc__Suc,axiom,
% 5.17/5.36 ! [M: nat,N: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.17/5.36 = ( minus_minus_nat @ M @ N ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_Suc_Suc
% 5.17/5.36 thf(fact_921_diff__self__eq__0,axiom,
% 5.17/5.36 ! [M: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ M @ M )
% 5.17/5.36 = zero_zero_nat ) ).
% 5.17/5.36
% 5.17/5.36 % diff_self_eq_0
% 5.17/5.36 thf(fact_922_diff__0__eq__0,axiom,
% 5.17/5.36 ! [N: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.17/5.36 = zero_zero_nat ) ).
% 5.17/5.36
% 5.17/5.36 % diff_0_eq_0
% 5.17/5.36 thf(fact_923_diff__diff__cancel,axiom,
% 5.17/5.36 ! [I: nat,N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ I @ N )
% 5.17/5.36 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.17/5.36 = I ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_diff_cancel
% 5.17/5.36 thf(fact_924_diff__ge__0__iff__ge,axiom,
% 5.17/5.36 ! [A: rat,B: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.17/5.36 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_ge_0_iff_ge
% 5.17/5.36 thf(fact_925_diff__ge__0__iff__ge,axiom,
% 5.17/5.36 ! [A: int,B: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.17/5.36 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_ge_0_iff_ge
% 5.17/5.36 thf(fact_926_diff__ge__0__iff__ge,axiom,
% 5.17/5.36 ! [A: real,B: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.17/5.36 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_ge_0_iff_ge
% 5.17/5.36 thf(fact_927_right__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [V: num,B: complex,C: complex] :
% 5.17/5.36 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.17/5.36 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib_numeral
% 5.17/5.36 thf(fact_928_right__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [V: num,B: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.17/5.36 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib_numeral
% 5.17/5.36 thf(fact_929_right__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [V: num,B: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.17/5.36 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib_numeral
% 5.17/5.36 thf(fact_930_right__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [V: num,B: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.17/5.36 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib_numeral
% 5.17/5.36 thf(fact_931_left__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [A: complex,B: complex,V: num] :
% 5.17/5.36 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.17/5.36 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib_numeral
% 5.17/5.36 thf(fact_932_left__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [A: real,B: real,V: num] :
% 5.17/5.36 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.36 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib_numeral
% 5.17/5.36 thf(fact_933_left__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [A: rat,B: rat,V: num] :
% 5.17/5.36 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.36 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib_numeral
% 5.17/5.36 thf(fact_934_left__diff__distrib__numeral,axiom,
% 5.17/5.36 ! [A: int,B: int,V: num] :
% 5.17/5.36 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.36 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib_numeral
% 5.17/5.36 thf(fact_935_div__diff,axiom,
% 5.17/5.36 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.36 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.17/5.36 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % div_diff
% 5.17/5.36 thf(fact_936_div__diff,axiom,
% 5.17/5.36 ! [C: int,A: int,B: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ C @ A )
% 5.17/5.36 => ( ( dvd_dvd_int @ C @ B )
% 5.17/5.36 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % div_diff
% 5.17/5.36 thf(fact_937_diff__is__0__eq,axiom,
% 5.17/5.36 ! [M: nat,N: nat] :
% 5.17/5.36 ( ( ( minus_minus_nat @ M @ N )
% 5.17/5.36 = zero_zero_nat )
% 5.17/5.36 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_is_0_eq
% 5.17/5.36 thf(fact_938_diff__is__0__eq_H,axiom,
% 5.17/5.36 ! [M: nat,N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.36 => ( ( minus_minus_nat @ M @ N )
% 5.17/5.36 = zero_zero_nat ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_is_0_eq'
% 5.17/5.36 thf(fact_939_half__nonnegative__int__iff,axiom,
% 5.17/5.36 ! [K: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.17/5.36 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.36
% 5.17/5.36 % half_nonnegative_int_iff
% 5.17/5.36 thf(fact_940_diff__eq__diff__eq,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.36 ( ( ( minus_minus_real @ A @ B )
% 5.17/5.36 = ( minus_minus_real @ C @ D ) )
% 5.17/5.36 => ( ( A = B )
% 5.17/5.36 = ( C = D ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_eq_diff_eq
% 5.17/5.36 thf(fact_941_diff__eq__diff__eq,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.36 ( ( ( minus_minus_rat @ A @ B )
% 5.17/5.36 = ( minus_minus_rat @ C @ D ) )
% 5.17/5.36 => ( ( A = B )
% 5.17/5.36 = ( C = D ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_eq_diff_eq
% 5.17/5.36 thf(fact_942_diff__eq__diff__eq,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.36 ( ( ( minus_minus_int @ A @ B )
% 5.17/5.36 = ( minus_minus_int @ C @ D ) )
% 5.17/5.36 => ( ( A = B )
% 5.17/5.36 = ( C = D ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_eq_diff_eq
% 5.17/5.36 thf(fact_943_diff__right__commute,axiom,
% 5.17/5.36 ! [A: real,C: real,B: real] :
% 5.17/5.36 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.17/5.36 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_commute
% 5.17/5.36 thf(fact_944_diff__right__commute,axiom,
% 5.17/5.36 ! [A: rat,C: rat,B: rat] :
% 5.17/5.36 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.17/5.36 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_commute
% 5.17/5.36 thf(fact_945_diff__right__commute,axiom,
% 5.17/5.36 ! [A: nat,C: nat,B: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.17/5.36 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_commute
% 5.17/5.36 thf(fact_946_diff__right__commute,axiom,
% 5.17/5.36 ! [A: int,C: int,B: int] :
% 5.17/5.36 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.17/5.36 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_commute
% 5.17/5.36 thf(fact_947_diff__commute,axiom,
% 5.17/5.36 ! [I: nat,J: nat,K: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.17/5.36 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_commute
% 5.17/5.36 thf(fact_948_diff__eq__diff__less__eq,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.36 ( ( ( minus_minus_rat @ A @ B )
% 5.17/5.36 = ( minus_minus_rat @ C @ D ) )
% 5.17/5.36 => ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_eq_diff_less_eq
% 5.17/5.36 thf(fact_949_diff__eq__diff__less__eq,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.36 ( ( ( minus_minus_int @ A @ B )
% 5.17/5.36 = ( minus_minus_int @ C @ D ) )
% 5.17/5.36 => ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_eq_diff_less_eq
% 5.17/5.36 thf(fact_950_diff__eq__diff__less__eq,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.36 ( ( ( minus_minus_real @ A @ B )
% 5.17/5.36 = ( minus_minus_real @ C @ D ) )
% 5.17/5.36 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_eq_diff_less_eq
% 5.17/5.36 thf(fact_951_diff__right__mono,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_mono
% 5.17/5.36 thf(fact_952_diff__right__mono,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_mono
% 5.17/5.36 thf(fact_953_diff__right__mono,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_right_mono
% 5.17/5.36 thf(fact_954_diff__left__mono,axiom,
% 5.17/5.36 ! [B: rat,A: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.36 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_left_mono
% 5.17/5.36 thf(fact_955_diff__left__mono,axiom,
% 5.17/5.36 ! [B: int,A: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.36 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_left_mono
% 5.17/5.36 thf(fact_956_diff__left__mono,axiom,
% 5.17/5.36 ! [B: real,A: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.36 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_left_mono
% 5.17/5.36 thf(fact_957_diff__mono,axiom,
% 5.17/5.36 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.17/5.36 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_rat @ D @ C )
% 5.17/5.36 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_mono
% 5.17/5.36 thf(fact_958_diff__mono,axiom,
% 5.17/5.36 ! [A: int,B: int,D: int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_int @ D @ C )
% 5.17/5.36 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_mono
% 5.17/5.36 thf(fact_959_diff__mono,axiom,
% 5.17/5.36 ! [A: real,B: real,D: real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.36 => ( ( ord_less_eq_real @ D @ C )
% 5.17/5.36 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_mono
% 5.17/5.36 thf(fact_960_eq__iff__diff__eq__0,axiom,
% 5.17/5.36 ( ( ^ [Y5: complex,Z4: complex] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: complex,B2: complex] :
% 5.17/5.36 ( ( minus_minus_complex @ A3 @ B2 )
% 5.17/5.36 = zero_zero_complex ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_iff_diff_eq_0
% 5.17/5.36 thf(fact_961_eq__iff__diff__eq__0,axiom,
% 5.17/5.36 ( ( ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: real,B2: real] :
% 5.17/5.36 ( ( minus_minus_real @ A3 @ B2 )
% 5.17/5.36 = zero_zero_real ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_iff_diff_eq_0
% 5.17/5.36 thf(fact_962_eq__iff__diff__eq__0,axiom,
% 5.17/5.36 ( ( ^ [Y5: rat,Z4: rat] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.36 ( ( minus_minus_rat @ A3 @ B2 )
% 5.17/5.36 = zero_zero_rat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_iff_diff_eq_0
% 5.17/5.36 thf(fact_963_eq__iff__diff__eq__0,axiom,
% 5.17/5.36 ( ( ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.36 = ( ^ [A3: int,B2: int] :
% 5.17/5.36 ( ( minus_minus_int @ A3 @ B2 )
% 5.17/5.36 = zero_zero_int ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_iff_diff_eq_0
% 5.17/5.36 thf(fact_964_of__nat__diff,axiom,
% 5.17/5.36 ! [N: nat,M: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_diff
% 5.17/5.36 thf(fact_965_of__nat__diff,axiom,
% 5.17/5.36 ! [N: nat,M: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_diff
% 5.17/5.36 thf(fact_966_of__nat__diff,axiom,
% 5.17/5.36 ! [N: nat,M: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_diff
% 5.17/5.36 thf(fact_967_of__nat__diff,axiom,
% 5.17/5.36 ! [N: nat,M: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_diff
% 5.17/5.36 thf(fact_968_of__nat__diff,axiom,
% 5.17/5.36 ! [N: nat,M: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % of_nat_diff
% 5.17/5.36 thf(fact_969_right__diff__distrib_H,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.17/5.36 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib'
% 5.17/5.36 thf(fact_970_right__diff__distrib_H,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.17/5.36 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib'
% 5.17/5.36 thf(fact_971_right__diff__distrib_H,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.17/5.36 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib'
% 5.17/5.36 thf(fact_972_right__diff__distrib_H,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.17/5.36 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib'
% 5.17/5.36 thf(fact_973_left__diff__distrib_H,axiom,
% 5.17/5.36 ! [B: real,C: real,A: real] :
% 5.17/5.36 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.17/5.36 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib'
% 5.17/5.36 thf(fact_974_left__diff__distrib_H,axiom,
% 5.17/5.36 ! [B: rat,C: rat,A: rat] :
% 5.17/5.36 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.17/5.36 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib'
% 5.17/5.36 thf(fact_975_left__diff__distrib_H,axiom,
% 5.17/5.36 ! [B: nat,C: nat,A: nat] :
% 5.17/5.36 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.17/5.36 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib'
% 5.17/5.36 thf(fact_976_left__diff__distrib_H,axiom,
% 5.17/5.36 ! [B: int,C: int,A: int] :
% 5.17/5.36 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.17/5.36 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib'
% 5.17/5.36 thf(fact_977_right__diff__distrib,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.17/5.36 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib
% 5.17/5.36 thf(fact_978_right__diff__distrib,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.17/5.36 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib
% 5.17/5.36 thf(fact_979_right__diff__distrib,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.17/5.36 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % right_diff_distrib
% 5.17/5.36 thf(fact_980_left__diff__distrib,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib
% 5.17/5.36 thf(fact_981_left__diff__distrib,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib
% 5.17/5.36 thf(fact_982_left__diff__distrib,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % left_diff_distrib
% 5.17/5.36 thf(fact_983_diff__divide__distrib,axiom,
% 5.17/5.36 ! [A: complex,B: complex,C: complex] :
% 5.17/5.36 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_divide_distrib
% 5.17/5.36 thf(fact_984_diff__divide__distrib,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_divide_distrib
% 5.17/5.36 thf(fact_985_diff__divide__distrib,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.17/5.36 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_divide_distrib
% 5.17/5.36 thf(fact_986_dvd__diff__commute,axiom,
% 5.17/5.36 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.17/5.36 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff_commute
% 5.17/5.36 thf(fact_987_dvd__diff__commute,axiom,
% 5.17/5.36 ! [A: int,C: int,B: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.17/5.36 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff_commute
% 5.17/5.36 thf(fact_988_dvd__diff,axiom,
% 5.17/5.36 ! [X: code_integer,Y4: code_integer,Z: code_integer] :
% 5.17/5.36 ( ( dvd_dvd_Code_integer @ X @ Y4 )
% 5.17/5.36 => ( ( dvd_dvd_Code_integer @ X @ Z )
% 5.17/5.36 => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y4 @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff
% 5.17/5.36 thf(fact_989_dvd__diff,axiom,
% 5.17/5.36 ! [X: real,Y4: real,Z: real] :
% 5.17/5.36 ( ( dvd_dvd_real @ X @ Y4 )
% 5.17/5.36 => ( ( dvd_dvd_real @ X @ Z )
% 5.17/5.36 => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y4 @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff
% 5.17/5.36 thf(fact_990_dvd__diff,axiom,
% 5.17/5.36 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.36 ( ( dvd_dvd_rat @ X @ Y4 )
% 5.17/5.36 => ( ( dvd_dvd_rat @ X @ Z )
% 5.17/5.36 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y4 @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff
% 5.17/5.36 thf(fact_991_dvd__diff,axiom,
% 5.17/5.36 ! [X: int,Y4: int,Z: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ X @ Y4 )
% 5.17/5.36 => ( ( dvd_dvd_int @ X @ Z )
% 5.17/5.36 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y4 @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff
% 5.17/5.36 thf(fact_992_zero__induct__lemma,axiom,
% 5.17/5.36 ! [P: nat > $o,K: nat,I: nat] :
% 5.17/5.36 ( ( P @ K )
% 5.17/5.36 => ( ! [N2: nat] :
% 5.17/5.36 ( ( P @ ( suc @ N2 ) )
% 5.17/5.36 => ( P @ N2 ) )
% 5.17/5.36 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_induct_lemma
% 5.17/5.36 thf(fact_993_diffs0__imp__equal,axiom,
% 5.17/5.36 ! [M: nat,N: nat] :
% 5.17/5.36 ( ( ( minus_minus_nat @ M @ N )
% 5.17/5.36 = zero_zero_nat )
% 5.17/5.36 => ( ( ( minus_minus_nat @ N @ M )
% 5.17/5.36 = zero_zero_nat )
% 5.17/5.36 => ( M = N ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diffs0_imp_equal
% 5.17/5.36 thf(fact_994_minus__nat_Odiff__0,axiom,
% 5.17/5.36 ! [M: nat] :
% 5.17/5.36 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.17/5.36 = M ) ).
% 5.17/5.36
% 5.17/5.36 % minus_nat.diff_0
% 5.17/5.36 thf(fact_995_eq__diff__iff,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.36 => ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.36 => ( ( ( minus_minus_nat @ M @ K )
% 5.17/5.36 = ( minus_minus_nat @ N @ K ) )
% 5.17/5.36 = ( M = N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % eq_diff_iff
% 5.17/5.36 thf(fact_996_le__diff__iff,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.36 => ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.36 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.17/5.36 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_diff_iff
% 5.17/5.36 thf(fact_997_Nat_Odiff__diff__eq,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.36 => ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.36 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.17/5.36 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Nat.diff_diff_eq
% 5.17/5.36 thf(fact_998_diff__le__mono,axiom,
% 5.17/5.36 ! [M: nat,N: nat,L: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.36 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_le_mono
% 5.17/5.36 thf(fact_999_diff__le__self,axiom,
% 5.17/5.36 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.17/5.36
% 5.17/5.36 % diff_le_self
% 5.17/5.36 thf(fact_1000_le__diff__iff_H,axiom,
% 5.17/5.36 ! [A: nat,C: nat,B: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ A @ C )
% 5.17/5.36 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.36 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.17/5.36 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_diff_iff'
% 5.17/5.36 thf(fact_1001_diff__le__mono2,axiom,
% 5.17/5.36 ! [M: nat,N: nat,L: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.36 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_le_mono2
% 5.17/5.36 thf(fact_1002_diff__mult__distrib,axiom,
% 5.17/5.36 ! [M: nat,N: nat,K: nat] :
% 5.17/5.36 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.17/5.36 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_mult_distrib
% 5.17/5.36 thf(fact_1003_diff__mult__distrib2,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_mult_distrib2
% 5.17/5.36 thf(fact_1004_dvd__diff__nat,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ K @ M )
% 5.17/5.36 => ( ( dvd_dvd_nat @ K @ N )
% 5.17/5.36 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diff_nat
% 5.17/5.36 thf(fact_1005_le__iff__diff__le__0,axiom,
% 5.17/5.36 ( ord_less_eq_rat
% 5.17/5.36 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_iff_diff_le_0
% 5.17/5.36 thf(fact_1006_le__iff__diff__le__0,axiom,
% 5.17/5.36 ( ord_less_eq_int
% 5.17/5.36 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_iff_diff_le_0
% 5.17/5.36 thf(fact_1007_le__iff__diff__le__0,axiom,
% 5.17/5.36 ( ord_less_eq_real
% 5.17/5.36 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % le_iff_diff_le_0
% 5.17/5.36 thf(fact_1008_less__eq__int__code_I1_J,axiom,
% 5.17/5.36 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.17/5.36
% 5.17/5.36 % less_eq_int_code(1)
% 5.17/5.36 thf(fact_1009_times__int__code_I1_J,axiom,
% 5.17/5.36 ! [K: int] :
% 5.17/5.36 ( ( times_times_int @ K @ zero_zero_int )
% 5.17/5.36 = zero_zero_int ) ).
% 5.17/5.36
% 5.17/5.36 % times_int_code(1)
% 5.17/5.36 thf(fact_1010_times__int__code_I2_J,axiom,
% 5.17/5.36 ! [L: int] :
% 5.17/5.36 ( ( times_times_int @ zero_zero_int @ L )
% 5.17/5.36 = zero_zero_int ) ).
% 5.17/5.36
% 5.17/5.36 % times_int_code(2)
% 5.17/5.36 thf(fact_1011_ile0__eq,axiom,
% 5.17/5.36 ! [N: extended_enat] :
% 5.17/5.36 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.17/5.36 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.17/5.36
% 5.17/5.36 % ile0_eq
% 5.17/5.36 thf(fact_1012_i0__lb,axiom,
% 5.17/5.36 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.17/5.36
% 5.17/5.36 % i0_lb
% 5.17/5.36 thf(fact_1013_unset__bit__less__eq,axiom,
% 5.17/5.36 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.17/5.36
% 5.17/5.36 % unset_bit_less_eq
% 5.17/5.36 thf(fact_1014_set__bit__greater__eq,axiom,
% 5.17/5.36 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.17/5.36
% 5.17/5.36 % set_bit_greater_eq
% 5.17/5.36 thf(fact_1015_Suc__diff__le,axiom,
% 5.17/5.36 ! [N: nat,M: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.17/5.36 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % Suc_diff_le
% 5.17/5.36 thf(fact_1016_dvd__diffD,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 => ( ( dvd_dvd_nat @ K @ N )
% 5.17/5.36 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diffD
% 5.17/5.36 thf(fact_1017_dvd__diffD1,axiom,
% 5.17/5.36 ! [K: nat,M: nat,N: nat] :
% 5.17/5.36 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.36 => ( ( dvd_dvd_nat @ K @ M )
% 5.17/5.36 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.36 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % dvd_diffD1
% 5.17/5.36 thf(fact_1018_less__eq__dvd__minus,axiom,
% 5.17/5.36 ! [M: nat,N: nat] :
% 5.17/5.36 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.36 => ( ( dvd_dvd_nat @ M @ N )
% 5.17/5.36 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % less_eq_dvd_minus
% 5.17/5.36 thf(fact_1019_int__ops_I1_J,axiom,
% 5.17/5.36 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.17/5.36 = zero_zero_int ) ).
% 5.17/5.36
% 5.17/5.36 % int_ops(1)
% 5.17/5.36 thf(fact_1020_nonneg__int__cases,axiom,
% 5.17/5.36 ! [K: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.36 => ~ ! [N2: nat] :
% 5.17/5.36 ( K
% 5.17/5.36 != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % nonneg_int_cases
% 5.17/5.36 thf(fact_1021_zero__le__imp__eq__int,axiom,
% 5.17/5.36 ! [K: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.36 => ? [N2: nat] :
% 5.17/5.36 ( K
% 5.17/5.36 = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_le_imp_eq_int
% 5.17/5.36 thf(fact_1022_zdvd__antisym__nonneg,axiom,
% 5.17/5.36 ! [M: int,N: int] :
% 5.17/5.36 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.17/5.36 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.17/5.36 => ( ( dvd_dvd_int @ M @ N )
% 5.17/5.36 => ( ( dvd_dvd_int @ N @ M )
% 5.17/5.36 => ( M = N ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % zdvd_antisym_nonneg
% 5.17/5.36 thf(fact_1023_zdvd__mult__cancel,axiom,
% 5.17/5.36 ! [K: int,M: int,N: int] :
% 5.17/5.36 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.17/5.36 => ( ( K != zero_zero_int )
% 5.17/5.36 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % zdvd_mult_cancel
% 5.17/5.36 thf(fact_1024_divide__diff__eq__iff,axiom,
% 5.17/5.36 ! [Z: complex,X: complex,Y4: complex] :
% 5.17/5.36 ( ( Z != zero_zero_complex )
% 5.17/5.36 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y4 )
% 5.17/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_diff_eq_iff
% 5.17/5.36 thf(fact_1025_divide__diff__eq__iff,axiom,
% 5.17/5.36 ! [Z: real,X: real,Y4: real] :
% 5.17/5.36 ( ( Z != zero_zero_real )
% 5.17/5.36 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y4 )
% 5.17/5.36 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_diff_eq_iff
% 5.17/5.36 thf(fact_1026_divide__diff__eq__iff,axiom,
% 5.17/5.36 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.36 ( ( Z != zero_zero_rat )
% 5.17/5.36 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y4 )
% 5.17/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % divide_diff_eq_iff
% 5.17/5.36 thf(fact_1027_diff__divide__eq__iff,axiom,
% 5.17/5.36 ! [Z: complex,X: complex,Y4: complex] :
% 5.17/5.36 ( ( Z != zero_zero_complex )
% 5.17/5.36 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y4 @ Z ) )
% 5.17/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_divide_eq_iff
% 5.17/5.36 thf(fact_1028_diff__divide__eq__iff,axiom,
% 5.17/5.36 ! [Z: real,X: real,Y4: real] :
% 5.17/5.36 ( ( Z != zero_zero_real )
% 5.17/5.36 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y4 @ Z ) )
% 5.17/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_divide_eq_iff
% 5.17/5.36 thf(fact_1029_diff__divide__eq__iff,axiom,
% 5.17/5.36 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.36 ( ( Z != zero_zero_rat )
% 5.17/5.36 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y4 @ Z ) )
% 5.17/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_divide_eq_iff
% 5.17/5.36 thf(fact_1030_diff__frac__eq,axiom,
% 5.17/5.36 ! [Y4: complex,Z: complex,X: complex,W: complex] :
% 5.17/5.36 ( ( Y4 != zero_zero_complex )
% 5.17/5.36 => ( ( Z != zero_zero_complex )
% 5.17/5.36 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.17/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y4 ) ) @ ( times_times_complex @ Y4 @ Z ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_frac_eq
% 5.17/5.36 thf(fact_1031_diff__frac__eq,axiom,
% 5.17/5.36 ! [Y4: real,Z: real,X: real,W: real] :
% 5.17/5.36 ( ( Y4 != zero_zero_real )
% 5.17/5.36 => ( ( Z != zero_zero_real )
% 5.17/5.36 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.17/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_frac_eq
% 5.17/5.36 thf(fact_1032_diff__frac__eq,axiom,
% 5.17/5.36 ! [Y4: rat,Z: rat,X: rat,W: rat] :
% 5.17/5.36 ( ( Y4 != zero_zero_rat )
% 5.17/5.36 => ( ( Z != zero_zero_rat )
% 5.17/5.36 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.17/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % diff_frac_eq
% 5.17/5.36 thf(fact_1033_add__divide__eq__if__simps_I4_J,axiom,
% 5.17/5.36 ! [Z: complex,A: complex,B: complex] :
% 5.17/5.36 ( ( ( Z = zero_zero_complex )
% 5.17/5.36 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.17/5.36 = A ) )
% 5.17/5.36 & ( ( Z != zero_zero_complex )
% 5.17/5.36 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.17/5.36 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % add_divide_eq_if_simps(4)
% 5.17/5.36 thf(fact_1034_add__divide__eq__if__simps_I4_J,axiom,
% 5.17/5.36 ! [Z: real,A: real,B: real] :
% 5.17/5.36 ( ( ( Z = zero_zero_real )
% 5.17/5.36 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.17/5.36 = A ) )
% 5.17/5.36 & ( ( Z != zero_zero_real )
% 5.17/5.36 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.17/5.36 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % add_divide_eq_if_simps(4)
% 5.17/5.36 thf(fact_1035_add__divide__eq__if__simps_I4_J,axiom,
% 5.17/5.36 ! [Z: rat,A: rat,B: rat] :
% 5.17/5.36 ( ( ( Z = zero_zero_rat )
% 5.17/5.36 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.17/5.36 = A ) )
% 5.17/5.36 & ( ( Z != zero_zero_rat )
% 5.17/5.36 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.17/5.36 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % add_divide_eq_if_simps(4)
% 5.17/5.36 thf(fact_1036_zero__reorient,axiom,
% 5.17/5.36 ! [X: complex] :
% 5.17/5.36 ( ( zero_zero_complex = X )
% 5.17/5.36 = ( X = zero_zero_complex ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_reorient
% 5.17/5.36 thf(fact_1037_zero__reorient,axiom,
% 5.17/5.36 ! [X: real] :
% 5.17/5.36 ( ( zero_zero_real = X )
% 5.17/5.36 = ( X = zero_zero_real ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_reorient
% 5.17/5.36 thf(fact_1038_zero__reorient,axiom,
% 5.17/5.36 ! [X: rat] :
% 5.17/5.36 ( ( zero_zero_rat = X )
% 5.17/5.36 = ( X = zero_zero_rat ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_reorient
% 5.17/5.36 thf(fact_1039_zero__reorient,axiom,
% 5.17/5.36 ! [X: nat] :
% 5.17/5.36 ( ( zero_zero_nat = X )
% 5.17/5.36 = ( X = zero_zero_nat ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_reorient
% 5.17/5.36 thf(fact_1040_zero__reorient,axiom,
% 5.17/5.36 ! [X: int] :
% 5.17/5.36 ( ( zero_zero_int = X )
% 5.17/5.36 = ( X = zero_zero_int ) ) ).
% 5.17/5.36
% 5.17/5.36 % zero_reorient
% 5.17/5.36 thf(fact_1041_mult_Oleft__commute,axiom,
% 5.17/5.36 ! [B: real,A: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.17/5.36 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.left_commute
% 5.17/5.36 thf(fact_1042_mult_Oleft__commute,axiom,
% 5.17/5.36 ! [B: rat,A: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.17/5.36 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.left_commute
% 5.17/5.36 thf(fact_1043_mult_Oleft__commute,axiom,
% 5.17/5.36 ! [B: nat,A: nat,C: nat] :
% 5.17/5.36 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.17/5.36 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.left_commute
% 5.17/5.36 thf(fact_1044_mult_Oleft__commute,axiom,
% 5.17/5.36 ! [B: int,A: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.17/5.36 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.left_commute
% 5.17/5.36 thf(fact_1045_mult_Ocommute,axiom,
% 5.17/5.36 ( times_times_real
% 5.17/5.36 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.commute
% 5.17/5.36 thf(fact_1046_mult_Ocommute,axiom,
% 5.17/5.36 ( times_times_rat
% 5.17/5.36 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.commute
% 5.17/5.36 thf(fact_1047_mult_Ocommute,axiom,
% 5.17/5.36 ( times_times_nat
% 5.17/5.36 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.commute
% 5.17/5.36 thf(fact_1048_mult_Ocommute,axiom,
% 5.17/5.36 ( times_times_int
% 5.17/5.36 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.commute
% 5.17/5.36 thf(fact_1049_mult_Oassoc,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.assoc
% 5.17/5.36 thf(fact_1050_mult_Oassoc,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.assoc
% 5.17/5.36 thf(fact_1051_mult_Oassoc,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.assoc
% 5.17/5.36 thf(fact_1052_mult_Oassoc,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % mult.assoc
% 5.17/5.36 thf(fact_1053_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.17/5.36 ! [A: real,B: real,C: real] :
% 5.17/5.36 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ab_semigroup_mult_class.mult_ac(1)
% 5.17/5.36 thf(fact_1054_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.17/5.36 ! [A: rat,B: rat,C: rat] :
% 5.17/5.36 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ab_semigroup_mult_class.mult_ac(1)
% 5.17/5.36 thf(fact_1055_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.17/5.36 ! [A: nat,B: nat,C: nat] :
% 5.17/5.36 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ab_semigroup_mult_class.mult_ac(1)
% 5.17/5.36 thf(fact_1056_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.17/5.36 ! [A: int,B: int,C: int] :
% 5.17/5.36 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.36 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % ab_semigroup_mult_class.mult_ac(1)
% 5.17/5.36 thf(fact_1057_in__mono,axiom,
% 5.17/5.36 ! [A2: set_complex,B4: set_complex,X: complex] :
% 5.17/5.36 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.17/5.36 => ( ( member_complex @ X @ A2 )
% 5.17/5.36 => ( member_complex @ X @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % in_mono
% 5.17/5.36 thf(fact_1058_in__mono,axiom,
% 5.17/5.36 ! [A2: set_real,B4: set_real,X: real] :
% 5.17/5.36 ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.17/5.36 => ( ( member_real @ X @ A2 )
% 5.17/5.36 => ( member_real @ X @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % in_mono
% 5.17/5.36 thf(fact_1059_in__mono,axiom,
% 5.17/5.36 ! [A2: set_set_nat,B4: set_set_nat,X: set_nat] :
% 5.17/5.36 ( ( ord_le6893508408891458716et_nat @ A2 @ B4 )
% 5.17/5.36 => ( ( member_set_nat @ X @ A2 )
% 5.17/5.36 => ( member_set_nat @ X @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % in_mono
% 5.17/5.36 thf(fact_1060_in__mono,axiom,
% 5.17/5.36 ! [A2: set_nat,B4: set_nat,X: nat] :
% 5.17/5.36 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.17/5.36 => ( ( member_nat @ X @ A2 )
% 5.17/5.36 => ( member_nat @ X @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % in_mono
% 5.17/5.36 thf(fact_1061_in__mono,axiom,
% 5.17/5.36 ! [A2: set_int,B4: set_int,X: int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.36 => ( ( member_int @ X @ A2 )
% 5.17/5.36 => ( member_int @ X @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % in_mono
% 5.17/5.36 thf(fact_1062_subsetD,axiom,
% 5.17/5.36 ! [A2: set_complex,B4: set_complex,C: complex] :
% 5.17/5.36 ( ( ord_le211207098394363844omplex @ A2 @ B4 )
% 5.17/5.36 => ( ( member_complex @ C @ A2 )
% 5.17/5.36 => ( member_complex @ C @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetD
% 5.17/5.36 thf(fact_1063_subsetD,axiom,
% 5.17/5.36 ! [A2: set_real,B4: set_real,C: real] :
% 5.17/5.36 ( ( ord_less_eq_set_real @ A2 @ B4 )
% 5.17/5.36 => ( ( member_real @ C @ A2 )
% 5.17/5.36 => ( member_real @ C @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetD
% 5.17/5.36 thf(fact_1064_subsetD,axiom,
% 5.17/5.36 ! [A2: set_set_nat,B4: set_set_nat,C: set_nat] :
% 5.17/5.36 ( ( ord_le6893508408891458716et_nat @ A2 @ B4 )
% 5.17/5.36 => ( ( member_set_nat @ C @ A2 )
% 5.17/5.36 => ( member_set_nat @ C @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetD
% 5.17/5.36 thf(fact_1065_subsetD,axiom,
% 5.17/5.36 ! [A2: set_nat,B4: set_nat,C: nat] :
% 5.17/5.36 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.17/5.36 => ( ( member_nat @ C @ A2 )
% 5.17/5.36 => ( member_nat @ C @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetD
% 5.17/5.36 thf(fact_1066_subsetD,axiom,
% 5.17/5.36 ! [A2: set_int,B4: set_int,C: int] :
% 5.17/5.36 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.36 => ( ( member_int @ C @ A2 )
% 5.17/5.36 => ( member_int @ C @ B4 ) ) ) ).
% 5.17/5.36
% 5.17/5.36 % subsetD
% 5.17/5.36 thf(fact_1067_equalityE,axiom,
% 5.17/5.36 ! [A2: set_int,B4: set_int] :
% 5.17/5.36 ( ( A2 = B4 )
% 5.17/5.36 => ~ ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.36 => ~ ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % equalityE
% 5.17/5.37 thf(fact_1068_subset__eq,axiom,
% 5.17/5.37 ( ord_le211207098394363844omplex
% 5.17/5.37 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.17/5.37 ! [X3: complex] :
% 5.17/5.37 ( ( member_complex @ X3 @ A5 )
% 5.17/5.37 => ( member_complex @ X3 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_eq
% 5.17/5.37 thf(fact_1069_subset__eq,axiom,
% 5.17/5.37 ( ord_less_eq_set_real
% 5.17/5.37 = ( ^ [A5: set_real,B5: set_real] :
% 5.17/5.37 ! [X3: real] :
% 5.17/5.37 ( ( member_real @ X3 @ A5 )
% 5.17/5.37 => ( member_real @ X3 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_eq
% 5.17/5.37 thf(fact_1070_subset__eq,axiom,
% 5.17/5.37 ( ord_le6893508408891458716et_nat
% 5.17/5.37 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.17/5.37 ! [X3: set_nat] :
% 5.17/5.37 ( ( member_set_nat @ X3 @ A5 )
% 5.17/5.37 => ( member_set_nat @ X3 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_eq
% 5.17/5.37 thf(fact_1071_subset__eq,axiom,
% 5.17/5.37 ( ord_less_eq_set_nat
% 5.17/5.37 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.17/5.37 ! [X3: nat] :
% 5.17/5.37 ( ( member_nat @ X3 @ A5 )
% 5.17/5.37 => ( member_nat @ X3 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_eq
% 5.17/5.37 thf(fact_1072_subset__eq,axiom,
% 5.17/5.37 ( ord_less_eq_set_int
% 5.17/5.37 = ( ^ [A5: set_int,B5: set_int] :
% 5.17/5.37 ! [X3: int] :
% 5.17/5.37 ( ( member_int @ X3 @ A5 )
% 5.17/5.37 => ( member_int @ X3 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_eq
% 5.17/5.37 thf(fact_1073_equalityD1,axiom,
% 5.17/5.37 ! [A2: set_int,B4: set_int] :
% 5.17/5.37 ( ( A2 = B4 )
% 5.17/5.37 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.17/5.37
% 5.17/5.37 % equalityD1
% 5.17/5.37 thf(fact_1074_equalityD2,axiom,
% 5.17/5.37 ! [A2: set_int,B4: set_int] :
% 5.17/5.37 ( ( A2 = B4 )
% 5.17/5.37 => ( ord_less_eq_set_int @ B4 @ A2 ) ) ).
% 5.17/5.37
% 5.17/5.37 % equalityD2
% 5.17/5.37 thf(fact_1075_subset__iff,axiom,
% 5.17/5.37 ( ord_le211207098394363844omplex
% 5.17/5.37 = ( ^ [A5: set_complex,B5: set_complex] :
% 5.17/5.37 ! [T2: complex] :
% 5.17/5.37 ( ( member_complex @ T2 @ A5 )
% 5.17/5.37 => ( member_complex @ T2 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_iff
% 5.17/5.37 thf(fact_1076_subset__iff,axiom,
% 5.17/5.37 ( ord_less_eq_set_real
% 5.17/5.37 = ( ^ [A5: set_real,B5: set_real] :
% 5.17/5.37 ! [T2: real] :
% 5.17/5.37 ( ( member_real @ T2 @ A5 )
% 5.17/5.37 => ( member_real @ T2 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_iff
% 5.17/5.37 thf(fact_1077_subset__iff,axiom,
% 5.17/5.37 ( ord_le6893508408891458716et_nat
% 5.17/5.37 = ( ^ [A5: set_set_nat,B5: set_set_nat] :
% 5.17/5.37 ! [T2: set_nat] :
% 5.17/5.37 ( ( member_set_nat @ T2 @ A5 )
% 5.17/5.37 => ( member_set_nat @ T2 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_iff
% 5.17/5.37 thf(fact_1078_subset__iff,axiom,
% 5.17/5.37 ( ord_less_eq_set_nat
% 5.17/5.37 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.17/5.37 ! [T2: nat] :
% 5.17/5.37 ( ( member_nat @ T2 @ A5 )
% 5.17/5.37 => ( member_nat @ T2 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_iff
% 5.17/5.37 thf(fact_1079_subset__iff,axiom,
% 5.17/5.37 ( ord_less_eq_set_int
% 5.17/5.37 = ( ^ [A5: set_int,B5: set_int] :
% 5.17/5.37 ! [T2: int] :
% 5.17/5.37 ( ( member_int @ T2 @ A5 )
% 5.17/5.37 => ( member_int @ T2 @ B5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_iff
% 5.17/5.37 thf(fact_1080_subset__refl,axiom,
% 5.17/5.37 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.17/5.37
% 5.17/5.37 % subset_refl
% 5.17/5.37 thf(fact_1081_Collect__mono,axiom,
% 5.17/5.37 ! [P: real > $o,Q: real > $o] :
% 5.17/5.37 ( ! [X4: real] :
% 5.17/5.37 ( ( P @ X4 )
% 5.17/5.37 => ( Q @ X4 ) )
% 5.17/5.37 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono
% 5.17/5.37 thf(fact_1082_Collect__mono,axiom,
% 5.17/5.37 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.17/5.37 ( ! [X4: list_nat] :
% 5.17/5.37 ( ( P @ X4 )
% 5.17/5.37 => ( Q @ X4 ) )
% 5.17/5.37 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono
% 5.17/5.37 thf(fact_1083_Collect__mono,axiom,
% 5.17/5.37 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.17/5.37 ( ! [X4: set_nat] :
% 5.17/5.37 ( ( P @ X4 )
% 5.17/5.37 => ( Q @ X4 ) )
% 5.17/5.37 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono
% 5.17/5.37 thf(fact_1084_Collect__mono,axiom,
% 5.17/5.37 ! [P: nat > $o,Q: nat > $o] :
% 5.17/5.37 ( ! [X4: nat] :
% 5.17/5.37 ( ( P @ X4 )
% 5.17/5.37 => ( Q @ X4 ) )
% 5.17/5.37 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono
% 5.17/5.37 thf(fact_1085_Collect__mono,axiom,
% 5.17/5.37 ! [P: int > $o,Q: int > $o] :
% 5.17/5.37 ( ! [X4: int] :
% 5.17/5.37 ( ( P @ X4 )
% 5.17/5.37 => ( Q @ X4 ) )
% 5.17/5.37 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono
% 5.17/5.37 thf(fact_1086_subset__trans,axiom,
% 5.17/5.37 ! [A2: set_int,B4: set_int,C2: set_int] :
% 5.17/5.37 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.37 => ( ( ord_less_eq_set_int @ B4 @ C2 )
% 5.17/5.37 => ( ord_less_eq_set_int @ A2 @ C2 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % subset_trans
% 5.17/5.37 thf(fact_1087_set__eq__subset,axiom,
% 5.17/5.37 ( ( ^ [Y5: set_int,Z4: set_int] : ( Y5 = Z4 ) )
% 5.17/5.37 = ( ^ [A5: set_int,B5: set_int] :
% 5.17/5.37 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.17/5.37 & ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % set_eq_subset
% 5.17/5.37 thf(fact_1088_Collect__mono__iff,axiom,
% 5.17/5.37 ! [P: real > $o,Q: real > $o] :
% 5.17/5.37 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.17/5.37 = ( ! [X3: real] :
% 5.17/5.37 ( ( P @ X3 )
% 5.17/5.37 => ( Q @ X3 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono_iff
% 5.17/5.37 thf(fact_1089_Collect__mono__iff,axiom,
% 5.17/5.37 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.17/5.37 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.17/5.37 = ( ! [X3: list_nat] :
% 5.17/5.37 ( ( P @ X3 )
% 5.17/5.37 => ( Q @ X3 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono_iff
% 5.17/5.37 thf(fact_1090_Collect__mono__iff,axiom,
% 5.17/5.37 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.17/5.37 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.17/5.37 = ( ! [X3: set_nat] :
% 5.17/5.37 ( ( P @ X3 )
% 5.17/5.37 => ( Q @ X3 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono_iff
% 5.17/5.37 thf(fact_1091_Collect__mono__iff,axiom,
% 5.17/5.37 ! [P: nat > $o,Q: nat > $o] :
% 5.17/5.37 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.17/5.37 = ( ! [X3: nat] :
% 5.17/5.37 ( ( P @ X3 )
% 5.17/5.37 => ( Q @ X3 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono_iff
% 5.17/5.37 thf(fact_1092_Collect__mono__iff,axiom,
% 5.17/5.37 ! [P: int > $o,Q: int > $o] :
% 5.17/5.37 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.17/5.37 = ( ! [X3: int] :
% 5.17/5.37 ( ( P @ X3 )
% 5.17/5.37 => ( Q @ X3 ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Collect_mono_iff
% 5.17/5.37 thf(fact_1093_zdiv__zmult2__eq,axiom,
% 5.17/5.37 ! [C: int,A: int,B: int] :
% 5.17/5.37 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.37 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.37 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zdiv_zmult2_eq
% 5.17/5.37 thf(fact_1094_frac__le__eq,axiom,
% 5.17/5.37 ! [Y4: rat,Z: rat,X: rat,W: rat] :
% 5.17/5.37 ( ( Y4 != zero_zero_rat )
% 5.17/5.37 => ( ( Z != zero_zero_rat )
% 5.17/5.37 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.17/5.37 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % frac_le_eq
% 5.17/5.37 thf(fact_1095_frac__le__eq,axiom,
% 5.17/5.37 ! [Y4: real,Z: real,X: real,W: real] :
% 5.17/5.37 ( ( Y4 != zero_zero_real )
% 5.17/5.37 => ( ( Z != zero_zero_real )
% 5.17/5.37 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.17/5.37 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % frac_le_eq
% 5.17/5.37 thf(fact_1096_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I1_J,axiom,
% 5.17/5.37 ( ( vEBT_V8346862874174094_d_u_p @ zero_zero_nat )
% 5.17/5.37 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(1)
% 5.17/5.37 thf(fact_1097_zero__le,axiom,
% 5.17/5.37 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.17/5.37
% 5.17/5.37 % zero_le
% 5.17/5.37 thf(fact_1098_bezout1__nat,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ? [D2: nat,X4: nat,Y: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ D2 @ A )
% 5.17/5.37 & ( dvd_dvd_nat @ D2 @ B )
% 5.17/5.37 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y ) )
% 5.17/5.37 = D2 )
% 5.17/5.37 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y ) )
% 5.17/5.37 = D2 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % bezout1_nat
% 5.17/5.37 thf(fact_1099_odd__two__times__div__two__nat,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.37 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.37 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % odd_two_times_div_two_nat
% 5.17/5.37 thf(fact_1100_buildup__build__time,axiom,
% 5.17/5.37 ! [N: nat] : ( ord_less_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % buildup_build_time
% 5.17/5.37 thf(fact_1101_zdvd__mono,axiom,
% 5.17/5.37 ! [K: int,M: int,T: int] :
% 5.17/5.37 ( ( K != zero_zero_int )
% 5.17/5.37 => ( ( dvd_dvd_int @ M @ T )
% 5.17/5.37 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zdvd_mono
% 5.17/5.37 thf(fact_1102_zero__le__power__eq__numeral,axiom,
% 5.17/5.37 ! [A: rat,W: num] :
% 5.17/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.17/5.37 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_le_power_eq_numeral
% 5.17/5.37 thf(fact_1103_zero__le__power__eq__numeral,axiom,
% 5.17/5.37 ! [A: int,W: num] :
% 5.17/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.17/5.37 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_le_power_eq_numeral
% 5.17/5.37 thf(fact_1104_zero__le__power__eq__numeral,axiom,
% 5.17/5.37 ! [A: real,W: num] :
% 5.17/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.17/5.37 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_le_power_eq_numeral
% 5.17/5.37 thf(fact_1105_gcd__nat_Oextremum,axiom,
% 5.17/5.37 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.17/5.37
% 5.17/5.37 % gcd_nat.extremum
% 5.17/5.37 thf(fact_1106_gcd__nat_Oextremum__strict,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.17/5.37 & ( zero_zero_nat != A ) ) ).
% 5.17/5.37
% 5.17/5.37 % gcd_nat.extremum_strict
% 5.17/5.37 thf(fact_1107_gcd__nat_Oextremum__unique,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.17/5.37 = ( A = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % gcd_nat.extremum_unique
% 5.17/5.37 thf(fact_1108_gcd__nat_Onot__eq__extremum,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( A != zero_zero_nat )
% 5.17/5.37 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 5.17/5.37 & ( A != zero_zero_nat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % gcd_nat.not_eq_extremum
% 5.17/5.37 thf(fact_1109_gcd__nat_Oextremum__uniqueI,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.17/5.37 => ( A = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % gcd_nat.extremum_uniqueI
% 5.17/5.37 thf(fact_1110_idiff__0,axiom,
% 5.17/5.37 ! [N: extended_enat] :
% 5.17/5.37 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.17/5.37 = zero_z5237406670263579293d_enat ) ).
% 5.17/5.37
% 5.17/5.37 % idiff_0
% 5.17/5.37 thf(fact_1111_idiff__0__right,axiom,
% 5.17/5.37 ! [N: extended_enat] :
% 5.17/5.37 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.17/5.37 = N ) ).
% 5.17/5.37
% 5.17/5.37 % idiff_0_right
% 5.17/5.37 thf(fact_1112_not__gr__zero,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.17/5.37 = ( N = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % not_gr_zero
% 5.17/5.37 thf(fact_1113_numeral__less__iff,axiom,
% 5.17/5.37 ! [M: num,N: num] :
% 5.17/5.37 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.37 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_less_iff
% 5.17/5.37 thf(fact_1114_numeral__less__iff,axiom,
% 5.17/5.37 ! [M: num,N: num] :
% 5.17/5.37 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.37 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_less_iff
% 5.17/5.37 thf(fact_1115_numeral__less__iff,axiom,
% 5.17/5.37 ! [M: num,N: num] :
% 5.17/5.37 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.37 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_less_iff
% 5.17/5.37 thf(fact_1116_numeral__less__iff,axiom,
% 5.17/5.37 ! [M: num,N: num] :
% 5.17/5.37 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.37 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_less_iff
% 5.17/5.37 thf(fact_1117_mult_Oright__neutral,axiom,
% 5.17/5.37 ! [A: complex] :
% 5.17/5.37 ( ( times_times_complex @ A @ one_one_complex )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult.right_neutral
% 5.17/5.37 thf(fact_1118_mult_Oright__neutral,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( times_times_real @ A @ one_one_real )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult.right_neutral
% 5.17/5.37 thf(fact_1119_mult_Oright__neutral,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( times_times_rat @ A @ one_one_rat )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult.right_neutral
% 5.17/5.37 thf(fact_1120_mult_Oright__neutral,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( times_times_nat @ A @ one_one_nat )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult.right_neutral
% 5.17/5.37 thf(fact_1121_mult_Oright__neutral,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( times_times_int @ A @ one_one_int )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult.right_neutral
% 5.17/5.37 thf(fact_1122_mult__1,axiom,
% 5.17/5.37 ! [A: complex] :
% 5.17/5.37 ( ( times_times_complex @ one_one_complex @ A )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult_1
% 5.17/5.37 thf(fact_1123_mult__1,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( times_times_real @ one_one_real @ A )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult_1
% 5.17/5.37 thf(fact_1124_mult__1,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( times_times_rat @ one_one_rat @ A )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult_1
% 5.17/5.37 thf(fact_1125_mult__1,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( times_times_nat @ one_one_nat @ A )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult_1
% 5.17/5.37 thf(fact_1126_mult__1,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( times_times_int @ one_one_int @ A )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % mult_1
% 5.17/5.37 thf(fact_1127_div__by__1,axiom,
% 5.17/5.37 ! [A: complex] :
% 5.17/5.37 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % div_by_1
% 5.17/5.37 thf(fact_1128_div__by__1,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( divide_divide_real @ A @ one_one_real )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % div_by_1
% 5.17/5.37 thf(fact_1129_div__by__1,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % div_by_1
% 5.17/5.37 thf(fact_1130_div__by__1,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % div_by_1
% 5.17/5.37 thf(fact_1131_div__by__1,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( divide_divide_int @ A @ one_one_int )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % div_by_1
% 5.17/5.37 thf(fact_1132_bits__div__by__1,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % bits_div_by_1
% 5.17/5.37 thf(fact_1133_bits__div__by__1,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( divide_divide_int @ A @ one_one_int )
% 5.17/5.37 = A ) ).
% 5.17/5.37
% 5.17/5.37 % bits_div_by_1
% 5.17/5.37 thf(fact_1134_lessI,axiom,
% 5.17/5.37 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % lessI
% 5.17/5.37 thf(fact_1135_Suc__mono,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ M @ N )
% 5.17/5.37 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Suc_mono
% 5.17/5.37 thf(fact_1136_Suc__less__eq,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.17/5.37 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % Suc_less_eq
% 5.17/5.37 thf(fact_1137_bot__nat__0_Onot__eq__extremum,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( A != zero_zero_nat )
% 5.17/5.37 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % bot_nat_0.not_eq_extremum
% 5.17/5.37 thf(fact_1138_neq0__conv,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( N != zero_zero_nat )
% 5.17/5.37 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % neq0_conv
% 5.17/5.37 thf(fact_1139_less__nat__zero__code,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.17/5.37
% 5.17/5.37 % less_nat_zero_code
% 5.17/5.37 thf(fact_1140_nat__mult__eq__1__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ( times_times_nat @ M @ N )
% 5.17/5.37 = one_one_nat )
% 5.17/5.37 = ( ( M = one_one_nat )
% 5.17/5.37 & ( N = one_one_nat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_mult_eq_1_iff
% 5.17/5.37 thf(fact_1141_nat__1__eq__mult__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( one_one_nat
% 5.17/5.37 = ( times_times_nat @ M @ N ) )
% 5.17/5.37 = ( ( M = one_one_nat )
% 5.17/5.37 & ( N = one_one_nat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_1_eq_mult_iff
% 5.17/5.37 thf(fact_1142_nat__dvd__1__iff__1,axiom,
% 5.17/5.37 ! [M: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.17/5.37 = ( M = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_dvd_1_iff_1
% 5.17/5.37 thf(fact_1143_diff__gt__0__iff__gt,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.17/5.37 = ( ord_less_real @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % diff_gt_0_iff_gt
% 5.17/5.37 thf(fact_1144_diff__gt__0__iff__gt,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.17/5.37 = ( ord_less_rat @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % diff_gt_0_iff_gt
% 5.17/5.37 thf(fact_1145_diff__gt__0__iff__gt,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.17/5.37 = ( ord_less_int @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % diff_gt_0_iff_gt
% 5.17/5.37 thf(fact_1146_mult__cancel__left1,axiom,
% 5.17/5.37 ! [C: complex,B: complex] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_complex @ C @ B ) )
% 5.17/5.37 = ( ( C = zero_zero_complex )
% 5.17/5.37 | ( B = one_one_complex ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left1
% 5.17/5.37 thf(fact_1147_mult__cancel__left1,axiom,
% 5.17/5.37 ! [C: real,B: real] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_real @ C @ B ) )
% 5.17/5.37 = ( ( C = zero_zero_real )
% 5.17/5.37 | ( B = one_one_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left1
% 5.17/5.37 thf(fact_1148_mult__cancel__left1,axiom,
% 5.17/5.37 ! [C: rat,B: rat] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_rat @ C @ B ) )
% 5.17/5.37 = ( ( C = zero_zero_rat )
% 5.17/5.37 | ( B = one_one_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left1
% 5.17/5.37 thf(fact_1149_mult__cancel__left1,axiom,
% 5.17/5.37 ! [C: int,B: int] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_int @ C @ B ) )
% 5.17/5.37 = ( ( C = zero_zero_int )
% 5.17/5.37 | ( B = one_one_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left1
% 5.17/5.37 thf(fact_1150_mult__cancel__left2,axiom,
% 5.17/5.37 ! [C: complex,A: complex] :
% 5.17/5.37 ( ( ( times_times_complex @ C @ A )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_complex )
% 5.17/5.37 | ( A = one_one_complex ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left2
% 5.17/5.37 thf(fact_1151_mult__cancel__left2,axiom,
% 5.17/5.37 ! [C: real,A: real] :
% 5.17/5.37 ( ( ( times_times_real @ C @ A )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_real )
% 5.17/5.37 | ( A = one_one_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left2
% 5.17/5.37 thf(fact_1152_mult__cancel__left2,axiom,
% 5.17/5.37 ! [C: rat,A: rat] :
% 5.17/5.37 ( ( ( times_times_rat @ C @ A )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_rat )
% 5.17/5.37 | ( A = one_one_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left2
% 5.17/5.37 thf(fact_1153_mult__cancel__left2,axiom,
% 5.17/5.37 ! [C: int,A: int] :
% 5.17/5.37 ( ( ( times_times_int @ C @ A )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_int )
% 5.17/5.37 | ( A = one_one_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_left2
% 5.17/5.37 thf(fact_1154_mult__cancel__right1,axiom,
% 5.17/5.37 ! [C: complex,B: complex] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_complex @ B @ C ) )
% 5.17/5.37 = ( ( C = zero_zero_complex )
% 5.17/5.37 | ( B = one_one_complex ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right1
% 5.17/5.37 thf(fact_1155_mult__cancel__right1,axiom,
% 5.17/5.37 ! [C: real,B: real] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_real @ B @ C ) )
% 5.17/5.37 = ( ( C = zero_zero_real )
% 5.17/5.37 | ( B = one_one_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right1
% 5.17/5.37 thf(fact_1156_mult__cancel__right1,axiom,
% 5.17/5.37 ! [C: rat,B: rat] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_rat @ B @ C ) )
% 5.17/5.37 = ( ( C = zero_zero_rat )
% 5.17/5.37 | ( B = one_one_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right1
% 5.17/5.37 thf(fact_1157_mult__cancel__right1,axiom,
% 5.17/5.37 ! [C: int,B: int] :
% 5.17/5.37 ( ( C
% 5.17/5.37 = ( times_times_int @ B @ C ) )
% 5.17/5.37 = ( ( C = zero_zero_int )
% 5.17/5.37 | ( B = one_one_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right1
% 5.17/5.37 thf(fact_1158_mult__cancel__right2,axiom,
% 5.17/5.37 ! [A: complex,C: complex] :
% 5.17/5.37 ( ( ( times_times_complex @ A @ C )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_complex )
% 5.17/5.37 | ( A = one_one_complex ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right2
% 5.17/5.37 thf(fact_1159_mult__cancel__right2,axiom,
% 5.17/5.37 ! [A: real,C: real] :
% 5.17/5.37 ( ( ( times_times_real @ A @ C )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_real )
% 5.17/5.37 | ( A = one_one_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right2
% 5.17/5.37 thf(fact_1160_mult__cancel__right2,axiom,
% 5.17/5.37 ! [A: rat,C: rat] :
% 5.17/5.37 ( ( ( times_times_rat @ A @ C )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_rat )
% 5.17/5.37 | ( A = one_one_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right2
% 5.17/5.37 thf(fact_1161_mult__cancel__right2,axiom,
% 5.17/5.37 ! [A: int,C: int] :
% 5.17/5.37 ( ( ( times_times_int @ A @ C )
% 5.17/5.37 = C )
% 5.17/5.37 = ( ( C = zero_zero_int )
% 5.17/5.37 | ( A = one_one_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_cancel_right2
% 5.17/5.37 thf(fact_1162_diff__numeral__special_I9_J,axiom,
% 5.17/5.37 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.17/5.37 = zero_zero_complex ) ).
% 5.17/5.37
% 5.17/5.37 % diff_numeral_special(9)
% 5.17/5.37 thf(fact_1163_diff__numeral__special_I9_J,axiom,
% 5.17/5.37 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.17/5.37 = zero_zero_real ) ).
% 5.17/5.37
% 5.17/5.37 % diff_numeral_special(9)
% 5.17/5.37 thf(fact_1164_diff__numeral__special_I9_J,axiom,
% 5.17/5.37 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.17/5.37 = zero_zero_rat ) ).
% 5.17/5.37
% 5.17/5.37 % diff_numeral_special(9)
% 5.17/5.37 thf(fact_1165_diff__numeral__special_I9_J,axiom,
% 5.17/5.37 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.17/5.37 = zero_zero_int ) ).
% 5.17/5.37
% 5.17/5.37 % diff_numeral_special(9)
% 5.17/5.37 thf(fact_1166_div__self,axiom,
% 5.17/5.37 ! [A: complex] :
% 5.17/5.37 ( ( A != zero_zero_complex )
% 5.17/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.17/5.37 = one_one_complex ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_self
% 5.17/5.37 thf(fact_1167_div__self,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( A != zero_zero_real )
% 5.17/5.37 => ( ( divide_divide_real @ A @ A )
% 5.17/5.37 = one_one_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_self
% 5.17/5.37 thf(fact_1168_div__self,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( A != zero_zero_rat )
% 5.17/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.17/5.37 = one_one_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_self
% 5.17/5.37 thf(fact_1169_div__self,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( A != zero_zero_nat )
% 5.17/5.37 => ( ( divide_divide_nat @ A @ A )
% 5.17/5.37 = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_self
% 5.17/5.37 thf(fact_1170_div__self,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( A != zero_zero_int )
% 5.17/5.37 => ( ( divide_divide_int @ A @ A )
% 5.17/5.37 = one_one_int ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_self
% 5.17/5.37 thf(fact_1171_divide__eq__1__iff,axiom,
% 5.17/5.37 ! [A: complex,B: complex] :
% 5.17/5.37 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.17/5.37 = one_one_complex )
% 5.17/5.37 = ( ( B != zero_zero_complex )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_eq_1_iff
% 5.17/5.37 thf(fact_1172_divide__eq__1__iff,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ( divide_divide_real @ A @ B )
% 5.17/5.37 = one_one_real )
% 5.17/5.37 = ( ( B != zero_zero_real )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_eq_1_iff
% 5.17/5.37 thf(fact_1173_divide__eq__1__iff,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ( divide_divide_rat @ A @ B )
% 5.17/5.37 = one_one_rat )
% 5.17/5.37 = ( ( B != zero_zero_rat )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_eq_1_iff
% 5.17/5.37 thf(fact_1174_one__eq__divide__iff,axiom,
% 5.17/5.37 ! [A: complex,B: complex] :
% 5.17/5.37 ( ( one_one_complex
% 5.17/5.37 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.37 = ( ( B != zero_zero_complex )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_divide_iff
% 5.17/5.37 thf(fact_1175_one__eq__divide__iff,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( one_one_real
% 5.17/5.37 = ( divide_divide_real @ A @ B ) )
% 5.17/5.37 = ( ( B != zero_zero_real )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_divide_iff
% 5.17/5.37 thf(fact_1176_one__eq__divide__iff,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( one_one_rat
% 5.17/5.37 = ( divide_divide_rat @ A @ B ) )
% 5.17/5.37 = ( ( B != zero_zero_rat )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_divide_iff
% 5.17/5.37 thf(fact_1177_divide__self,axiom,
% 5.17/5.37 ! [A: complex] :
% 5.17/5.37 ( ( A != zero_zero_complex )
% 5.17/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.17/5.37 = one_one_complex ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_self
% 5.17/5.37 thf(fact_1178_divide__self,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( A != zero_zero_real )
% 5.17/5.37 => ( ( divide_divide_real @ A @ A )
% 5.17/5.37 = one_one_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_self
% 5.17/5.37 thf(fact_1179_divide__self,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( A != zero_zero_rat )
% 5.17/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.17/5.37 = one_one_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_self
% 5.17/5.37 thf(fact_1180_divide__self__if,axiom,
% 5.17/5.37 ! [A: complex] :
% 5.17/5.37 ( ( ( A = zero_zero_complex )
% 5.17/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.17/5.37 = zero_zero_complex ) )
% 5.17/5.37 & ( ( A != zero_zero_complex )
% 5.17/5.37 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.17/5.37 = one_one_complex ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_self_if
% 5.17/5.37 thf(fact_1181_divide__self__if,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( ( A = zero_zero_real )
% 5.17/5.37 => ( ( divide_divide_real @ A @ A )
% 5.17/5.37 = zero_zero_real ) )
% 5.17/5.37 & ( ( A != zero_zero_real )
% 5.17/5.37 => ( ( divide_divide_real @ A @ A )
% 5.17/5.37 = one_one_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_self_if
% 5.17/5.37 thf(fact_1182_divide__self__if,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( ( A = zero_zero_rat )
% 5.17/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.17/5.37 = zero_zero_rat ) )
% 5.17/5.37 & ( ( A != zero_zero_rat )
% 5.17/5.37 => ( ( divide_divide_rat @ A @ A )
% 5.17/5.37 = one_one_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_self_if
% 5.17/5.37 thf(fact_1183_divide__eq__eq__1,axiom,
% 5.17/5.37 ! [B: real,A: real] :
% 5.17/5.37 ( ( ( divide_divide_real @ B @ A )
% 5.17/5.37 = one_one_real )
% 5.17/5.37 = ( ( A != zero_zero_real )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_eq_eq_1
% 5.17/5.37 thf(fact_1184_divide__eq__eq__1,axiom,
% 5.17/5.37 ! [B: rat,A: rat] :
% 5.17/5.37 ( ( ( divide_divide_rat @ B @ A )
% 5.17/5.37 = one_one_rat )
% 5.17/5.37 = ( ( A != zero_zero_rat )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_eq_eq_1
% 5.17/5.37 thf(fact_1185_eq__divide__eq__1,axiom,
% 5.17/5.37 ! [B: real,A: real] :
% 5.17/5.37 ( ( one_one_real
% 5.17/5.37 = ( divide_divide_real @ B @ A ) )
% 5.17/5.37 = ( ( A != zero_zero_real )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % eq_divide_eq_1
% 5.17/5.37 thf(fact_1186_eq__divide__eq__1,axiom,
% 5.17/5.37 ! [B: rat,A: rat] :
% 5.17/5.37 ( ( one_one_rat
% 5.17/5.37 = ( divide_divide_rat @ B @ A ) )
% 5.17/5.37 = ( ( A != zero_zero_rat )
% 5.17/5.37 & ( A = B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % eq_divide_eq_1
% 5.17/5.37 thf(fact_1187_one__divide__eq__0__iff,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.17/5.37 = zero_zero_real )
% 5.17/5.37 = ( A = zero_zero_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_divide_eq_0_iff
% 5.17/5.37 thf(fact_1188_one__divide__eq__0__iff,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.17/5.37 = zero_zero_rat )
% 5.17/5.37 = ( A = zero_zero_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_divide_eq_0_iff
% 5.17/5.37 thf(fact_1189_zero__eq__1__divide__iff,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( zero_zero_real
% 5.17/5.37 = ( divide_divide_real @ one_one_real @ A ) )
% 5.17/5.37 = ( A = zero_zero_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_eq_1_divide_iff
% 5.17/5.37 thf(fact_1190_zero__eq__1__divide__iff,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( zero_zero_rat
% 5.17/5.37 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.17/5.37 = ( A = zero_zero_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_eq_1_divide_iff
% 5.17/5.37 thf(fact_1191_numeral__eq__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ( numera6690914467698888265omplex @ N )
% 5.17/5.37 = one_one_complex )
% 5.17/5.37 = ( N = one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_eq_one_iff
% 5.17/5.37 thf(fact_1192_numeral__eq__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ( numeral_numeral_real @ N )
% 5.17/5.37 = one_one_real )
% 5.17/5.37 = ( N = one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_eq_one_iff
% 5.17/5.37 thf(fact_1193_numeral__eq__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ( numeral_numeral_rat @ N )
% 5.17/5.37 = one_one_rat )
% 5.17/5.37 = ( N = one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_eq_one_iff
% 5.17/5.37 thf(fact_1194_numeral__eq__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ( numeral_numeral_nat @ N )
% 5.17/5.37 = one_one_nat )
% 5.17/5.37 = ( N = one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_eq_one_iff
% 5.17/5.37 thf(fact_1195_numeral__eq__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ( numeral_numeral_int @ N )
% 5.17/5.37 = one_one_int )
% 5.17/5.37 = ( N = one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_eq_one_iff
% 5.17/5.37 thf(fact_1196_one__eq__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( one_one_complex
% 5.17/5.37 = ( numera6690914467698888265omplex @ N ) )
% 5.17/5.37 = ( one = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_numeral_iff
% 5.17/5.37 thf(fact_1197_one__eq__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( one_one_real
% 5.17/5.37 = ( numeral_numeral_real @ N ) )
% 5.17/5.37 = ( one = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_numeral_iff
% 5.17/5.37 thf(fact_1198_one__eq__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( one_one_rat
% 5.17/5.37 = ( numeral_numeral_rat @ N ) )
% 5.17/5.37 = ( one = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_numeral_iff
% 5.17/5.37 thf(fact_1199_one__eq__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( one_one_nat
% 5.17/5.37 = ( numeral_numeral_nat @ N ) )
% 5.17/5.37 = ( one = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_numeral_iff
% 5.17/5.37 thf(fact_1200_one__eq__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( one_one_int
% 5.17/5.37 = ( numeral_numeral_int @ N ) )
% 5.17/5.37 = ( one = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_eq_numeral_iff
% 5.17/5.37 thf(fact_1201_unit__prod,axiom,
% 5.17/5.37 ! [A: code_integer,B: code_integer] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.37 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_prod
% 5.17/5.37 thf(fact_1202_unit__prod,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.37 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_prod
% 5.17/5.37 thf(fact_1203_unit__prod,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.37 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_prod
% 5.17/5.37 thf(fact_1204_unit__div,axiom,
% 5.17/5.37 ! [A: code_integer,B: code_integer] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.37 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.37 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div
% 5.17/5.37 thf(fact_1205_unit__div,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.37 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.37 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div
% 5.17/5.37 thf(fact_1206_unit__div,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.37 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.37 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div
% 5.17/5.37 thf(fact_1207_unit__div__1__unit,axiom,
% 5.17/5.37 ! [A: code_integer] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.37 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_1_unit
% 5.17/5.37 thf(fact_1208_unit__div__1__unit,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.37 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_1_unit
% 5.17/5.37 thf(fact_1209_unit__div__1__unit,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.37 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_1_unit
% 5.17/5.37 thf(fact_1210_unit__div__1__div__1,axiom,
% 5.17/5.37 ! [A: code_integer] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.37 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.17/5.37 = A ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_1_div_1
% 5.17/5.37 thf(fact_1211_unit__div__1__div__1,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.37 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.17/5.37 = A ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_1_div_1
% 5.17/5.37 thf(fact_1212_unit__div__1__div__1,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.37 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.17/5.37 = A ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_1_div_1
% 5.17/5.37 thf(fact_1213_of__nat__less__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.37 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_less_iff
% 5.17/5.37 thf(fact_1214_of__nat__less__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.37 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_less_iff
% 5.17/5.37 thf(fact_1215_of__nat__less__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.37 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_less_iff
% 5.17/5.37 thf(fact_1216_of__nat__less__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.37 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_less_iff
% 5.17/5.37 thf(fact_1217_zero__less__Suc,axiom,
% 5.17/5.37 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_Suc
% 5.17/5.37 thf(fact_1218_less__Suc0,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.37 = ( N = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_Suc0
% 5.17/5.37 thf(fact_1219_zero__less__diff,axiom,
% 5.17/5.37 ! [N: nat,M: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.37 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_diff
% 5.17/5.37 thf(fact_1220_nat__mult__less__cancel__disj,axiom,
% 5.17/5.37 ! [K: nat,M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.37 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_mult_less_cancel_disj
% 5.17/5.37 thf(fact_1221_nat__0__less__mult__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.37 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_0_less_mult_iff
% 5.17/5.37 thf(fact_1222_mult__less__cancel2,axiom,
% 5.17/5.37 ! [M: nat,K: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.37 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_less_cancel2
% 5.17/5.37 thf(fact_1223_of__nat__eq__1__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ( semiri8010041392384452111omplex @ N )
% 5.17/5.37 = one_one_complex )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_eq_1_iff
% 5.17/5.37 thf(fact_1224_of__nat__eq__1__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ( semiri5074537144036343181t_real @ N )
% 5.17/5.37 = one_one_real )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_eq_1_iff
% 5.17/5.37 thf(fact_1225_of__nat__eq__1__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ( semiri681578069525770553at_rat @ N )
% 5.17/5.37 = one_one_rat )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_eq_1_iff
% 5.17/5.37 thf(fact_1226_of__nat__eq__1__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.17/5.37 = one_one_nat )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_eq_1_iff
% 5.17/5.37 thf(fact_1227_of__nat__eq__1__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ( semiri1314217659103216013at_int @ N )
% 5.17/5.37 = one_one_int )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_eq_1_iff
% 5.17/5.37 thf(fact_1228_of__nat__1__eq__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( one_one_complex
% 5.17/5.37 = ( semiri8010041392384452111omplex @ N ) )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1_eq_iff
% 5.17/5.37 thf(fact_1229_of__nat__1__eq__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( one_one_real
% 5.17/5.37 = ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1_eq_iff
% 5.17/5.37 thf(fact_1230_of__nat__1__eq__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( one_one_rat
% 5.17/5.37 = ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1_eq_iff
% 5.17/5.37 thf(fact_1231_of__nat__1__eq__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( one_one_nat
% 5.17/5.37 = ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1_eq_iff
% 5.17/5.37 thf(fact_1232_of__nat__1__eq__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( one_one_int
% 5.17/5.37 = ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.37 = ( N = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1_eq_iff
% 5.17/5.37 thf(fact_1233_of__nat__1,axiom,
% 5.17/5.37 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.17/5.37 = one_one_complex ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1
% 5.17/5.37 thf(fact_1234_of__nat__1,axiom,
% 5.17/5.37 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.17/5.37 = one_one_real ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1
% 5.17/5.37 thf(fact_1235_of__nat__1,axiom,
% 5.17/5.37 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.17/5.37 = one_one_rat ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1
% 5.17/5.37 thf(fact_1236_of__nat__1,axiom,
% 5.17/5.37 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.17/5.37 = one_one_nat ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1
% 5.17/5.37 thf(fact_1237_of__nat__1,axiom,
% 5.17/5.37 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.17/5.37 = one_one_int ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_1
% 5.17/5.37 thf(fact_1238_less__one,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ N @ one_one_nat )
% 5.17/5.37 = ( N = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_one
% 5.17/5.37 thf(fact_1239_div__less,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ M @ N )
% 5.17/5.37 => ( ( divide_divide_nat @ M @ N )
% 5.17/5.37 = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_less
% 5.17/5.37 thf(fact_1240_diff__Suc__1,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.17/5.37 = N ) ).
% 5.17/5.37
% 5.17/5.37 % diff_Suc_1
% 5.17/5.37 thf(fact_1241_divide__le__0__1__iff,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.17/5.37 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_le_0_1_iff
% 5.17/5.37 thf(fact_1242_divide__le__0__1__iff,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.17/5.37 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_le_0_1_iff
% 5.17/5.37 thf(fact_1243_zero__le__divide__1__iff,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.17/5.37 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_le_divide_1_iff
% 5.17/5.37 thf(fact_1244_zero__le__divide__1__iff,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.17/5.37 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_le_divide_1_iff
% 5.17/5.37 thf(fact_1245_zero__less__divide__1__iff,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.17/5.37 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_divide_1_iff
% 5.17/5.37 thf(fact_1246_zero__less__divide__1__iff,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.17/5.37 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_divide_1_iff
% 5.17/5.37 thf(fact_1247_less__divide__eq__1__pos,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.37 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.17/5.37 = ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_divide_eq_1_pos
% 5.17/5.37 thf(fact_1248_less__divide__eq__1__pos,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.37 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.17/5.37 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_divide_eq_1_pos
% 5.17/5.37 thf(fact_1249_less__divide__eq__1__neg,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.37 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.17/5.37 = ( ord_less_real @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_divide_eq_1_neg
% 5.17/5.37 thf(fact_1250_less__divide__eq__1__neg,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.37 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.17/5.37 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_divide_eq_1_neg
% 5.17/5.37 thf(fact_1251_divide__less__eq__1__pos,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.37 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.17/5.37 = ( ord_less_real @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_eq_1_pos
% 5.17/5.37 thf(fact_1252_divide__less__eq__1__pos,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.37 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.17/5.37 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_eq_1_pos
% 5.17/5.37 thf(fact_1253_divide__less__eq__1__neg,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.37 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.17/5.37 = ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_eq_1_neg
% 5.17/5.37 thf(fact_1254_divide__less__eq__1__neg,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.37 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.17/5.37 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_eq_1_neg
% 5.17/5.37 thf(fact_1255_divide__less__0__1__iff,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.17/5.37 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_0_1_iff
% 5.17/5.37 thf(fact_1256_divide__less__0__1__iff,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.17/5.37 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_0_1_iff
% 5.17/5.37 thf(fact_1257_one__less__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.17/5.37 = ( ord_less_num @ one @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_less_numeral_iff
% 5.17/5.37 thf(fact_1258_one__less__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.17/5.37 = ( ord_less_num @ one @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_less_numeral_iff
% 5.17/5.37 thf(fact_1259_one__less__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.17/5.37 = ( ord_less_num @ one @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_less_numeral_iff
% 5.17/5.37 thf(fact_1260_one__less__numeral__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.17/5.37 = ( ord_less_num @ one @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_less_numeral_iff
% 5.17/5.37 thf(fact_1261_divide__less__eq__numeral1_I1_J,axiom,
% 5.17/5.37 ! [B: real,W: num,A: real] :
% 5.17/5.37 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.17/5.37 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_eq_numeral1(1)
% 5.17/5.37 thf(fact_1262_divide__less__eq__numeral1_I1_J,axiom,
% 5.17/5.37 ! [B: rat,W: num,A: rat] :
% 5.17/5.37 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.17/5.37 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_less_eq_numeral1(1)
% 5.17/5.37 thf(fact_1263_less__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.37 ! [A: real,B: real,W: num] :
% 5.17/5.37 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.37 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_divide_eq_numeral1(1)
% 5.17/5.37 thf(fact_1264_less__divide__eq__numeral1_I1_J,axiom,
% 5.17/5.37 ! [A: rat,B: rat,W: num] :
% 5.17/5.37 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.37 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_divide_eq_numeral1(1)
% 5.17/5.37 thf(fact_1265_nonzero__divide__mult__cancel__left,axiom,
% 5.17/5.37 ! [A: complex,B: complex] :
% 5.17/5.37 ( ( A != zero_zero_complex )
% 5.17/5.37 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.17/5.37 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nonzero_divide_mult_cancel_left
% 5.17/5.37 thf(fact_1266_nonzero__divide__mult__cancel__left,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( A != zero_zero_real )
% 5.17/5.37 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.17/5.37 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nonzero_divide_mult_cancel_left
% 5.17/5.37 thf(fact_1267_nonzero__divide__mult__cancel__left,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( A != zero_zero_rat )
% 5.17/5.37 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.17/5.37 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nonzero_divide_mult_cancel_left
% 5.17/5.37 thf(fact_1268_nonzero__divide__mult__cancel__right,axiom,
% 5.17/5.37 ! [B: complex,A: complex] :
% 5.17/5.37 ( ( B != zero_zero_complex )
% 5.17/5.37 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.17/5.37 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nonzero_divide_mult_cancel_right
% 5.17/5.37 thf(fact_1269_nonzero__divide__mult__cancel__right,axiom,
% 5.17/5.37 ! [B: real,A: real] :
% 5.17/5.37 ( ( B != zero_zero_real )
% 5.17/5.37 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.17/5.37 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nonzero_divide_mult_cancel_right
% 5.17/5.37 thf(fact_1270_nonzero__divide__mult__cancel__right,axiom,
% 5.17/5.37 ! [B: rat,A: rat] :
% 5.17/5.37 ( ( B != zero_zero_rat )
% 5.17/5.37 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.17/5.37 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nonzero_divide_mult_cancel_right
% 5.17/5.37 thf(fact_1271_unit__mult__div__div,axiom,
% 5.17/5.37 ! [A: code_integer,B: code_integer] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.37 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.17/5.37 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_mult_div_div
% 5.17/5.37 thf(fact_1272_unit__mult__div__div,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.37 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.17/5.37 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_mult_div_div
% 5.17/5.37 thf(fact_1273_unit__mult__div__div,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.37 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.17/5.37 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_mult_div_div
% 5.17/5.37 thf(fact_1274_unit__div__mult__self,axiom,
% 5.17/5.37 ! [A: code_integer,B: code_integer] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.37 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.17/5.37 = B ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_mult_self
% 5.17/5.37 thf(fact_1275_unit__div__mult__self,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.37 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.17/5.37 = B ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_mult_self
% 5.17/5.37 thf(fact_1276_unit__div__mult__self,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.37 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.17/5.37 = B ) ) ).
% 5.17/5.37
% 5.17/5.37 % unit_div_mult_self
% 5.17/5.37 thf(fact_1277_pow__divides__pow__iff,axiom,
% 5.17/5.37 ! [N: nat,A: int,B: int] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.37 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.17/5.37 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % pow_divides_pow_iff
% 5.17/5.37 thf(fact_1278_pow__divides__pow__iff,axiom,
% 5.17/5.37 ! [N: nat,A: nat,B: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.37 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.17/5.37 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % pow_divides_pow_iff
% 5.17/5.37 thf(fact_1279_Suc__pred,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.37 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.17/5.37 = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % Suc_pred
% 5.17/5.37 thf(fact_1280_nat__mult__le__cancel__disj,axiom,
% 5.17/5.37 ! [K: nat,M: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.37 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_mult_le_cancel_disj
% 5.17/5.37 thf(fact_1281_mult__le__cancel2,axiom,
% 5.17/5.37 ! [M: nat,K: nat,N: nat] :
% 5.17/5.37 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.37 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % mult_le_cancel2
% 5.17/5.37 thf(fact_1282_div__mult__self1__is__m,axiom,
% 5.17/5.37 ! [N: nat,M: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.17/5.37 = M ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_mult_self1_is_m
% 5.17/5.37 thf(fact_1283_div__mult__self__is__m,axiom,
% 5.17/5.37 ! [N: nat,M: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.37 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.17/5.37 = M ) ) ).
% 5.17/5.37
% 5.17/5.37 % div_mult_self_is_m
% 5.17/5.37 thf(fact_1284_divide__le__eq__1__neg,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.37 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.17/5.37 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_le_eq_1_neg
% 5.17/5.37 thf(fact_1285_divide__le__eq__1__neg,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.37 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.17/5.37 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_le_eq_1_neg
% 5.17/5.37 thf(fact_1286_divide__le__eq__1__pos,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.37 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.17/5.37 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_le_eq_1_pos
% 5.17/5.37 thf(fact_1287_divide__le__eq__1__pos,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.37 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.17/5.37 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % divide_le_eq_1_pos
% 5.17/5.37 thf(fact_1288_le__divide__eq__1__neg,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.37 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.17/5.37 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % le_divide_eq_1_neg
% 5.17/5.37 thf(fact_1289_le__divide__eq__1__neg,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.37 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.17/5.37 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % le_divide_eq_1_neg
% 5.17/5.37 thf(fact_1290_le__divide__eq__1__pos,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.37 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.17/5.37 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % le_divide_eq_1_pos
% 5.17/5.37 thf(fact_1291_le__divide__eq__1__pos,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.37 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.17/5.37 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % le_divide_eq_1_pos
% 5.17/5.37 thf(fact_1292_of__nat__0__less__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.37 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_0_less_iff
% 5.17/5.37 thf(fact_1293_of__nat__0__less__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.37 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_0_less_iff
% 5.17/5.37 thf(fact_1294_of__nat__0__less__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.37 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_0_less_iff
% 5.17/5.37 thf(fact_1295_of__nat__0__less__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.37 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % of_nat_0_less_iff
% 5.17/5.37 thf(fact_1296_Suc__1,axiom,
% 5.17/5.37 ( ( suc @ one_one_nat )
% 5.17/5.37 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % Suc_1
% 5.17/5.37 thf(fact_1297_Suc__diff__1,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.37 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.17/5.37 = N ) ) ).
% 5.17/5.37
% 5.17/5.37 % Suc_diff_1
% 5.17/5.37 thf(fact_1298_numeral__le__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.17/5.37 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_le_one_iff
% 5.17/5.37 thf(fact_1299_numeral__le__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.17/5.37 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_le_one_iff
% 5.17/5.37 thf(fact_1300_numeral__le__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.17/5.37 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_le_one_iff
% 5.17/5.37 thf(fact_1301_numeral__le__one__iff,axiom,
% 5.17/5.37 ! [N: num] :
% 5.17/5.37 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.17/5.37 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.17/5.37
% 5.17/5.37 % numeral_le_one_iff
% 5.17/5.37 thf(fact_1302_one__div__two__eq__zero,axiom,
% 5.17/5.37 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.37 = zero_zero_nat ) ).
% 5.17/5.37
% 5.17/5.37 % one_div_two_eq_zero
% 5.17/5.37 thf(fact_1303_one__div__two__eq__zero,axiom,
% 5.17/5.37 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.37 = zero_zero_int ) ).
% 5.17/5.37
% 5.17/5.37 % one_div_two_eq_zero
% 5.17/5.37 thf(fact_1304_bits__1__div__2,axiom,
% 5.17/5.37 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.37 = zero_zero_nat ) ).
% 5.17/5.37
% 5.17/5.37 % bits_1_div_2
% 5.17/5.37 thf(fact_1305_bits__1__div__2,axiom,
% 5.17/5.37 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.37 = zero_zero_int ) ).
% 5.17/5.37
% 5.17/5.37 % bits_1_div_2
% 5.17/5.37 thf(fact_1306_even__power,axiom,
% 5.17/5.37 ! [A: code_integer,N: nat] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.17/5.37 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.37 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % even_power
% 5.17/5.37 thf(fact_1307_even__power,axiom,
% 5.17/5.37 ! [A: nat,N: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.17/5.37 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.37 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % even_power
% 5.17/5.37 thf(fact_1308_even__power,axiom,
% 5.17/5.37 ! [A: int,N: nat] :
% 5.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.17/5.37 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.37 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % even_power
% 5.17/5.37 thf(fact_1309_power__less__zero__eq,axiom,
% 5.17/5.37 ! [A: real,N: nat] :
% 5.17/5.37 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.37 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_less_zero_eq
% 5.17/5.37 thf(fact_1310_power__less__zero__eq,axiom,
% 5.17/5.37 ! [A: rat,N: nat] :
% 5.17/5.37 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.37 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_less_zero_eq
% 5.17/5.37 thf(fact_1311_power__less__zero__eq,axiom,
% 5.17/5.37 ! [A: int,N: nat] :
% 5.17/5.37 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.37 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_less_zero_eq
% 5.17/5.37 thf(fact_1312_power__less__zero__eq__numeral,axiom,
% 5.17/5.37 ! [A: real,W: num] :
% 5.17/5.37 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_less_zero_eq_numeral
% 5.17/5.37 thf(fact_1313_power__less__zero__eq__numeral,axiom,
% 5.17/5.37 ! [A: rat,W: num] :
% 5.17/5.37 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_less_zero_eq_numeral
% 5.17/5.37 thf(fact_1314_power__less__zero__eq__numeral,axiom,
% 5.17/5.37 ! [A: int,W: num] :
% 5.17/5.37 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.17/5.37 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_less_zero_eq_numeral
% 5.17/5.37 thf(fact_1315_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.17/5.37 = ( N = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % semiring_parity_class.even_mask_iff
% 5.17/5.37 thf(fact_1316_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.17/5.37 = ( N = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % semiring_parity_class.even_mask_iff
% 5.17/5.37 thf(fact_1317_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.17/5.37 = ( N = zero_zero_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % semiring_parity_class.even_mask_iff
% 5.17/5.37 thf(fact_1318_zero__less__power__eq__numeral,axiom,
% 5.17/5.37 ! [A: real,W: num] :
% 5.17/5.37 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.17/5.37 = ( ( ( numeral_numeral_nat @ W )
% 5.17/5.37 = zero_zero_nat )
% 5.17/5.37 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( A != zero_zero_real ) )
% 5.17/5.37 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_power_eq_numeral
% 5.17/5.37 thf(fact_1319_zero__less__power__eq__numeral,axiom,
% 5.17/5.37 ! [A: rat,W: num] :
% 5.17/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.17/5.37 = ( ( ( numeral_numeral_nat @ W )
% 5.17/5.37 = zero_zero_nat )
% 5.17/5.37 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( A != zero_zero_rat ) )
% 5.17/5.37 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_power_eq_numeral
% 5.17/5.37 thf(fact_1320_zero__less__power__eq__numeral,axiom,
% 5.17/5.37 ! [A: int,W: num] :
% 5.17/5.37 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.17/5.37 = ( ( ( numeral_numeral_nat @ W )
% 5.17/5.37 = zero_zero_nat )
% 5.17/5.37 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( A != zero_zero_int ) )
% 5.17/5.37 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % zero_less_power_eq_numeral
% 5.17/5.37 thf(fact_1321_power__le__zero__eq__numeral,axiom,
% 5.17/5.37 ! [A: rat,W: num] :
% 5.17/5.37 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.17/5.37 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_le_zero_eq_numeral
% 5.17/5.37 thf(fact_1322_power__le__zero__eq__numeral,axiom,
% 5.17/5.37 ! [A: int,W: num] :
% 5.17/5.37 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.17/5.37 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_le_zero_eq_numeral
% 5.17/5.37 thf(fact_1323_power__le__zero__eq__numeral,axiom,
% 5.17/5.37 ! [A: real,W: num] :
% 5.17/5.37 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.17/5.37 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.17/5.37 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.37 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % power_le_zero_eq_numeral
% 5.17/5.37 thf(fact_1324_minus__int__code_I1_J,axiom,
% 5.17/5.37 ! [K: int] :
% 5.17/5.37 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.17/5.37 = K ) ).
% 5.17/5.37
% 5.17/5.37 % minus_int_code(1)
% 5.17/5.37 thf(fact_1325_imult__is__0,axiom,
% 5.17/5.37 ! [M: extended_enat,N: extended_enat] :
% 5.17/5.37 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.17/5.37 = zero_z5237406670263579293d_enat )
% 5.17/5.37 = ( ( M = zero_z5237406670263579293d_enat )
% 5.17/5.37 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % imult_is_0
% 5.17/5.37 thf(fact_1326_one__reorient,axiom,
% 5.17/5.37 ! [X: complex] :
% 5.17/5.37 ( ( one_one_complex = X )
% 5.17/5.37 = ( X = one_one_complex ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_reorient
% 5.17/5.37 thf(fact_1327_one__reorient,axiom,
% 5.17/5.37 ! [X: real] :
% 5.17/5.37 ( ( one_one_real = X )
% 5.17/5.37 = ( X = one_one_real ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_reorient
% 5.17/5.37 thf(fact_1328_one__reorient,axiom,
% 5.17/5.37 ! [X: rat] :
% 5.17/5.37 ( ( one_one_rat = X )
% 5.17/5.37 = ( X = one_one_rat ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_reorient
% 5.17/5.37 thf(fact_1329_one__reorient,axiom,
% 5.17/5.37 ! [X: nat] :
% 5.17/5.37 ( ( one_one_nat = X )
% 5.17/5.37 = ( X = one_one_nat ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_reorient
% 5.17/5.37 thf(fact_1330_one__reorient,axiom,
% 5.17/5.37 ! [X: int] :
% 5.17/5.37 ( ( one_one_int = X )
% 5.17/5.37 = ( X = one_one_int ) ) ).
% 5.17/5.37
% 5.17/5.37 % one_reorient
% 5.17/5.37 thf(fact_1331_linordered__field__no__lb,axiom,
% 5.17/5.37 ! [X5: real] :
% 5.17/5.37 ? [Y: real] : ( ord_less_real @ Y @ X5 ) ).
% 5.17/5.37
% 5.17/5.37 % linordered_field_no_lb
% 5.17/5.37 thf(fact_1332_linordered__field__no__lb,axiom,
% 5.17/5.37 ! [X5: rat] :
% 5.17/5.37 ? [Y: rat] : ( ord_less_rat @ Y @ X5 ) ).
% 5.17/5.37
% 5.17/5.37 % linordered_field_no_lb
% 5.17/5.37 thf(fact_1333_linordered__field__no__ub,axiom,
% 5.17/5.37 ! [X5: real] :
% 5.17/5.37 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 5.17/5.37
% 5.17/5.37 % linordered_field_no_ub
% 5.17/5.37 thf(fact_1334_linordered__field__no__ub,axiom,
% 5.17/5.37 ! [X5: rat] :
% 5.17/5.37 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 5.17/5.37
% 5.17/5.37 % linordered_field_no_ub
% 5.17/5.37 thf(fact_1335_less__numeral__extra_I4_J,axiom,
% 5.17/5.37 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.17/5.37
% 5.17/5.37 % less_numeral_extra(4)
% 5.17/5.37 thf(fact_1336_less__numeral__extra_I4_J,axiom,
% 5.17/5.37 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.17/5.37
% 5.17/5.37 % less_numeral_extra(4)
% 5.17/5.37 thf(fact_1337_less__numeral__extra_I4_J,axiom,
% 5.17/5.37 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.17/5.37
% 5.17/5.37 % less_numeral_extra(4)
% 5.17/5.37 thf(fact_1338_less__numeral__extra_I4_J,axiom,
% 5.17/5.37 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.17/5.37
% 5.17/5.37 % less_numeral_extra(4)
% 5.17/5.37 thf(fact_1339_nat__neq__iff,axiom,
% 5.17/5.37 ! [M: nat,N: nat] :
% 5.17/5.37 ( ( M != N )
% 5.17/5.37 = ( ( ord_less_nat @ M @ N )
% 5.17/5.37 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_neq_iff
% 5.17/5.37 thf(fact_1340_less__not__refl,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ~ ( ord_less_nat @ N @ N ) ).
% 5.17/5.37
% 5.17/5.37 % less_not_refl
% 5.17/5.37 thf(fact_1341_less__not__refl2,axiom,
% 5.17/5.37 ! [N: nat,M: nat] :
% 5.17/5.37 ( ( ord_less_nat @ N @ M )
% 5.17/5.37 => ( M != N ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_not_refl2
% 5.17/5.37 thf(fact_1342_less__not__refl3,axiom,
% 5.17/5.37 ! [S2: nat,T: nat] :
% 5.17/5.37 ( ( ord_less_nat @ S2 @ T )
% 5.17/5.37 => ( S2 != T ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_not_refl3
% 5.17/5.37 thf(fact_1343_less__irrefl__nat,axiom,
% 5.17/5.37 ! [N: nat] :
% 5.17/5.37 ~ ( ord_less_nat @ N @ N ) ).
% 5.17/5.37
% 5.17/5.37 % less_irrefl_nat
% 5.17/5.37 thf(fact_1344_nat__less__induct,axiom,
% 5.17/5.37 ! [P: nat > $o,N: nat] :
% 5.17/5.37 ( ! [N2: nat] :
% 5.17/5.37 ( ! [M2: nat] :
% 5.17/5.37 ( ( ord_less_nat @ M2 @ N2 )
% 5.17/5.37 => ( P @ M2 ) )
% 5.17/5.37 => ( P @ N2 ) )
% 5.17/5.37 => ( P @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % nat_less_induct
% 5.17/5.37 thf(fact_1345_infinite__descent,axiom,
% 5.17/5.37 ! [P: nat > $o,N: nat] :
% 5.17/5.37 ( ! [N2: nat] :
% 5.17/5.37 ( ~ ( P @ N2 )
% 5.17/5.37 => ? [M2: nat] :
% 5.17/5.37 ( ( ord_less_nat @ M2 @ N2 )
% 5.17/5.37 & ~ ( P @ M2 ) ) )
% 5.17/5.37 => ( P @ N ) ) ).
% 5.17/5.37
% 5.17/5.37 % infinite_descent
% 5.17/5.37 thf(fact_1346_linorder__neqE__nat,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE_nat
% 5.17/5.37 thf(fact_1347_linorder__neqE__linordered__idom,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE_linordered_idom
% 5.17/5.37 thf(fact_1348_linorder__neqE__linordered__idom,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE_linordered_idom
% 5.17/5.37 thf(fact_1349_linorder__neqE__linordered__idom,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_int @ X @ Y4 )
% 5.17/5.37 => ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE_linordered_idom
% 5.17/5.37 thf(fact_1350_verit__comp__simplify1_I1_J,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ~ ( ord_less_real @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % verit_comp_simplify1(1)
% 5.17/5.37 thf(fact_1351_verit__comp__simplify1_I1_J,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ~ ( ord_less_rat @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % verit_comp_simplify1(1)
% 5.17/5.37 thf(fact_1352_verit__comp__simplify1_I1_J,axiom,
% 5.17/5.37 ! [A: num] :
% 5.17/5.37 ~ ( ord_less_num @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % verit_comp_simplify1(1)
% 5.17/5.37 thf(fact_1353_verit__comp__simplify1_I1_J,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ~ ( ord_less_nat @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % verit_comp_simplify1(1)
% 5.17/5.37 thf(fact_1354_verit__comp__simplify1_I1_J,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ~ ( ord_less_int @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % verit_comp_simplify1(1)
% 5.17/5.37 thf(fact_1355_lt__ex,axiom,
% 5.17/5.37 ! [X: real] :
% 5.17/5.37 ? [Y: real] : ( ord_less_real @ Y @ X ) ).
% 5.17/5.37
% 5.17/5.37 % lt_ex
% 5.17/5.37 thf(fact_1356_lt__ex,axiom,
% 5.17/5.37 ! [X: rat] :
% 5.17/5.37 ? [Y: rat] : ( ord_less_rat @ Y @ X ) ).
% 5.17/5.37
% 5.17/5.37 % lt_ex
% 5.17/5.37 thf(fact_1357_lt__ex,axiom,
% 5.17/5.37 ! [X: int] :
% 5.17/5.37 ? [Y: int] : ( ord_less_int @ Y @ X ) ).
% 5.17/5.37
% 5.17/5.37 % lt_ex
% 5.17/5.37 thf(fact_1358_gt__ex,axiom,
% 5.17/5.37 ! [X: real] :
% 5.17/5.37 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.17/5.37
% 5.17/5.37 % gt_ex
% 5.17/5.37 thf(fact_1359_gt__ex,axiom,
% 5.17/5.37 ! [X: rat] :
% 5.17/5.37 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.17/5.37
% 5.17/5.37 % gt_ex
% 5.17/5.37 thf(fact_1360_gt__ex,axiom,
% 5.17/5.37 ! [X: nat] :
% 5.17/5.37 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.17/5.37
% 5.17/5.37 % gt_ex
% 5.17/5.37 thf(fact_1361_gt__ex,axiom,
% 5.17/5.37 ! [X: int] :
% 5.17/5.37 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.17/5.37
% 5.17/5.37 % gt_ex
% 5.17/5.37 thf(fact_1362_dense,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ? [Z2: real] :
% 5.17/5.37 ( ( ord_less_real @ X @ Z2 )
% 5.17/5.37 & ( ord_less_real @ Z2 @ Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dense
% 5.17/5.37 thf(fact_1363_dense,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ? [Z2: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X @ Z2 )
% 5.17/5.37 & ( ord_less_rat @ Z2 @ Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dense
% 5.17/5.37 thf(fact_1364_less__imp__neq,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ( X != Y4 ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_imp_neq
% 5.17/5.37 thf(fact_1365_less__imp__neq,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ( X != Y4 ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_imp_neq
% 5.17/5.37 thf(fact_1366_less__imp__neq,axiom,
% 5.17/5.37 ! [X: num,Y4: num] :
% 5.17/5.37 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.37 => ( X != Y4 ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_imp_neq
% 5.17/5.37 thf(fact_1367_less__imp__neq,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 => ( X != Y4 ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_imp_neq
% 5.17/5.37 thf(fact_1368_less__imp__neq,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.37 => ( X != Y4 ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_imp_neq
% 5.17/5.37 thf(fact_1369_order_Oasym,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.asym
% 5.17/5.37 thf(fact_1370_order_Oasym,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.asym
% 5.17/5.37 thf(fact_1371_order_Oasym,axiom,
% 5.17/5.37 ! [A: num,B: num] :
% 5.17/5.37 ( ( ord_less_num @ A @ B )
% 5.17/5.37 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.asym
% 5.17/5.37 thf(fact_1372_order_Oasym,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( ord_less_nat @ A @ B )
% 5.17/5.37 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.asym
% 5.17/5.37 thf(fact_1373_order_Oasym,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( ord_less_int @ A @ B )
% 5.17/5.37 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.asym
% 5.17/5.37 thf(fact_1374_ord__eq__less__trans,axiom,
% 5.17/5.37 ! [A: real,B: real,C: real] :
% 5.17/5.37 ( ( A = B )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ord_less_real @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_trans
% 5.17/5.37 thf(fact_1375_ord__eq__less__trans,axiom,
% 5.17/5.37 ! [A: rat,B: rat,C: rat] :
% 5.17/5.37 ( ( A = B )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_trans
% 5.17/5.37 thf(fact_1376_ord__eq__less__trans,axiom,
% 5.17/5.37 ! [A: num,B: num,C: num] :
% 5.17/5.37 ( ( A = B )
% 5.17/5.37 => ( ( ord_less_num @ B @ C )
% 5.17/5.37 => ( ord_less_num @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_trans
% 5.17/5.37 thf(fact_1377_ord__eq__less__trans,axiom,
% 5.17/5.37 ! [A: nat,B: nat,C: nat] :
% 5.17/5.37 ( ( A = B )
% 5.17/5.37 => ( ( ord_less_nat @ B @ C )
% 5.17/5.37 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_trans
% 5.17/5.37 thf(fact_1378_ord__eq__less__trans,axiom,
% 5.17/5.37 ! [A: int,B: int,C: int] :
% 5.17/5.37 ( ( A = B )
% 5.17/5.37 => ( ( ord_less_int @ B @ C )
% 5.17/5.37 => ( ord_less_int @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_trans
% 5.17/5.37 thf(fact_1379_ord__less__eq__trans,axiom,
% 5.17/5.37 ! [A: real,B: real,C: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( B = C )
% 5.17/5.37 => ( ord_less_real @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_trans
% 5.17/5.37 thf(fact_1380_ord__less__eq__trans,axiom,
% 5.17/5.37 ! [A: rat,B: rat,C: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( B = C )
% 5.17/5.37 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_trans
% 5.17/5.37 thf(fact_1381_ord__less__eq__trans,axiom,
% 5.17/5.37 ! [A: num,B: num,C: num] :
% 5.17/5.37 ( ( ord_less_num @ A @ B )
% 5.17/5.37 => ( ( B = C )
% 5.17/5.37 => ( ord_less_num @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_trans
% 5.17/5.37 thf(fact_1382_ord__less__eq__trans,axiom,
% 5.17/5.37 ! [A: nat,B: nat,C: nat] :
% 5.17/5.37 ( ( ord_less_nat @ A @ B )
% 5.17/5.37 => ( ( B = C )
% 5.17/5.37 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_trans
% 5.17/5.37 thf(fact_1383_ord__less__eq__trans,axiom,
% 5.17/5.37 ! [A: int,B: int,C: int] :
% 5.17/5.37 ( ( ord_less_int @ A @ B )
% 5.17/5.37 => ( ( B = C )
% 5.17/5.37 => ( ord_less_int @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_trans
% 5.17/5.37 thf(fact_1384_less__induct,axiom,
% 5.17/5.37 ! [P: nat > $o,A: nat] :
% 5.17/5.37 ( ! [X4: nat] :
% 5.17/5.37 ( ! [Y3: nat] :
% 5.17/5.37 ( ( ord_less_nat @ Y3 @ X4 )
% 5.17/5.37 => ( P @ Y3 ) )
% 5.17/5.37 => ( P @ X4 ) )
% 5.17/5.37 => ( P @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % less_induct
% 5.17/5.37 thf(fact_1385_antisym__conv3,axiom,
% 5.17/5.37 ! [Y4: real,X: real] :
% 5.17/5.37 ( ~ ( ord_less_real @ Y4 @ X )
% 5.17/5.37 => ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.17/5.37 = ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % antisym_conv3
% 5.17/5.37 thf(fact_1386_antisym__conv3,axiom,
% 5.17/5.37 ! [Y4: rat,X: rat] :
% 5.17/5.37 ( ~ ( ord_less_rat @ Y4 @ X )
% 5.17/5.37 => ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.17/5.37 = ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % antisym_conv3
% 5.17/5.37 thf(fact_1387_antisym__conv3,axiom,
% 5.17/5.37 ! [Y4: num,X: num] :
% 5.17/5.37 ( ~ ( ord_less_num @ Y4 @ X )
% 5.17/5.37 => ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.17/5.37 = ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % antisym_conv3
% 5.17/5.37 thf(fact_1388_antisym__conv3,axiom,
% 5.17/5.37 ! [Y4: nat,X: nat] :
% 5.17/5.37 ( ~ ( ord_less_nat @ Y4 @ X )
% 5.17/5.37 => ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.17/5.37 = ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % antisym_conv3
% 5.17/5.37 thf(fact_1389_antisym__conv3,axiom,
% 5.17/5.37 ! [Y4: int,X: int] :
% 5.17/5.37 ( ~ ( ord_less_int @ Y4 @ X )
% 5.17/5.37 => ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.17/5.37 = ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % antisym_conv3
% 5.17/5.37 thf(fact_1390_linorder__cases,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ~ ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ( ( X != Y4 )
% 5.17/5.37 => ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_cases
% 5.17/5.37 thf(fact_1391_linorder__cases,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ~ ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ( ( X != Y4 )
% 5.17/5.37 => ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_cases
% 5.17/5.37 thf(fact_1392_linorder__cases,axiom,
% 5.17/5.37 ! [X: num,Y4: num] :
% 5.17/5.37 ( ~ ( ord_less_num @ X @ Y4 )
% 5.17/5.37 => ( ( X != Y4 )
% 5.17/5.37 => ( ord_less_num @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_cases
% 5.17/5.37 thf(fact_1393_linorder__cases,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ~ ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 => ( ( X != Y4 )
% 5.17/5.37 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_cases
% 5.17/5.37 thf(fact_1394_linorder__cases,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ~ ( ord_less_int @ X @ Y4 )
% 5.17/5.37 => ( ( X != Y4 )
% 5.17/5.37 => ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_cases
% 5.17/5.37 thf(fact_1395_dual__order_Oasym,axiom,
% 5.17/5.37 ! [B: real,A: real] :
% 5.17/5.37 ( ( ord_less_real @ B @ A )
% 5.17/5.37 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.asym
% 5.17/5.37 thf(fact_1396_dual__order_Oasym,axiom,
% 5.17/5.37 ! [B: rat,A: rat] :
% 5.17/5.37 ( ( ord_less_rat @ B @ A )
% 5.17/5.37 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.asym
% 5.17/5.37 thf(fact_1397_dual__order_Oasym,axiom,
% 5.17/5.37 ! [B: num,A: num] :
% 5.17/5.37 ( ( ord_less_num @ B @ A )
% 5.17/5.37 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.asym
% 5.17/5.37 thf(fact_1398_dual__order_Oasym,axiom,
% 5.17/5.37 ! [B: nat,A: nat] :
% 5.17/5.37 ( ( ord_less_nat @ B @ A )
% 5.17/5.37 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.asym
% 5.17/5.37 thf(fact_1399_dual__order_Oasym,axiom,
% 5.17/5.37 ! [B: int,A: int] :
% 5.17/5.37 ( ( ord_less_int @ B @ A )
% 5.17/5.37 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.asym
% 5.17/5.37 thf(fact_1400_dual__order_Oirrefl,axiom,
% 5.17/5.37 ! [A: real] :
% 5.17/5.37 ~ ( ord_less_real @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.irrefl
% 5.17/5.37 thf(fact_1401_dual__order_Oirrefl,axiom,
% 5.17/5.37 ! [A: rat] :
% 5.17/5.37 ~ ( ord_less_rat @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.irrefl
% 5.17/5.37 thf(fact_1402_dual__order_Oirrefl,axiom,
% 5.17/5.37 ! [A: num] :
% 5.17/5.37 ~ ( ord_less_num @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.irrefl
% 5.17/5.37 thf(fact_1403_dual__order_Oirrefl,axiom,
% 5.17/5.37 ! [A: nat] :
% 5.17/5.37 ~ ( ord_less_nat @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.irrefl
% 5.17/5.37 thf(fact_1404_dual__order_Oirrefl,axiom,
% 5.17/5.37 ! [A: int] :
% 5.17/5.37 ~ ( ord_less_int @ A @ A ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.irrefl
% 5.17/5.37 thf(fact_1405_exists__least__iff,axiom,
% 5.17/5.37 ( ( ^ [P2: nat > $o] :
% 5.17/5.37 ? [X6: nat] : ( P2 @ X6 ) )
% 5.17/5.37 = ( ^ [P3: nat > $o] :
% 5.17/5.37 ? [N4: nat] :
% 5.17/5.37 ( ( P3 @ N4 )
% 5.17/5.37 & ! [M5: nat] :
% 5.17/5.37 ( ( ord_less_nat @ M5 @ N4 )
% 5.17/5.37 => ~ ( P3 @ M5 ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % exists_least_iff
% 5.17/5.37 thf(fact_1406_linorder__less__wlog,axiom,
% 5.17/5.37 ! [P: real > real > $o,A: real,B: real] :
% 5.17/5.37 ( ! [A4: real,B3: real] :
% 5.17/5.37 ( ( ord_less_real @ A4 @ B3 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( ! [A4: real] : ( P @ A4 @ A4 )
% 5.17/5.37 => ( ! [A4: real,B3: real] :
% 5.17/5.37 ( ( P @ B3 @ A4 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_less_wlog
% 5.17/5.37 thf(fact_1407_linorder__less__wlog,axiom,
% 5.17/5.37 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.17/5.37 ( ! [A4: rat,B3: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A4 @ B3 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 5.17/5.37 => ( ! [A4: rat,B3: rat] :
% 5.17/5.37 ( ( P @ B3 @ A4 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_less_wlog
% 5.17/5.37 thf(fact_1408_linorder__less__wlog,axiom,
% 5.17/5.37 ! [P: num > num > $o,A: num,B: num] :
% 5.17/5.37 ( ! [A4: num,B3: num] :
% 5.17/5.37 ( ( ord_less_num @ A4 @ B3 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( ! [A4: num] : ( P @ A4 @ A4 )
% 5.17/5.37 => ( ! [A4: num,B3: num] :
% 5.17/5.37 ( ( P @ B3 @ A4 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_less_wlog
% 5.17/5.37 thf(fact_1409_linorder__less__wlog,axiom,
% 5.17/5.37 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.17/5.37 ( ! [A4: nat,B3: nat] :
% 5.17/5.37 ( ( ord_less_nat @ A4 @ B3 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 5.17/5.37 => ( ! [A4: nat,B3: nat] :
% 5.17/5.37 ( ( P @ B3 @ A4 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_less_wlog
% 5.17/5.37 thf(fact_1410_linorder__less__wlog,axiom,
% 5.17/5.37 ! [P: int > int > $o,A: int,B: int] :
% 5.17/5.37 ( ! [A4: int,B3: int] :
% 5.17/5.37 ( ( ord_less_int @ A4 @ B3 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 5.17/5.37 => ( ! [A4: int,B3: int] :
% 5.17/5.37 ( ( P @ B3 @ A4 )
% 5.17/5.37 => ( P @ A4 @ B3 ) )
% 5.17/5.37 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_less_wlog
% 5.17/5.37 thf(fact_1411_order_Ostrict__trans,axiom,
% 5.17/5.37 ! [A: real,B: real,C: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ord_less_real @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_trans
% 5.17/5.37 thf(fact_1412_order_Ostrict__trans,axiom,
% 5.17/5.37 ! [A: rat,B: rat,C: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_trans
% 5.17/5.37 thf(fact_1413_order_Ostrict__trans,axiom,
% 5.17/5.37 ! [A: num,B: num,C: num] :
% 5.17/5.37 ( ( ord_less_num @ A @ B )
% 5.17/5.37 => ( ( ord_less_num @ B @ C )
% 5.17/5.37 => ( ord_less_num @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_trans
% 5.17/5.37 thf(fact_1414_order_Ostrict__trans,axiom,
% 5.17/5.37 ! [A: nat,B: nat,C: nat] :
% 5.17/5.37 ( ( ord_less_nat @ A @ B )
% 5.17/5.37 => ( ( ord_less_nat @ B @ C )
% 5.17/5.37 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_trans
% 5.17/5.37 thf(fact_1415_order_Ostrict__trans,axiom,
% 5.17/5.37 ! [A: int,B: int,C: int] :
% 5.17/5.37 ( ( ord_less_int @ A @ B )
% 5.17/5.37 => ( ( ord_less_int @ B @ C )
% 5.17/5.37 => ( ord_less_int @ A @ C ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_trans
% 5.17/5.37 thf(fact_1416_not__less__iff__gr__or__eq,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.17/5.37 = ( ( ord_less_real @ Y4 @ X )
% 5.17/5.37 | ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % not_less_iff_gr_or_eq
% 5.17/5.37 thf(fact_1417_not__less__iff__gr__or__eq,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.17/5.37 = ( ( ord_less_rat @ Y4 @ X )
% 5.17/5.37 | ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % not_less_iff_gr_or_eq
% 5.17/5.37 thf(fact_1418_not__less__iff__gr__or__eq,axiom,
% 5.17/5.37 ! [X: num,Y4: num] :
% 5.17/5.37 ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.17/5.37 = ( ( ord_less_num @ Y4 @ X )
% 5.17/5.37 | ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % not_less_iff_gr_or_eq
% 5.17/5.37 thf(fact_1419_not__less__iff__gr__or__eq,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.17/5.37 = ( ( ord_less_nat @ Y4 @ X )
% 5.17/5.37 | ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % not_less_iff_gr_or_eq
% 5.17/5.37 thf(fact_1420_not__less__iff__gr__or__eq,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.17/5.37 = ( ( ord_less_int @ Y4 @ X )
% 5.17/5.37 | ( X = Y4 ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % not_less_iff_gr_or_eq
% 5.17/5.37 thf(fact_1421_dual__order_Ostrict__trans,axiom,
% 5.17/5.37 ! [B: real,A: real,C: real] :
% 5.17/5.37 ( ( ord_less_real @ B @ A )
% 5.17/5.37 => ( ( ord_less_real @ C @ B )
% 5.17/5.37 => ( ord_less_real @ C @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_trans
% 5.17/5.37 thf(fact_1422_dual__order_Ostrict__trans,axiom,
% 5.17/5.37 ! [B: rat,A: rat,C: rat] :
% 5.17/5.37 ( ( ord_less_rat @ B @ A )
% 5.17/5.37 => ( ( ord_less_rat @ C @ B )
% 5.17/5.37 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_trans
% 5.17/5.37 thf(fact_1423_dual__order_Ostrict__trans,axiom,
% 5.17/5.37 ! [B: num,A: num,C: num] :
% 5.17/5.37 ( ( ord_less_num @ B @ A )
% 5.17/5.37 => ( ( ord_less_num @ C @ B )
% 5.17/5.37 => ( ord_less_num @ C @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_trans
% 5.17/5.37 thf(fact_1424_dual__order_Ostrict__trans,axiom,
% 5.17/5.37 ! [B: nat,A: nat,C: nat] :
% 5.17/5.37 ( ( ord_less_nat @ B @ A )
% 5.17/5.37 => ( ( ord_less_nat @ C @ B )
% 5.17/5.37 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_trans
% 5.17/5.37 thf(fact_1425_dual__order_Ostrict__trans,axiom,
% 5.17/5.37 ! [B: int,A: int,C: int] :
% 5.17/5.37 ( ( ord_less_int @ B @ A )
% 5.17/5.37 => ( ( ord_less_int @ C @ B )
% 5.17/5.37 => ( ord_less_int @ C @ A ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_trans
% 5.17/5.37 thf(fact_1426_order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1427_order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1428_order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [A: num,B: num] :
% 5.17/5.37 ( ( ord_less_num @ A @ B )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1429_order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( ord_less_nat @ A @ B )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1430_order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( ord_less_int @ A @ B )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1431_dual__order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [B: real,A: real] :
% 5.17/5.37 ( ( ord_less_real @ B @ A )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1432_dual__order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [B: rat,A: rat] :
% 5.17/5.37 ( ( ord_less_rat @ B @ A )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1433_dual__order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [B: num,A: num] :
% 5.17/5.37 ( ( ord_less_num @ B @ A )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1434_dual__order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [B: nat,A: nat] :
% 5.17/5.37 ( ( ord_less_nat @ B @ A )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1435_dual__order_Ostrict__implies__not__eq,axiom,
% 5.17/5.37 ! [B: int,A: int] :
% 5.17/5.37 ( ( ord_less_int @ B @ A )
% 5.17/5.37 => ( A != B ) ) ).
% 5.17/5.37
% 5.17/5.37 % dual_order.strict_implies_not_eq
% 5.17/5.37 thf(fact_1436_linorder__neqE,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE
% 5.17/5.37 thf(fact_1437_linorder__neqE,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE
% 5.17/5.37 thf(fact_1438_linorder__neqE,axiom,
% 5.17/5.37 ! [X: num,Y4: num] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_num @ X @ Y4 )
% 5.17/5.37 => ( ord_less_num @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE
% 5.17/5.37 thf(fact_1439_linorder__neqE,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 => ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE
% 5.17/5.37 thf(fact_1440_linorder__neqE,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 => ( ~ ( ord_less_int @ X @ Y4 )
% 5.17/5.37 => ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neqE
% 5.17/5.37 thf(fact_1441_order__less__asym,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ~ ( ord_less_real @ Y4 @ X ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym
% 5.17/5.37 thf(fact_1442_order__less__asym,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ~ ( ord_less_rat @ Y4 @ X ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym
% 5.17/5.37 thf(fact_1443_order__less__asym,axiom,
% 5.17/5.37 ! [X: num,Y4: num] :
% 5.17/5.37 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.37 => ~ ( ord_less_num @ Y4 @ X ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym
% 5.17/5.37 thf(fact_1444_order__less__asym,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 => ~ ( ord_less_nat @ Y4 @ X ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym
% 5.17/5.37 thf(fact_1445_order__less__asym,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.37 => ~ ( ord_less_int @ Y4 @ X ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym
% 5.17/5.37 thf(fact_1446_linorder__neq__iff,axiom,
% 5.17/5.37 ! [X: real,Y4: real] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 = ( ( ord_less_real @ X @ Y4 )
% 5.17/5.37 | ( ord_less_real @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neq_iff
% 5.17/5.37 thf(fact_1447_linorder__neq__iff,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 = ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 | ( ord_less_rat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neq_iff
% 5.17/5.37 thf(fact_1448_linorder__neq__iff,axiom,
% 5.17/5.37 ! [X: num,Y4: num] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 = ( ( ord_less_num @ X @ Y4 )
% 5.17/5.37 | ( ord_less_num @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neq_iff
% 5.17/5.37 thf(fact_1449_linorder__neq__iff,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 = ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 | ( ord_less_nat @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neq_iff
% 5.17/5.37 thf(fact_1450_linorder__neq__iff,axiom,
% 5.17/5.37 ! [X: int,Y4: int] :
% 5.17/5.37 ( ( X != Y4 )
% 5.17/5.37 = ( ( ord_less_int @ X @ Y4 )
% 5.17/5.37 | ( ord_less_int @ Y4 @ X ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % linorder_neq_iff
% 5.17/5.37 thf(fact_1451_order__less__asym_H,axiom,
% 5.17/5.37 ! [A: real,B: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym'
% 5.17/5.37 thf(fact_1452_order__less__asym_H,axiom,
% 5.17/5.37 ! [A: rat,B: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym'
% 5.17/5.37 thf(fact_1453_order__less__asym_H,axiom,
% 5.17/5.37 ! [A: num,B: num] :
% 5.17/5.37 ( ( ord_less_num @ A @ B )
% 5.17/5.37 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym'
% 5.17/5.37 thf(fact_1454_order__less__asym_H,axiom,
% 5.17/5.37 ! [A: nat,B: nat] :
% 5.17/5.37 ( ( ord_less_nat @ A @ B )
% 5.17/5.37 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym'
% 5.17/5.37 thf(fact_1455_order__less__asym_H,axiom,
% 5.17/5.37 ! [A: int,B: int] :
% 5.17/5.37 ( ( ord_less_int @ A @ B )
% 5.17/5.37 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_asym'
% 5.17/5.37 thf(fact_1456_order__less__trans,axiom,
% 5.17/5.37 ! [X: real,Y4: real,Z: real] :
% 5.17/5.37 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.37 => ( ( ord_less_real @ Y4 @ Z )
% 5.17/5.37 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_trans
% 5.17/5.37 thf(fact_1457_order__less__trans,axiom,
% 5.17/5.37 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.37 => ( ( ord_less_rat @ Y4 @ Z )
% 5.17/5.37 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_trans
% 5.17/5.37 thf(fact_1458_order__less__trans,axiom,
% 5.17/5.37 ! [X: num,Y4: num,Z: num] :
% 5.17/5.37 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.37 => ( ( ord_less_num @ Y4 @ Z )
% 5.17/5.37 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_trans
% 5.17/5.37 thf(fact_1459_order__less__trans,axiom,
% 5.17/5.37 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.37 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.37 => ( ( ord_less_nat @ Y4 @ Z )
% 5.17/5.37 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_trans
% 5.17/5.37 thf(fact_1460_order__less__trans,axiom,
% 5.17/5.37 ! [X: int,Y4: int,Z: int] :
% 5.17/5.37 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.37 => ( ( ord_less_int @ Y4 @ Z )
% 5.17/5.37 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_trans
% 5.17/5.37 thf(fact_1461_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: real,F: real > real,B: real,C: real] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1462_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1463_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: num,F: real > num,B: real,C: real] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1464_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1465_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: int,F: real > int,B: real,C: real] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1466_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1467_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1468_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1469_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1470_ord__eq__less__subst,axiom,
% 5.17/5.37 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.17/5.37 ( ( A
% 5.17/5.37 = ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_eq_less_subst
% 5.17/5.37 thf(fact_1471_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > real,C: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1472_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1473_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > num,C: num] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1474_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1475_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > int,C: int] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1476_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1477_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1478_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1479_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1480_ord__less__eq__subst,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ( F @ B )
% 5.17/5.37 = C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % ord_less_eq_subst
% 5.17/5.37 thf(fact_1481_order__less__irrefl,axiom,
% 5.17/5.37 ! [X: real] :
% 5.17/5.37 ~ ( ord_less_real @ X @ X ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_irrefl
% 5.17/5.37 thf(fact_1482_order__less__irrefl,axiom,
% 5.17/5.37 ! [X: rat] :
% 5.17/5.37 ~ ( ord_less_rat @ X @ X ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_irrefl
% 5.17/5.37 thf(fact_1483_order__less__irrefl,axiom,
% 5.17/5.37 ! [X: num] :
% 5.17/5.37 ~ ( ord_less_num @ X @ X ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_irrefl
% 5.17/5.37 thf(fact_1484_order__less__irrefl,axiom,
% 5.17/5.37 ! [X: nat] :
% 5.17/5.37 ~ ( ord_less_nat @ X @ X ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_irrefl
% 5.17/5.37 thf(fact_1485_order__less__irrefl,axiom,
% 5.17/5.37 ! [X: int] :
% 5.17/5.37 ~ ( ord_less_int @ X @ X ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_irrefl
% 5.17/5.37 thf(fact_1486_order__less__subst1,axiom,
% 5.17/5.37 ! [A: real,F: real > real,B: real,C: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1487_order__less__subst1,axiom,
% 5.17/5.37 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.17/5.37 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1488_order__less__subst1,axiom,
% 5.17/5.37 ! [A: real,F: num > real,B: num,C: num] :
% 5.17/5.37 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_num @ B @ C )
% 5.17/5.37 => ( ! [X4: num,Y: num] :
% 5.17/5.37 ( ( ord_less_num @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1489_order__less__subst1,axiom,
% 5.17/5.37 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.17/5.37 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_nat @ B @ C )
% 5.17/5.37 => ( ! [X4: nat,Y: nat] :
% 5.17/5.37 ( ( ord_less_nat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1490_order__less__subst1,axiom,
% 5.17/5.37 ! [A: real,F: int > real,B: int,C: int] :
% 5.17/5.37 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_int @ B @ C )
% 5.17/5.37 => ( ! [X4: int,Y: int] :
% 5.17/5.37 ( ( ord_less_int @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1491_order__less__subst1,axiom,
% 5.17/5.37 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.17/5.37 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_real @ B @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1492_order__less__subst1,axiom,
% 5.17/5.37 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_rat @ B @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1493_order__less__subst1,axiom,
% 5.17/5.37 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.17/5.37 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_num @ B @ C )
% 5.17/5.37 => ( ! [X4: num,Y: num] :
% 5.17/5.37 ( ( ord_less_num @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1494_order__less__subst1,axiom,
% 5.17/5.37 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_nat @ B @ C )
% 5.17/5.37 => ( ! [X4: nat,Y: nat] :
% 5.17/5.37 ( ( ord_less_nat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1495_order__less__subst1,axiom,
% 5.17/5.37 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.17/5.37 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.37 => ( ( ord_less_int @ B @ C )
% 5.17/5.37 => ( ! [X4: int,Y: int] :
% 5.17/5.37 ( ( ord_less_int @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst1
% 5.17/5.37 thf(fact_1496_order__less__subst2,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > real,C: real] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1497_order__less__subst2,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1498_order__less__subst2,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > num,C: num] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1499_order__less__subst2,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1500_order__less__subst2,axiom,
% 5.17/5.37 ! [A: real,B: real,F: real > int,C: int] :
% 5.17/5.37 ( ( ord_less_real @ A @ B )
% 5.17/5.37 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: real,Y: real] :
% 5.17/5.37 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.37 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1501_order__less__subst2,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1502_order__less__subst2,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1503_order__less__subst2,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1504_order__less__subst2,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.37
% 5.17/5.37 % order_less_subst2
% 5.17/5.37 thf(fact_1505_order__less__subst2,axiom,
% 5.17/5.37 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.17/5.37 ( ( ord_less_rat @ A @ B )
% 5.17/5.37 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.17/5.37 => ( ! [X4: rat,Y: rat] :
% 5.17/5.37 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.37 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.37 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_subst2
% 5.17/5.38 thf(fact_1506_order__less__not__sym,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_not_sym
% 5.17/5.38 thf(fact_1507_order__less__not__sym,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_not_sym
% 5.17/5.38 thf(fact_1508_order__less__not__sym,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_not_sym
% 5.17/5.38 thf(fact_1509_order__less__not__sym,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_not_sym
% 5.17/5.38 thf(fact_1510_order__less__not__sym,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_not_sym
% 5.17/5.38 thf(fact_1511_order__less__imp__triv,axiom,
% 5.17/5.38 ! [X: real,Y4: real,P: $o] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_real @ Y4 @ X )
% 5.17/5.38 => P ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_triv
% 5.17/5.38 thf(fact_1512_order__less__imp__triv,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat,P: $o] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_rat @ Y4 @ X )
% 5.17/5.38 => P ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_triv
% 5.17/5.38 thf(fact_1513_order__less__imp__triv,axiom,
% 5.17/5.38 ! [X: num,Y4: num,P: $o] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_num @ Y4 @ X )
% 5.17/5.38 => P ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_triv
% 5.17/5.38 thf(fact_1514_order__less__imp__triv,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat,P: $o] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_nat @ Y4 @ X )
% 5.17/5.38 => P ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_triv
% 5.17/5.38 thf(fact_1515_order__less__imp__triv,axiom,
% 5.17/5.38 ! [X: int,Y4: int,P: $o] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_int @ Y4 @ X )
% 5.17/5.38 => P ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_triv
% 5.17/5.38 thf(fact_1516_linorder__less__linear,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 )
% 5.17/5.38 | ( ord_less_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_less_linear
% 5.17/5.38 thf(fact_1517_linorder__less__linear,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 )
% 5.17/5.38 | ( ord_less_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_less_linear
% 5.17/5.38 thf(fact_1518_linorder__less__linear,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 )
% 5.17/5.38 | ( ord_less_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_less_linear
% 5.17/5.38 thf(fact_1519_linorder__less__linear,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 )
% 5.17/5.38 | ( ord_less_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_less_linear
% 5.17/5.38 thf(fact_1520_linorder__less__linear,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 )
% 5.17/5.38 | ( ord_less_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_less_linear
% 5.17/5.38 thf(fact_1521_order__less__imp__not__eq,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( X != Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq
% 5.17/5.38 thf(fact_1522_order__less__imp__not__eq,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( X != Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq
% 5.17/5.38 thf(fact_1523_order__less__imp__not__eq,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( X != Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq
% 5.17/5.38 thf(fact_1524_order__less__imp__not__eq,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( X != Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq
% 5.17/5.38 thf(fact_1525_order__less__imp__not__eq,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( X != Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq
% 5.17/5.38 thf(fact_1526_order__less__imp__not__eq2,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( Y4 != X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq2
% 5.17/5.38 thf(fact_1527_order__less__imp__not__eq2,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( Y4 != X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq2
% 5.17/5.38 thf(fact_1528_order__less__imp__not__eq2,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( Y4 != X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq2
% 5.17/5.38 thf(fact_1529_order__less__imp__not__eq2,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( Y4 != X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq2
% 5.17/5.38 thf(fact_1530_order__less__imp__not__eq2,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( Y4 != X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_eq2
% 5.17/5.38 thf(fact_1531_order__less__imp__not__less,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_less
% 5.17/5.38 thf(fact_1532_order__less__imp__not__less,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_less
% 5.17/5.38 thf(fact_1533_order__less__imp__not__less,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_less
% 5.17/5.38 thf(fact_1534_order__less__imp__not__less,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_less
% 5.17/5.38 thf(fact_1535_order__less__imp__not__less,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ~ ( ord_less_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_not_less
% 5.17/5.38 thf(fact_1536_less__numeral__extra_I1_J,axiom,
% 5.17/5.38 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(1)
% 5.17/5.38 thf(fact_1537_less__numeral__extra_I1_J,axiom,
% 5.17/5.38 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(1)
% 5.17/5.38 thf(fact_1538_less__numeral__extra_I1_J,axiom,
% 5.17/5.38 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(1)
% 5.17/5.38 thf(fact_1539_less__numeral__extra_I1_J,axiom,
% 5.17/5.38 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(1)
% 5.17/5.38 thf(fact_1540_zero__less__one,axiom,
% 5.17/5.38 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.17/5.38
% 5.17/5.38 % zero_less_one
% 5.17/5.38 thf(fact_1541_zero__less__one,axiom,
% 5.17/5.38 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.17/5.38
% 5.17/5.38 % zero_less_one
% 5.17/5.38 thf(fact_1542_zero__less__one,axiom,
% 5.17/5.38 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.17/5.38
% 5.17/5.38 % zero_less_one
% 5.17/5.38 thf(fact_1543_zero__less__one,axiom,
% 5.17/5.38 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.17/5.38
% 5.17/5.38 % zero_less_one
% 5.17/5.38 thf(fact_1544_not__one__less__zero,axiom,
% 5.17/5.38 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.17/5.38
% 5.17/5.38 % not_one_less_zero
% 5.17/5.38 thf(fact_1545_not__one__less__zero,axiom,
% 5.17/5.38 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.17/5.38
% 5.17/5.38 % not_one_less_zero
% 5.17/5.38 thf(fact_1546_not__one__less__zero,axiom,
% 5.17/5.38 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.17/5.38
% 5.17/5.38 % not_one_less_zero
% 5.17/5.38 thf(fact_1547_not__one__less__zero,axiom,
% 5.17/5.38 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.17/5.38
% 5.17/5.38 % not_one_less_zero
% 5.17/5.38 thf(fact_1548_not__numeral__less__one,axiom,
% 5.17/5.38 ! [N: num] :
% 5.17/5.38 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.17/5.38
% 5.17/5.38 % not_numeral_less_one
% 5.17/5.38 thf(fact_1549_not__numeral__less__one,axiom,
% 5.17/5.38 ! [N: num] :
% 5.17/5.38 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.17/5.38
% 5.17/5.38 % not_numeral_less_one
% 5.17/5.38 thf(fact_1550_not__numeral__less__one,axiom,
% 5.17/5.38 ! [N: num] :
% 5.17/5.38 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.17/5.38
% 5.17/5.38 % not_numeral_less_one
% 5.17/5.38 thf(fact_1551_not__numeral__less__one,axiom,
% 5.17/5.38 ! [N: num] :
% 5.17/5.38 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.17/5.38
% 5.17/5.38 % not_numeral_less_one
% 5.17/5.38 thf(fact_1552_less__1__mult,axiom,
% 5.17/5.38 ! [M: real,N: real] :
% 5.17/5.38 ( ( ord_less_real @ one_one_real @ M )
% 5.17/5.38 => ( ( ord_less_real @ one_one_real @ N )
% 5.17/5.38 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_1_mult
% 5.17/5.38 thf(fact_1553_less__1__mult,axiom,
% 5.17/5.38 ! [M: rat,N: rat] :
% 5.17/5.38 ( ( ord_less_rat @ one_one_rat @ M )
% 5.17/5.38 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.17/5.38 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_1_mult
% 5.17/5.38 thf(fact_1554_less__1__mult,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ one_one_nat @ M )
% 5.17/5.38 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.17/5.38 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_1_mult
% 5.17/5.38 thf(fact_1555_less__1__mult,axiom,
% 5.17/5.38 ! [M: int,N: int] :
% 5.17/5.38 ( ( ord_less_int @ one_one_int @ M )
% 5.17/5.38 => ( ( ord_less_int @ one_one_int @ N )
% 5.17/5.38 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_1_mult
% 5.17/5.38 thf(fact_1556_lift__Suc__mono__less__iff,axiom,
% 5.17/5.38 ! [F: nat > real,N: nat,M: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.17/5.38 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less_iff
% 5.17/5.38 thf(fact_1557_lift__Suc__mono__less__iff,axiom,
% 5.17/5.38 ! [F: nat > rat,N: nat,M: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.17/5.38 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less_iff
% 5.17/5.38 thf(fact_1558_lift__Suc__mono__less__iff,axiom,
% 5.17/5.38 ! [F: nat > num,N: nat,M: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.17/5.38 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less_iff
% 5.17/5.38 thf(fact_1559_lift__Suc__mono__less__iff,axiom,
% 5.17/5.38 ! [F: nat > nat,N: nat,M: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.17/5.38 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less_iff
% 5.17/5.38 thf(fact_1560_lift__Suc__mono__less__iff,axiom,
% 5.17/5.38 ! [F: nat > int,N: nat,M: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.17/5.38 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less_iff
% 5.17/5.38 thf(fact_1561_lift__Suc__mono__less,axiom,
% 5.17/5.38 ! [F: nat > real,N: nat,N3: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_nat @ N @ N3 )
% 5.17/5.38 => ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less
% 5.17/5.38 thf(fact_1562_lift__Suc__mono__less,axiom,
% 5.17/5.38 ! [F: nat > rat,N: nat,N3: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_nat @ N @ N3 )
% 5.17/5.38 => ( ord_less_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less
% 5.17/5.38 thf(fact_1563_lift__Suc__mono__less,axiom,
% 5.17/5.38 ! [F: nat > num,N: nat,N3: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_nat @ N @ N3 )
% 5.17/5.38 => ( ord_less_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less
% 5.17/5.38 thf(fact_1564_lift__Suc__mono__less,axiom,
% 5.17/5.38 ! [F: nat > nat,N: nat,N3: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_nat @ N @ N3 )
% 5.17/5.38 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less
% 5.17/5.38 thf(fact_1565_lift__Suc__mono__less,axiom,
% 5.17/5.38 ! [F: nat > int,N: nat,N3: nat] :
% 5.17/5.38 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.38 => ( ( ord_less_nat @ N @ N3 )
% 5.17/5.38 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % lift_Suc_mono_less
% 5.17/5.38 thf(fact_1566_of__nat__less__imp__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % of_nat_less_imp_less
% 5.17/5.38 thf(fact_1567_of__nat__less__imp__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % of_nat_less_imp_less
% 5.17/5.38 thf(fact_1568_of__nat__less__imp__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % of_nat_less_imp_less
% 5.17/5.38 thf(fact_1569_of__nat__less__imp__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % of_nat_less_imp_less
% 5.17/5.38 thf(fact_1570_less__imp__of__nat__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_imp_of_nat_less
% 5.17/5.38 thf(fact_1571_less__imp__of__nat__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_imp_of_nat_less
% 5.17/5.38 thf(fact_1572_less__imp__of__nat__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_imp_of_nat_less
% 5.17/5.38 thf(fact_1573_less__imp__of__nat__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_imp_of_nat_less
% 5.17/5.38 thf(fact_1574_minf_I8_J,axiom,
% 5.17/5.38 ! [T: rat] :
% 5.17/5.38 ? [Z2: rat] :
% 5.17/5.38 ! [X5: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X5 @ Z2 )
% 5.17/5.38 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(8)
% 5.17/5.38 thf(fact_1575_minf_I8_J,axiom,
% 5.17/5.38 ! [T: num] :
% 5.17/5.38 ? [Z2: num] :
% 5.17/5.38 ! [X5: num] :
% 5.17/5.38 ( ( ord_less_num @ X5 @ Z2 )
% 5.17/5.38 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(8)
% 5.17/5.38 thf(fact_1576_minf_I8_J,axiom,
% 5.17/5.38 ! [T: nat] :
% 5.17/5.38 ? [Z2: nat] :
% 5.17/5.38 ! [X5: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X5 @ Z2 )
% 5.17/5.38 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(8)
% 5.17/5.38 thf(fact_1577_minf_I8_J,axiom,
% 5.17/5.38 ! [T: int] :
% 5.17/5.38 ? [Z2: int] :
% 5.17/5.38 ! [X5: int] :
% 5.17/5.38 ( ( ord_less_int @ X5 @ Z2 )
% 5.17/5.38 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(8)
% 5.17/5.38 thf(fact_1578_minf_I8_J,axiom,
% 5.17/5.38 ! [T: real] :
% 5.17/5.38 ? [Z2: real] :
% 5.17/5.38 ! [X5: real] :
% 5.17/5.38 ( ( ord_less_real @ X5 @ Z2 )
% 5.17/5.38 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(8)
% 5.17/5.38 thf(fact_1579_minf_I6_J,axiom,
% 5.17/5.38 ! [T: rat] :
% 5.17/5.38 ? [Z2: rat] :
% 5.17/5.38 ! [X5: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X5 @ Z2 )
% 5.17/5.38 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(6)
% 5.17/5.38 thf(fact_1580_minf_I6_J,axiom,
% 5.17/5.38 ! [T: num] :
% 5.17/5.38 ? [Z2: num] :
% 5.17/5.38 ! [X5: num] :
% 5.17/5.38 ( ( ord_less_num @ X5 @ Z2 )
% 5.17/5.38 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(6)
% 5.17/5.38 thf(fact_1581_minf_I6_J,axiom,
% 5.17/5.38 ! [T: nat] :
% 5.17/5.38 ? [Z2: nat] :
% 5.17/5.38 ! [X5: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X5 @ Z2 )
% 5.17/5.38 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(6)
% 5.17/5.38 thf(fact_1582_minf_I6_J,axiom,
% 5.17/5.38 ! [T: int] :
% 5.17/5.38 ? [Z2: int] :
% 5.17/5.38 ! [X5: int] :
% 5.17/5.38 ( ( ord_less_int @ X5 @ Z2 )
% 5.17/5.38 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(6)
% 5.17/5.38 thf(fact_1583_minf_I6_J,axiom,
% 5.17/5.38 ! [T: real] :
% 5.17/5.38 ? [Z2: real] :
% 5.17/5.38 ! [X5: real] :
% 5.17/5.38 ( ( ord_less_real @ X5 @ Z2 )
% 5.17/5.38 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % minf(6)
% 5.17/5.38 thf(fact_1584_pinf_I8_J,axiom,
% 5.17/5.38 ! [T: rat] :
% 5.17/5.38 ? [Z2: rat] :
% 5.17/5.38 ! [X5: rat] :
% 5.17/5.38 ( ( ord_less_rat @ Z2 @ X5 )
% 5.17/5.38 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(8)
% 5.17/5.38 thf(fact_1585_pinf_I8_J,axiom,
% 5.17/5.38 ! [T: num] :
% 5.17/5.38 ? [Z2: num] :
% 5.17/5.38 ! [X5: num] :
% 5.17/5.38 ( ( ord_less_num @ Z2 @ X5 )
% 5.17/5.38 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(8)
% 5.17/5.38 thf(fact_1586_pinf_I8_J,axiom,
% 5.17/5.38 ! [T: nat] :
% 5.17/5.38 ? [Z2: nat] :
% 5.17/5.38 ! [X5: nat] :
% 5.17/5.38 ( ( ord_less_nat @ Z2 @ X5 )
% 5.17/5.38 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(8)
% 5.17/5.38 thf(fact_1587_pinf_I8_J,axiom,
% 5.17/5.38 ! [T: int] :
% 5.17/5.38 ? [Z2: int] :
% 5.17/5.38 ! [X5: int] :
% 5.17/5.38 ( ( ord_less_int @ Z2 @ X5 )
% 5.17/5.38 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(8)
% 5.17/5.38 thf(fact_1588_pinf_I8_J,axiom,
% 5.17/5.38 ! [T: real] :
% 5.17/5.38 ? [Z2: real] :
% 5.17/5.38 ! [X5: real] :
% 5.17/5.38 ( ( ord_less_real @ Z2 @ X5 )
% 5.17/5.38 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(8)
% 5.17/5.38 thf(fact_1589_pinf_I6_J,axiom,
% 5.17/5.38 ! [T: rat] :
% 5.17/5.38 ? [Z2: rat] :
% 5.17/5.38 ! [X5: rat] :
% 5.17/5.38 ( ( ord_less_rat @ Z2 @ X5 )
% 5.17/5.38 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(6)
% 5.17/5.38 thf(fact_1590_pinf_I6_J,axiom,
% 5.17/5.38 ! [T: num] :
% 5.17/5.38 ? [Z2: num] :
% 5.17/5.38 ! [X5: num] :
% 5.17/5.38 ( ( ord_less_num @ Z2 @ X5 )
% 5.17/5.38 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(6)
% 5.17/5.38 thf(fact_1591_pinf_I6_J,axiom,
% 5.17/5.38 ! [T: nat] :
% 5.17/5.38 ? [Z2: nat] :
% 5.17/5.38 ! [X5: nat] :
% 5.17/5.38 ( ( ord_less_nat @ Z2 @ X5 )
% 5.17/5.38 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(6)
% 5.17/5.38 thf(fact_1592_pinf_I6_J,axiom,
% 5.17/5.38 ! [T: int] :
% 5.17/5.38 ? [Z2: int] :
% 5.17/5.38 ! [X5: int] :
% 5.17/5.38 ( ( ord_less_int @ Z2 @ X5 )
% 5.17/5.38 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(6)
% 5.17/5.38 thf(fact_1593_pinf_I6_J,axiom,
% 5.17/5.38 ! [T: real] :
% 5.17/5.38 ? [Z2: real] :
% 5.17/5.38 ! [X5: real] :
% 5.17/5.38 ( ( ord_less_real @ Z2 @ X5 )
% 5.17/5.38 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 5.17/5.38
% 5.17/5.38 % pinf(6)
% 5.17/5.38 thf(fact_1594_less__divide__eq__1,axiom,
% 5.17/5.38 ! [B: real,A: real] :
% 5.17/5.38 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.17/5.38 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.38 & ( ord_less_real @ A @ B ) )
% 5.17/5.38 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.38 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_divide_eq_1
% 5.17/5.38 thf(fact_1595_less__divide__eq__1,axiom,
% 5.17/5.38 ! [B: rat,A: rat] :
% 5.17/5.38 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.17/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.38 & ( ord_less_rat @ A @ B ) )
% 5.17/5.38 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.38 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_divide_eq_1
% 5.17/5.38 thf(fact_1596_divide__less__eq__1,axiom,
% 5.17/5.38 ! [B: real,A: real] :
% 5.17/5.38 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.17/5.38 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.38 & ( ord_less_real @ B @ A ) )
% 5.17/5.38 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.38 & ( ord_less_real @ A @ B ) )
% 5.17/5.38 | ( A = zero_zero_real ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % divide_less_eq_1
% 5.17/5.38 thf(fact_1597_divide__less__eq__1,axiom,
% 5.17/5.38 ! [B: rat,A: rat] :
% 5.17/5.38 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.17/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.38 & ( ord_less_rat @ B @ A ) )
% 5.17/5.38 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.38 & ( ord_less_rat @ A @ B ) )
% 5.17/5.38 | ( A = zero_zero_rat ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % divide_less_eq_1
% 5.17/5.38 thf(fact_1598_nat__induct__non__zero,axiom,
% 5.17/5.38 ! [N: nat,P: nat > $o] :
% 5.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.38 => ( ( P @ one_one_nat )
% 5.17/5.38 => ( ! [N2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.38 => ( ( P @ N2 )
% 5.17/5.38 => ( P @ ( suc @ N2 ) ) ) )
% 5.17/5.38 => ( P @ N ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nat_induct_non_zero
% 5.17/5.38 thf(fact_1599_div__eq__dividend__iff,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.38 => ( ( ( divide_divide_nat @ M @ N )
% 5.17/5.38 = M )
% 5.17/5.38 = ( N = one_one_nat ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % div_eq_dividend_iff
% 5.17/5.38 thf(fact_1600_div__less__dividend,axiom,
% 5.17/5.38 ! [N: nat,M: nat] :
% 5.17/5.38 ( ( ord_less_nat @ one_one_nat @ N )
% 5.17/5.38 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.38 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % div_less_dividend
% 5.17/5.38 thf(fact_1601_verit__comp__simplify1_I3_J,axiom,
% 5.17/5.38 ! [B6: rat,A6: rat] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_rat @ B6 @ A6 ) )
% 5.17/5.38 = ( ord_less_rat @ A6 @ B6 ) ) ).
% 5.17/5.38
% 5.17/5.38 % verit_comp_simplify1(3)
% 5.17/5.38 thf(fact_1602_verit__comp__simplify1_I3_J,axiom,
% 5.17/5.38 ! [B6: num,A6: num] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_num @ B6 @ A6 ) )
% 5.17/5.38 = ( ord_less_num @ A6 @ B6 ) ) ).
% 5.17/5.38
% 5.17/5.38 % verit_comp_simplify1(3)
% 5.17/5.38 thf(fact_1603_verit__comp__simplify1_I3_J,axiom,
% 5.17/5.38 ! [B6: nat,A6: nat] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_nat @ B6 @ A6 ) )
% 5.17/5.38 = ( ord_less_nat @ A6 @ B6 ) ) ).
% 5.17/5.38
% 5.17/5.38 % verit_comp_simplify1(3)
% 5.17/5.38 thf(fact_1604_verit__comp__simplify1_I3_J,axiom,
% 5.17/5.38 ! [B6: int,A6: int] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_int @ B6 @ A6 ) )
% 5.17/5.38 = ( ord_less_int @ A6 @ B6 ) ) ).
% 5.17/5.38
% 5.17/5.38 % verit_comp_simplify1(3)
% 5.17/5.38 thf(fact_1605_verit__comp__simplify1_I3_J,axiom,
% 5.17/5.38 ! [B6: real,A6: real] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_real @ B6 @ A6 ) )
% 5.17/5.38 = ( ord_less_real @ A6 @ B6 ) ) ).
% 5.17/5.38
% 5.17/5.38 % verit_comp_simplify1(3)
% 5.17/5.38 thf(fact_1606_leD,axiom,
% 5.17/5.38 ! [Y4: set_int,X: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ Y4 @ X )
% 5.17/5.38 => ~ ( ord_less_set_int @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % leD
% 5.17/5.38 thf(fact_1607_leD,axiom,
% 5.17/5.38 ! [Y4: rat,X: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.38 => ~ ( ord_less_rat @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % leD
% 5.17/5.38 thf(fact_1608_leD,axiom,
% 5.17/5.38 ! [Y4: num,X: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ Y4 @ X )
% 5.17/5.38 => ~ ( ord_less_num @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % leD
% 5.17/5.38 thf(fact_1609_leD,axiom,
% 5.17/5.38 ! [Y4: nat,X: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.38 => ~ ( ord_less_nat @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % leD
% 5.17/5.38 thf(fact_1610_leD,axiom,
% 5.17/5.38 ! [Y4: int,X: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ Y4 @ X )
% 5.17/5.38 => ~ ( ord_less_int @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % leD
% 5.17/5.38 thf(fact_1611_leD,axiom,
% 5.17/5.38 ! [Y4: real,X: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.38 => ~ ( ord_less_real @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % leD
% 5.17/5.38 thf(fact_1612_leI,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ~ ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % leI
% 5.17/5.38 thf(fact_1613_leI,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ~ ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % leI
% 5.17/5.38 thf(fact_1614_leI,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ~ ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % leI
% 5.17/5.38 thf(fact_1615_leI,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ~ ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % leI
% 5.17/5.38 thf(fact_1616_leI,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ~ ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % leI
% 5.17/5.38 thf(fact_1617_nless__le,axiom,
% 5.17/5.38 ! [A: set_int,B: set_int] :
% 5.17/5.38 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.17/5.38 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.17/5.38 | ( A = B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nless_le
% 5.17/5.38 thf(fact_1618_nless__le,axiom,
% 5.17/5.38 ! [A: rat,B: rat] :
% 5.17/5.38 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.17/5.38 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 | ( A = B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nless_le
% 5.17/5.38 thf(fact_1619_nless__le,axiom,
% 5.17/5.38 ! [A: num,B: num] :
% 5.17/5.38 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.17/5.38 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.17/5.38 | ( A = B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nless_le
% 5.17/5.38 thf(fact_1620_nless__le,axiom,
% 5.17/5.38 ! [A: nat,B: nat] :
% 5.17/5.38 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.17/5.38 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.17/5.38 | ( A = B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nless_le
% 5.17/5.38 thf(fact_1621_nless__le,axiom,
% 5.17/5.38 ! [A: int,B: int] :
% 5.17/5.38 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.17/5.38 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.17/5.38 | ( A = B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nless_le
% 5.17/5.38 thf(fact_1622_nless__le,axiom,
% 5.17/5.38 ! [A: real,B: real] :
% 5.17/5.38 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.17/5.38 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.17/5.38 | ( A = B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nless_le
% 5.17/5.38 thf(fact_1623_antisym__conv1,axiom,
% 5.17/5.38 ! [X: set_int,Y4: set_int] :
% 5.17/5.38 ( ~ ( ord_less_set_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv1
% 5.17/5.38 thf(fact_1624_antisym__conv1,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ~ ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv1
% 5.17/5.38 thf(fact_1625_antisym__conv1,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ~ ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv1
% 5.17/5.38 thf(fact_1626_antisym__conv1,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ~ ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv1
% 5.17/5.38 thf(fact_1627_antisym__conv1,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ~ ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv1
% 5.17/5.38 thf(fact_1628_antisym__conv1,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ~ ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv1
% 5.17/5.38 thf(fact_1629_antisym__conv2,axiom,
% 5.17/5.38 ! [X: set_int,Y4: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.38 => ( ( ~ ( ord_less_set_int @ X @ Y4 ) )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv2
% 5.17/5.38 thf(fact_1630_antisym__conv2,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.38 => ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv2
% 5.17/5.38 thf(fact_1631_antisym__conv2,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.38 => ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv2
% 5.17/5.38 thf(fact_1632_antisym__conv2,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.38 => ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv2
% 5.17/5.38 thf(fact_1633_antisym__conv2,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.38 => ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv2
% 5.17/5.38 thf(fact_1634_antisym__conv2,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.38 => ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.17/5.38 = ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % antisym_conv2
% 5.17/5.38 thf(fact_1635_dense__ge,axiom,
% 5.17/5.38 ! [Z: rat,Y4: rat] :
% 5.17/5.38 ( ! [X4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ Z @ X4 )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ X4 ) )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ Z ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_ge
% 5.17/5.38 thf(fact_1636_dense__ge,axiom,
% 5.17/5.38 ! [Z: real,Y4: real] :
% 5.17/5.38 ( ! [X4: real] :
% 5.17/5.38 ( ( ord_less_real @ Z @ X4 )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ X4 ) )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ Z ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_ge
% 5.17/5.38 thf(fact_1637_dense__le,axiom,
% 5.17/5.38 ! [Y4: rat,Z: rat] :
% 5.17/5.38 ( ! [X4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X4 @ Y4 )
% 5.17/5.38 => ( ord_less_eq_rat @ X4 @ Z ) )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ Z ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_le
% 5.17/5.38 thf(fact_1638_dense__le,axiom,
% 5.17/5.38 ! [Y4: real,Z: real] :
% 5.17/5.38 ( ! [X4: real] :
% 5.17/5.38 ( ( ord_less_real @ X4 @ Y4 )
% 5.17/5.38 => ( ord_less_eq_real @ X4 @ Z ) )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ Z ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_le
% 5.17/5.38 thf(fact_1639_less__le__not__le,axiom,
% 5.17/5.38 ( ord_less_set_int
% 5.17/5.38 = ( ^ [X3: set_int,Y6: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ X3 @ Y6 )
% 5.17/5.38 & ~ ( ord_less_eq_set_int @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_le_not_le
% 5.17/5.38 thf(fact_1640_less__le__not__le,axiom,
% 5.17/5.38 ( ord_less_rat
% 5.17/5.38 = ( ^ [X3: rat,Y6: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X3 @ Y6 )
% 5.17/5.38 & ~ ( ord_less_eq_rat @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_le_not_le
% 5.17/5.38 thf(fact_1641_less__le__not__le,axiom,
% 5.17/5.38 ( ord_less_num
% 5.17/5.38 = ( ^ [X3: num,Y6: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X3 @ Y6 )
% 5.17/5.38 & ~ ( ord_less_eq_num @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_le_not_le
% 5.17/5.38 thf(fact_1642_less__le__not__le,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [X3: nat,Y6: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 5.17/5.38 & ~ ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_le_not_le
% 5.17/5.38 thf(fact_1643_less__le__not__le,axiom,
% 5.17/5.38 ( ord_less_int
% 5.17/5.38 = ( ^ [X3: int,Y6: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ X3 @ Y6 )
% 5.17/5.38 & ~ ( ord_less_eq_int @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_le_not_le
% 5.17/5.38 thf(fact_1644_less__le__not__le,axiom,
% 5.17/5.38 ( ord_less_real
% 5.17/5.38 = ( ^ [X3: real,Y6: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ X3 @ Y6 )
% 5.17/5.38 & ~ ( ord_less_eq_real @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_le_not_le
% 5.17/5.38 thf(fact_1645_not__le__imp__less,axiom,
% 5.17/5.38 ! [Y4: rat,X: rat] :
% 5.17/5.38 ( ~ ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.38 => ( ord_less_rat @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_le_imp_less
% 5.17/5.38 thf(fact_1646_not__le__imp__less,axiom,
% 5.17/5.38 ! [Y4: num,X: num] :
% 5.17/5.38 ( ~ ( ord_less_eq_num @ Y4 @ X )
% 5.17/5.38 => ( ord_less_num @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_le_imp_less
% 5.17/5.38 thf(fact_1647_not__le__imp__less,axiom,
% 5.17/5.38 ! [Y4: nat,X: nat] :
% 5.17/5.38 ( ~ ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.38 => ( ord_less_nat @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_le_imp_less
% 5.17/5.38 thf(fact_1648_not__le__imp__less,axiom,
% 5.17/5.38 ! [Y4: int,X: int] :
% 5.17/5.38 ( ~ ( ord_less_eq_int @ Y4 @ X )
% 5.17/5.38 => ( ord_less_int @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_le_imp_less
% 5.17/5.38 thf(fact_1649_not__le__imp__less,axiom,
% 5.17/5.38 ! [Y4: real,X: real] :
% 5.17/5.38 ( ~ ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.38 => ( ord_less_real @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_le_imp_less
% 5.17/5.38 thf(fact_1650_order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_set_int
% 5.17/5.38 = ( ^ [A3: set_int,B2: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ A3 @ B2 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.order_iff_strict
% 5.17/5.38 thf(fact_1651_order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_rat
% 5.17/5.38 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A3 @ B2 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.order_iff_strict
% 5.17/5.38 thf(fact_1652_order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_num
% 5.17/5.38 = ( ^ [A3: num,B2: num] :
% 5.17/5.38 ( ( ord_less_num @ A3 @ B2 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.order_iff_strict
% 5.17/5.38 thf(fact_1653_order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_nat
% 5.17/5.38 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ A3 @ B2 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.order_iff_strict
% 5.17/5.38 thf(fact_1654_order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_int
% 5.17/5.38 = ( ^ [A3: int,B2: int] :
% 5.17/5.38 ( ( ord_less_int @ A3 @ B2 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.order_iff_strict
% 5.17/5.38 thf(fact_1655_order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_real
% 5.17/5.38 = ( ^ [A3: real,B2: real] :
% 5.17/5.38 ( ( ord_less_real @ A3 @ B2 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.order_iff_strict
% 5.17/5.38 thf(fact_1656_order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_set_int
% 5.17/5.38 = ( ^ [A3: set_int,B2: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_order
% 5.17/5.38 thf(fact_1657_order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_rat
% 5.17/5.38 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_order
% 5.17/5.38 thf(fact_1658_order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_num
% 5.17/5.38 = ( ^ [A3: num,B2: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_order
% 5.17/5.38 thf(fact_1659_order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_order
% 5.17/5.38 thf(fact_1660_order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_int
% 5.17/5.38 = ( ^ [A3: int,B2: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_order
% 5.17/5.38 thf(fact_1661_order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_real
% 5.17/5.38 = ( ^ [A3: real,B2: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_order
% 5.17/5.38 thf(fact_1662_order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [A: set_int,B: set_int,C: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_set_int @ B @ C )
% 5.17/5.38 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans1
% 5.17/5.38 thf(fact_1663_order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [A: rat,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_rat @ B @ C )
% 5.17/5.38 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans1
% 5.17/5.38 thf(fact_1664_order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [A: num,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_num @ B @ C )
% 5.17/5.38 => ( ord_less_num @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans1
% 5.17/5.38 thf(fact_1665_order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [A: nat,B: nat,C: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.38 => ( ( ord_less_nat @ B @ C )
% 5.17/5.38 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans1
% 5.17/5.38 thf(fact_1666_order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [A: int,B: int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_int @ B @ C )
% 5.17/5.38 => ( ord_less_int @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans1
% 5.17/5.38 thf(fact_1667_order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [A: real,B: real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.38 => ( ( ord_less_real @ B @ C )
% 5.17/5.38 => ( ord_less_real @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans1
% 5.17/5.38 thf(fact_1668_order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [A: set_int,B: set_int,C: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ B @ C )
% 5.17/5.38 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans2
% 5.17/5.38 thf(fact_1669_order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.38 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans2
% 5.17/5.38 thf(fact_1670_order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [A: num,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.38 => ( ord_less_num @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans2
% 5.17/5.38 thf(fact_1671_order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [A: nat,B: nat,C: nat] :
% 5.17/5.38 ( ( ord_less_nat @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.38 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans2
% 5.17/5.38 thf(fact_1672_order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [A: int,B: int,C: int] :
% 5.17/5.38 ( ( ord_less_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.38 => ( ord_less_int @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans2
% 5.17/5.38 thf(fact_1673_order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [A: real,B: real,C: real] :
% 5.17/5.38 ( ( ord_less_real @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.38 => ( ord_less_real @ A @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_trans2
% 5.17/5.38 thf(fact_1674_order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_set_int
% 5.17/5.38 = ( ^ [A3: set_int,B2: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.17/5.38 & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_not
% 5.17/5.38 thf(fact_1675_order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_rat
% 5.17/5.38 = ( ^ [A3: rat,B2: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.17/5.38 & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_not
% 5.17/5.38 thf(fact_1676_order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_num
% 5.17/5.38 = ( ^ [A3: num,B2: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.17/5.38 & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_not
% 5.17/5.38 thf(fact_1677_order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.17/5.38 & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_not
% 5.17/5.38 thf(fact_1678_order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_int
% 5.17/5.38 = ( ^ [A3: int,B2: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.17/5.38 & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_not
% 5.17/5.38 thf(fact_1679_order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_real
% 5.17/5.38 = ( ^ [A3: real,B2: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.17/5.38 & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_iff_not
% 5.17/5.38 thf(fact_1680_dense__ge__bounded,axiom,
% 5.17/5.38 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ Z @ X )
% 5.17/5.38 => ( ! [W2: rat] :
% 5.17/5.38 ( ( ord_less_rat @ Z @ W2 )
% 5.17/5.38 => ( ( ord_less_rat @ W2 @ X )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ W2 ) ) )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_ge_bounded
% 5.17/5.38 thf(fact_1681_dense__ge__bounded,axiom,
% 5.17/5.38 ! [Z: real,X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ Z @ X )
% 5.17/5.38 => ( ! [W2: real] :
% 5.17/5.38 ( ( ord_less_real @ Z @ W2 )
% 5.17/5.38 => ( ( ord_less_real @ W2 @ X )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ W2 ) ) )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_ge_bounded
% 5.17/5.38 thf(fact_1682_dense__le__bounded,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( ! [W2: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ W2 )
% 5.17/5.38 => ( ( ord_less_rat @ W2 @ Y4 )
% 5.17/5.38 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.17/5.38 => ( ord_less_eq_rat @ Y4 @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_le_bounded
% 5.17/5.38 thf(fact_1683_dense__le__bounded,axiom,
% 5.17/5.38 ! [X: real,Y4: real,Z: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( ! [W2: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ W2 )
% 5.17/5.38 => ( ( ord_less_real @ W2 @ Y4 )
% 5.17/5.38 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.17/5.38 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dense_le_bounded
% 5.17/5.38 thf(fact_1684_dual__order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_set_int
% 5.17/5.38 = ( ^ [B2: set_int,A3: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ B2 @ A3 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.order_iff_strict
% 5.17/5.38 thf(fact_1685_dual__order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_rat
% 5.17/5.38 = ( ^ [B2: rat,A3: rat] :
% 5.17/5.38 ( ( ord_less_rat @ B2 @ A3 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.order_iff_strict
% 5.17/5.38 thf(fact_1686_dual__order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_num
% 5.17/5.38 = ( ^ [B2: num,A3: num] :
% 5.17/5.38 ( ( ord_less_num @ B2 @ A3 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.order_iff_strict
% 5.17/5.38 thf(fact_1687_dual__order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_nat
% 5.17/5.38 = ( ^ [B2: nat,A3: nat] :
% 5.17/5.38 ( ( ord_less_nat @ B2 @ A3 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.order_iff_strict
% 5.17/5.38 thf(fact_1688_dual__order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_int
% 5.17/5.38 = ( ^ [B2: int,A3: int] :
% 5.17/5.38 ( ( ord_less_int @ B2 @ A3 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.order_iff_strict
% 5.17/5.38 thf(fact_1689_dual__order_Oorder__iff__strict,axiom,
% 5.17/5.38 ( ord_less_eq_real
% 5.17/5.38 = ( ^ [B2: real,A3: real] :
% 5.17/5.38 ( ( ord_less_real @ B2 @ A3 )
% 5.17/5.38 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.order_iff_strict
% 5.17/5.38 thf(fact_1690_dual__order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_set_int
% 5.17/5.38 = ( ^ [B2: set_int,A3: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_order
% 5.17/5.38 thf(fact_1691_dual__order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_rat
% 5.17/5.38 = ( ^ [B2: rat,A3: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_order
% 5.17/5.38 thf(fact_1692_dual__order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_num
% 5.17/5.38 = ( ^ [B2: num,A3: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_order
% 5.17/5.38 thf(fact_1693_dual__order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [B2: nat,A3: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_order
% 5.17/5.38 thf(fact_1694_dual__order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_int
% 5.17/5.38 = ( ^ [B2: int,A3: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_order
% 5.17/5.38 thf(fact_1695_dual__order_Ostrict__iff__order,axiom,
% 5.17/5.38 ( ord_less_real
% 5.17/5.38 = ( ^ [B2: real,A3: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.17/5.38 & ( A3 != B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_order
% 5.17/5.38 thf(fact_1696_dual__order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [B: set_int,A: set_int,C: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ B @ A )
% 5.17/5.38 => ( ( ord_less_set_int @ C @ B )
% 5.17/5.38 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans1
% 5.17/5.38 thf(fact_1697_dual__order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [B: rat,A: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.38 => ( ( ord_less_rat @ C @ B )
% 5.17/5.38 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans1
% 5.17/5.38 thf(fact_1698_dual__order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [B: num,A: num,C: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ B @ A )
% 5.17/5.38 => ( ( ord_less_num @ C @ B )
% 5.17/5.38 => ( ord_less_num @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans1
% 5.17/5.38 thf(fact_1699_dual__order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [B: nat,A: nat,C: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.38 => ( ( ord_less_nat @ C @ B )
% 5.17/5.38 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans1
% 5.17/5.38 thf(fact_1700_dual__order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [B: int,A: int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.38 => ( ( ord_less_int @ C @ B )
% 5.17/5.38 => ( ord_less_int @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans1
% 5.17/5.38 thf(fact_1701_dual__order_Ostrict__trans1,axiom,
% 5.17/5.38 ! [B: real,A: real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.38 => ( ( ord_less_real @ C @ B )
% 5.17/5.38 => ( ord_less_real @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans1
% 5.17/5.38 thf(fact_1702_dual__order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [B: set_int,A: set_int,C: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ B @ A )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ C @ B )
% 5.17/5.38 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans2
% 5.17/5.38 thf(fact_1703_dual__order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [B: rat,A: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ B @ A )
% 5.17/5.38 => ( ( ord_less_eq_rat @ C @ B )
% 5.17/5.38 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans2
% 5.17/5.38 thf(fact_1704_dual__order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [B: num,A: num,C: num] :
% 5.17/5.38 ( ( ord_less_num @ B @ A )
% 5.17/5.38 => ( ( ord_less_eq_num @ C @ B )
% 5.17/5.38 => ( ord_less_num @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans2
% 5.17/5.38 thf(fact_1705_dual__order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [B: nat,A: nat,C: nat] :
% 5.17/5.38 ( ( ord_less_nat @ B @ A )
% 5.17/5.38 => ( ( ord_less_eq_nat @ C @ B )
% 5.17/5.38 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans2
% 5.17/5.38 thf(fact_1706_dual__order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [B: int,A: int,C: int] :
% 5.17/5.38 ( ( ord_less_int @ B @ A )
% 5.17/5.38 => ( ( ord_less_eq_int @ C @ B )
% 5.17/5.38 => ( ord_less_int @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans2
% 5.17/5.38 thf(fact_1707_dual__order_Ostrict__trans2,axiom,
% 5.17/5.38 ! [B: real,A: real,C: real] :
% 5.17/5.38 ( ( ord_less_real @ B @ A )
% 5.17/5.38 => ( ( ord_less_eq_real @ C @ B )
% 5.17/5.38 => ( ord_less_real @ C @ A ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_trans2
% 5.17/5.38 thf(fact_1708_dual__order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_set_int
% 5.17/5.38 = ( ^ [B2: set_int,A3: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.17/5.38 & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_not
% 5.17/5.38 thf(fact_1709_dual__order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_rat
% 5.17/5.38 = ( ^ [B2: rat,A3: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.17/5.38 & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_not
% 5.17/5.38 thf(fact_1710_dual__order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_num
% 5.17/5.38 = ( ^ [B2: num,A3: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.17/5.38 & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_not
% 5.17/5.38 thf(fact_1711_dual__order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [B2: nat,A3: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.17/5.38 & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_not
% 5.17/5.38 thf(fact_1712_dual__order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_int
% 5.17/5.38 = ( ^ [B2: int,A3: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.17/5.38 & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_not
% 5.17/5.38 thf(fact_1713_dual__order_Ostrict__iff__not,axiom,
% 5.17/5.38 ( ord_less_real
% 5.17/5.38 = ( ^ [B2: real,A3: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.17/5.38 & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_iff_not
% 5.17/5.38 thf(fact_1714_order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [A: set_int,B: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ A @ B )
% 5.17/5.38 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_implies_order
% 5.17/5.38 thf(fact_1715_order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [A: rat,B: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A @ B )
% 5.17/5.38 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_implies_order
% 5.17/5.38 thf(fact_1716_order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [A: num,B: num] :
% 5.17/5.38 ( ( ord_less_num @ A @ B )
% 5.17/5.38 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_implies_order
% 5.17/5.38 thf(fact_1717_order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [A: nat,B: nat] :
% 5.17/5.38 ( ( ord_less_nat @ A @ B )
% 5.17/5.38 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_implies_order
% 5.17/5.38 thf(fact_1718_order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [A: int,B: int] :
% 5.17/5.38 ( ( ord_less_int @ A @ B )
% 5.17/5.38 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_implies_order
% 5.17/5.38 thf(fact_1719_order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [A: real,B: real] :
% 5.17/5.38 ( ( ord_less_real @ A @ B )
% 5.17/5.38 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.38
% 5.17/5.38 % order.strict_implies_order
% 5.17/5.38 thf(fact_1720_dual__order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [B: set_int,A: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ B @ A )
% 5.17/5.38 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_implies_order
% 5.17/5.38 thf(fact_1721_dual__order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [B: rat,A: rat] :
% 5.17/5.38 ( ( ord_less_rat @ B @ A )
% 5.17/5.38 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_implies_order
% 5.17/5.38 thf(fact_1722_dual__order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [B: num,A: num] :
% 5.17/5.38 ( ( ord_less_num @ B @ A )
% 5.17/5.38 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_implies_order
% 5.17/5.38 thf(fact_1723_dual__order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [B: nat,A: nat] :
% 5.17/5.38 ( ( ord_less_nat @ B @ A )
% 5.17/5.38 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_implies_order
% 5.17/5.38 thf(fact_1724_dual__order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [B: int,A: int] :
% 5.17/5.38 ( ( ord_less_int @ B @ A )
% 5.17/5.38 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_implies_order
% 5.17/5.38 thf(fact_1725_dual__order_Ostrict__implies__order,axiom,
% 5.17/5.38 ! [B: real,A: real] :
% 5.17/5.38 ( ( ord_less_real @ B @ A )
% 5.17/5.38 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % dual_order.strict_implies_order
% 5.17/5.38 thf(fact_1726_order__le__less,axiom,
% 5.17/5.38 ( ord_less_eq_set_int
% 5.17/5.38 = ( ^ [X3: set_int,Y6: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ X3 @ Y6 )
% 5.17/5.38 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less
% 5.17/5.38 thf(fact_1727_order__le__less,axiom,
% 5.17/5.38 ( ord_less_eq_rat
% 5.17/5.38 = ( ^ [X3: rat,Y6: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X3 @ Y6 )
% 5.17/5.38 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less
% 5.17/5.38 thf(fact_1728_order__le__less,axiom,
% 5.17/5.38 ( ord_less_eq_num
% 5.17/5.38 = ( ^ [X3: num,Y6: num] :
% 5.17/5.38 ( ( ord_less_num @ X3 @ Y6 )
% 5.17/5.38 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less
% 5.17/5.38 thf(fact_1729_order__le__less,axiom,
% 5.17/5.38 ( ord_less_eq_nat
% 5.17/5.38 = ( ^ [X3: nat,Y6: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X3 @ Y6 )
% 5.17/5.38 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less
% 5.17/5.38 thf(fact_1730_order__le__less,axiom,
% 5.17/5.38 ( ord_less_eq_int
% 5.17/5.38 = ( ^ [X3: int,Y6: int] :
% 5.17/5.38 ( ( ord_less_int @ X3 @ Y6 )
% 5.17/5.38 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less
% 5.17/5.38 thf(fact_1731_order__le__less,axiom,
% 5.17/5.38 ( ord_less_eq_real
% 5.17/5.38 = ( ^ [X3: real,Y6: real] :
% 5.17/5.38 ( ( ord_less_real @ X3 @ Y6 )
% 5.17/5.38 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less
% 5.17/5.38 thf(fact_1732_order__less__le,axiom,
% 5.17/5.38 ( ord_less_set_int
% 5.17/5.38 = ( ^ [X3: set_int,Y6: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ X3 @ Y6 )
% 5.17/5.38 & ( X3 != Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le
% 5.17/5.38 thf(fact_1733_order__less__le,axiom,
% 5.17/5.38 ( ord_less_rat
% 5.17/5.38 = ( ^ [X3: rat,Y6: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X3 @ Y6 )
% 5.17/5.38 & ( X3 != Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le
% 5.17/5.38 thf(fact_1734_order__less__le,axiom,
% 5.17/5.38 ( ord_less_num
% 5.17/5.38 = ( ^ [X3: num,Y6: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X3 @ Y6 )
% 5.17/5.38 & ( X3 != Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le
% 5.17/5.38 thf(fact_1735_order__less__le,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [X3: nat,Y6: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 5.17/5.38 & ( X3 != Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le
% 5.17/5.38 thf(fact_1736_order__less__le,axiom,
% 5.17/5.38 ( ord_less_int
% 5.17/5.38 = ( ^ [X3: int,Y6: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ X3 @ Y6 )
% 5.17/5.38 & ( X3 != Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le
% 5.17/5.38 thf(fact_1737_order__less__le,axiom,
% 5.17/5.38 ( ord_less_real
% 5.17/5.38 = ( ^ [X3: real,Y6: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ X3 @ Y6 )
% 5.17/5.38 & ( X3 != Y6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le
% 5.17/5.38 thf(fact_1738_linorder__not__le,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_rat @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_le
% 5.17/5.38 thf(fact_1739_linorder__not__le,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_num @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_le
% 5.17/5.38 thf(fact_1740_linorder__not__le,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_nat @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_le
% 5.17/5.38 thf(fact_1741_linorder__not__le,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_int @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_le
% 5.17/5.38 thf(fact_1742_linorder__not__le,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ~ ( ord_less_eq_real @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_le
% 5.17/5.38 thf(fact_1743_linorder__not__less,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ~ ( ord_less_rat @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_eq_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_less
% 5.17/5.38 thf(fact_1744_linorder__not__less,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ~ ( ord_less_num @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_eq_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_less
% 5.17/5.38 thf(fact_1745_linorder__not__less,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ~ ( ord_less_nat @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_eq_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_less
% 5.17/5.38 thf(fact_1746_linorder__not__less,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ~ ( ord_less_int @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_eq_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_less
% 5.17/5.38 thf(fact_1747_linorder__not__less,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ~ ( ord_less_real @ X @ Y4 ) )
% 5.17/5.38 = ( ord_less_eq_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_not_less
% 5.17/5.38 thf(fact_1748_order__less__imp__le,axiom,
% 5.17/5.38 ! [X: set_int,Y4: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_set_int @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_le
% 5.17/5.38 thf(fact_1749_order__less__imp__le,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_le
% 5.17/5.38 thf(fact_1750_order__less__imp__le,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_num @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_le
% 5.17/5.38 thf(fact_1751_order__less__imp__le,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_nat @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_le
% 5.17/5.38 thf(fact_1752_order__less__imp__le,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_int @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_le
% 5.17/5.38 thf(fact_1753_order__less__imp__le,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_imp_le
% 5.17/5.38 thf(fact_1754_order__le__neq__trans,axiom,
% 5.17/5.38 ! [A: set_int,B: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.38 => ( ( A != B )
% 5.17/5.38 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_neq_trans
% 5.17/5.38 thf(fact_1755_order__le__neq__trans,axiom,
% 5.17/5.38 ! [A: rat,B: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( A != B )
% 5.17/5.38 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_neq_trans
% 5.17/5.38 thf(fact_1756_order__le__neq__trans,axiom,
% 5.17/5.38 ! [A: num,B: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( A != B )
% 5.17/5.38 => ( ord_less_num @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_neq_trans
% 5.17/5.38 thf(fact_1757_order__le__neq__trans,axiom,
% 5.17/5.38 ! [A: nat,B: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.38 => ( ( A != B )
% 5.17/5.38 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_neq_trans
% 5.17/5.38 thf(fact_1758_order__le__neq__trans,axiom,
% 5.17/5.38 ! [A: int,B: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.38 => ( ( A != B )
% 5.17/5.38 => ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_neq_trans
% 5.17/5.38 thf(fact_1759_order__le__neq__trans,axiom,
% 5.17/5.38 ! [A: real,B: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.38 => ( ( A != B )
% 5.17/5.38 => ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_neq_trans
% 5.17/5.38 thf(fact_1760_order__neq__le__trans,axiom,
% 5.17/5.38 ! [A: set_int,B: set_int] :
% 5.17/5.38 ( ( A != B )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ A @ B )
% 5.17/5.38 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_neq_le_trans
% 5.17/5.38 thf(fact_1761_order__neq__le__trans,axiom,
% 5.17/5.38 ! [A: rat,B: rat] :
% 5.17/5.38 ( ( A != B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_neq_le_trans
% 5.17/5.38 thf(fact_1762_order__neq__le__trans,axiom,
% 5.17/5.38 ! [A: num,B: num] :
% 5.17/5.38 ( ( A != B )
% 5.17/5.38 => ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ord_less_num @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_neq_le_trans
% 5.17/5.38 thf(fact_1763_order__neq__le__trans,axiom,
% 5.17/5.38 ! [A: nat,B: nat] :
% 5.17/5.38 ( ( A != B )
% 5.17/5.38 => ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.38 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_neq_le_trans
% 5.17/5.38 thf(fact_1764_order__neq__le__trans,axiom,
% 5.17/5.38 ! [A: int,B: int] :
% 5.17/5.38 ( ( A != B )
% 5.17/5.38 => ( ( ord_less_eq_int @ A @ B )
% 5.17/5.38 => ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_neq_le_trans
% 5.17/5.38 thf(fact_1765_order__neq__le__trans,axiom,
% 5.17/5.38 ! [A: real,B: real] :
% 5.17/5.38 ( ( A != B )
% 5.17/5.38 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.38 => ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_neq_le_trans
% 5.17/5.38 thf(fact_1766_order__le__less__trans,axiom,
% 5.17/5.38 ! [X: set_int,Y4: set_int,Z: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_set_int @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_trans
% 5.17/5.38 thf(fact_1767_order__le__less__trans,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_rat @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_trans
% 5.17/5.38 thf(fact_1768_order__le__less__trans,axiom,
% 5.17/5.38 ! [X: num,Y4: num,Z: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_num @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_trans
% 5.17/5.38 thf(fact_1769_order__le__less__trans,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_nat @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_trans
% 5.17/5.38 thf(fact_1770_order__le__less__trans,axiom,
% 5.17/5.38 ! [X: int,Y4: int,Z: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_int @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_trans
% 5.17/5.38 thf(fact_1771_order__le__less__trans,axiom,
% 5.17/5.38 ! [X: real,Y4: real,Z: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_real @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_trans
% 5.17/5.38 thf(fact_1772_order__less__le__trans,axiom,
% 5.17/5.38 ! [X: set_int,Y4: set_int,Z: set_int] :
% 5.17/5.38 ( ( ord_less_set_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_trans
% 5.17/5.38 thf(fact_1773_order__less__le__trans,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_rat @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_trans
% 5.17/5.38 thf(fact_1774_order__less__le__trans,axiom,
% 5.17/5.38 ! [X: num,Y4: num,Z: num] :
% 5.17/5.38 ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_num @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_trans
% 5.17/5.38 thf(fact_1775_order__less__le__trans,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_nat @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_trans
% 5.17/5.38 thf(fact_1776_order__less__le__trans,axiom,
% 5.17/5.38 ! [X: int,Y4: int,Z: int] :
% 5.17/5.38 ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_int @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_trans
% 5.17/5.38 thf(fact_1777_order__less__le__trans,axiom,
% 5.17/5.38 ! [X: real,Y4: real,Z: real] :
% 5.17/5.38 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_eq_real @ Y4 @ Z )
% 5.17/5.38 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_trans
% 5.17/5.38 thf(fact_1778_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_real @ B @ C )
% 5.17/5.38 => ( ! [X4: real,Y: real] :
% 5.17/5.38 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1779_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1780_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1781_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_nat @ B @ C )
% 5.17/5.38 => ( ! [X4: nat,Y: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1782_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_int @ B @ C )
% 5.17/5.38 => ( ! [X4: int,Y: int] :
% 5.17/5.38 ( ( ord_less_int @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1783_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: num,F: real > num,B: real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_real @ B @ C )
% 5.17/5.38 => ( ! [X4: real,Y: real] :
% 5.17/5.38 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1784_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1785_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: num,F: num > num,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1786_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_nat @ B @ C )
% 5.17/5.38 => ( ! [X4: nat,Y: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1787_order__le__less__subst1,axiom,
% 5.17/5.38 ! [A: num,F: int > num,B: int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_int @ B @ C )
% 5.17/5.38 => ( ! [X4: int,Y: int] :
% 5.17/5.38 ( ( ord_less_int @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst1
% 5.17/5.38 thf(fact_1788_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1789_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1790_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1791_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1792_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1793_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1794_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > num,C: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1795_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1796_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1797_order__le__less__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_less_subst2
% 5.17/5.38 thf(fact_1798_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1799_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1800_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1801_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1802_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1803_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1804_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: num,F: num > num,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1805_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1806_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: int,F: num > int,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1807_order__less__le__subst1,axiom,
% 5.17/5.38 ! [A: real,F: num > real,B: num,C: num] :
% 5.17/5.38 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.17/5.38 => ( ( ord_less_eq_num @ B @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst1
% 5.17/5.38 thf(fact_1808_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_real @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: real,Y: real] :
% 5.17/5.38 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1809_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1810_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1811_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_nat @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: nat,Y: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1812_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.17/5.38 ( ( ord_less_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: int,Y: int] :
% 5.17/5.38 ( ( ord_less_int @ X4 @ Y )
% 5.17/5.38 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1813_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: real,B: real,F: real > num,C: num] :
% 5.17/5.38 ( ( ord_less_real @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: real,Y: real] :
% 5.17/5.38 ( ( ord_less_real @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1814_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.17/5.38 ( ( ord_less_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: rat,Y: rat] :
% 5.17/5.38 ( ( ord_less_rat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1815_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: num,B: num,F: num > num,C: num] :
% 5.17/5.38 ( ( ord_less_num @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: num,Y: num] :
% 5.17/5.38 ( ( ord_less_num @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1816_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.17/5.38 ( ( ord_less_nat @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: nat,Y: nat] :
% 5.17/5.38 ( ( ord_less_nat @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1817_order__less__le__subst2,axiom,
% 5.17/5.38 ! [A: int,B: int,F: int > num,C: num] :
% 5.17/5.38 ( ( ord_less_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.17/5.38 => ( ! [X4: int,Y: int] :
% 5.17/5.38 ( ( ord_less_int @ X4 @ Y )
% 5.17/5.38 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y ) ) )
% 5.17/5.38 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_less_le_subst2
% 5.17/5.38 thf(fact_1818_linorder__le__less__linear,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.38 | ( ord_less_rat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_le_less_linear
% 5.17/5.38 thf(fact_1819_linorder__le__less__linear,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.38 | ( ord_less_num @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_le_less_linear
% 5.17/5.38 thf(fact_1820_linorder__le__less__linear,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.38 | ( ord_less_nat @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_le_less_linear
% 5.17/5.38 thf(fact_1821_linorder__le__less__linear,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.38 | ( ord_less_int @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_le_less_linear
% 5.17/5.38 thf(fact_1822_linorder__le__less__linear,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.38 | ( ord_less_real @ Y4 @ X ) ) ).
% 5.17/5.38
% 5.17/5.38 % linorder_le_less_linear
% 5.17/5.38 thf(fact_1823_order__le__imp__less__or__eq,axiom,
% 5.17/5.38 ! [X: set_int,Y4: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_set_int @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_imp_less_or_eq
% 5.17/5.38 thf(fact_1824_order__le__imp__less__or__eq,axiom,
% 5.17/5.38 ! [X: rat,Y4: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_imp_less_or_eq
% 5.17/5.38 thf(fact_1825_order__le__imp__less__or__eq,axiom,
% 5.17/5.38 ! [X: num,Y4: num] :
% 5.17/5.38 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_num @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_imp_less_or_eq
% 5.17/5.38 thf(fact_1826_order__le__imp__less__or__eq,axiom,
% 5.17/5.38 ! [X: nat,Y4: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_imp_less_or_eq
% 5.17/5.38 thf(fact_1827_order__le__imp__less__or__eq,axiom,
% 5.17/5.38 ! [X: int,Y4: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_int @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_imp_less_or_eq
% 5.17/5.38 thf(fact_1828_order__le__imp__less__or__eq,axiom,
% 5.17/5.38 ! [X: real,Y4: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.38 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.38 | ( X = Y4 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % order_le_imp_less_or_eq
% 5.17/5.38 thf(fact_1829_less__numeral__extra_I3_J,axiom,
% 5.17/5.38 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(3)
% 5.17/5.38 thf(fact_1830_less__numeral__extra_I3_J,axiom,
% 5.17/5.38 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(3)
% 5.17/5.38 thf(fact_1831_less__numeral__extra_I3_J,axiom,
% 5.17/5.38 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(3)
% 5.17/5.38 thf(fact_1832_less__numeral__extra_I3_J,axiom,
% 5.17/5.38 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.17/5.38
% 5.17/5.38 % less_numeral_extra(3)
% 5.17/5.38 thf(fact_1833_field__lbound__gt__zero,axiom,
% 5.17/5.38 ! [D1: real,D22: real] :
% 5.17/5.38 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.17/5.38 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.17/5.38 => ? [E: real] :
% 5.17/5.38 ( ( ord_less_real @ zero_zero_real @ E )
% 5.17/5.38 & ( ord_less_real @ E @ D1 )
% 5.17/5.38 & ( ord_less_real @ E @ D22 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % field_lbound_gt_zero
% 5.17/5.38 thf(fact_1834_field__lbound__gt__zero,axiom,
% 5.17/5.38 ! [D1: rat,D22: rat] :
% 5.17/5.38 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.17/5.38 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.17/5.38 => ? [E: rat] :
% 5.17/5.38 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.17/5.38 & ( ord_less_rat @ E @ D1 )
% 5.17/5.38 & ( ord_less_rat @ E @ D22 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % field_lbound_gt_zero
% 5.17/5.38 thf(fact_1835_zero__less__iff__neq__zero,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.38 = ( N != zero_zero_nat ) ) ).
% 5.17/5.38
% 5.17/5.38 % zero_less_iff_neq_zero
% 5.17/5.38 thf(fact_1836_gr__implies__not__zero,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( N != zero_zero_nat ) ) ).
% 5.17/5.38
% 5.17/5.38 % gr_implies_not_zero
% 5.17/5.38 thf(fact_1837_not__less__zero,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.17/5.38
% 5.17/5.38 % not_less_zero
% 5.17/5.38 thf(fact_1838_gr__zeroI,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ( ( N != zero_zero_nat )
% 5.17/5.38 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % gr_zeroI
% 5.17/5.38 thf(fact_1839_zdiff__int__split,axiom,
% 5.17/5.38 ! [P: int > $o,X: nat,Y4: nat] :
% 5.17/5.38 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y4 ) ) )
% 5.17/5.38 = ( ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.38 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) )
% 5.17/5.38 & ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.38 => ( P @ zero_zero_int ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % zdiff_int_split
% 5.17/5.38 thf(fact_1840_diff__strict__right__mono,axiom,
% 5.17/5.38 ! [A: real,B: real,C: real] :
% 5.17/5.38 ( ( ord_less_real @ A @ B )
% 5.17/5.38 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_right_mono
% 5.17/5.38 thf(fact_1841_diff__strict__right__mono,axiom,
% 5.17/5.38 ! [A: rat,B: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A @ B )
% 5.17/5.38 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_right_mono
% 5.17/5.38 thf(fact_1842_diff__strict__right__mono,axiom,
% 5.17/5.38 ! [A: int,B: int,C: int] :
% 5.17/5.38 ( ( ord_less_int @ A @ B )
% 5.17/5.38 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_right_mono
% 5.17/5.38 thf(fact_1843_diff__strict__left__mono,axiom,
% 5.17/5.38 ! [B: real,A: real,C: real] :
% 5.17/5.38 ( ( ord_less_real @ B @ A )
% 5.17/5.38 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_left_mono
% 5.17/5.38 thf(fact_1844_diff__strict__left__mono,axiom,
% 5.17/5.38 ! [B: rat,A: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ B @ A )
% 5.17/5.38 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_left_mono
% 5.17/5.38 thf(fact_1845_diff__strict__left__mono,axiom,
% 5.17/5.38 ! [B: int,A: int,C: int] :
% 5.17/5.38 ( ( ord_less_int @ B @ A )
% 5.17/5.38 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_left_mono
% 5.17/5.38 thf(fact_1846_diff__eq__diff__less,axiom,
% 5.17/5.38 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.38 ( ( ( minus_minus_real @ A @ B )
% 5.17/5.38 = ( minus_minus_real @ C @ D ) )
% 5.17/5.38 => ( ( ord_less_real @ A @ B )
% 5.17/5.38 = ( ord_less_real @ C @ D ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_eq_diff_less
% 5.17/5.38 thf(fact_1847_diff__eq__diff__less,axiom,
% 5.17/5.38 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.38 ( ( ( minus_minus_rat @ A @ B )
% 5.17/5.38 = ( minus_minus_rat @ C @ D ) )
% 5.17/5.38 => ( ( ord_less_rat @ A @ B )
% 5.17/5.38 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_eq_diff_less
% 5.17/5.38 thf(fact_1848_diff__eq__diff__less,axiom,
% 5.17/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.38 ( ( ( minus_minus_int @ A @ B )
% 5.17/5.38 = ( minus_minus_int @ C @ D ) )
% 5.17/5.38 => ( ( ord_less_int @ A @ B )
% 5.17/5.38 = ( ord_less_int @ C @ D ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_eq_diff_less
% 5.17/5.38 thf(fact_1849_diff__strict__mono,axiom,
% 5.17/5.38 ! [A: real,B: real,D: real,C: real] :
% 5.17/5.38 ( ( ord_less_real @ A @ B )
% 5.17/5.38 => ( ( ord_less_real @ D @ C )
% 5.17/5.38 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_mono
% 5.17/5.38 thf(fact_1850_diff__strict__mono,axiom,
% 5.17/5.38 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ A @ B )
% 5.17/5.38 => ( ( ord_less_rat @ D @ C )
% 5.17/5.38 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_mono
% 5.17/5.38 thf(fact_1851_diff__strict__mono,axiom,
% 5.17/5.38 ! [A: int,B: int,D: int,C: int] :
% 5.17/5.38 ( ( ord_less_int @ A @ B )
% 5.17/5.38 => ( ( ord_less_int @ D @ C )
% 5.17/5.38 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_strict_mono
% 5.17/5.38 thf(fact_1852_double__diff,axiom,
% 5.17/5.38 ! [A2: set_nat,B4: set_nat,C2: set_nat] :
% 5.17/5.38 ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 5.17/5.38 => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 5.17/5.38 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 5.17/5.38 = A2 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % double_diff
% 5.17/5.38 thf(fact_1853_double__diff,axiom,
% 5.17/5.38 ! [A2: set_int,B4: set_int,C2: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ B4 @ C2 )
% 5.17/5.38 => ( ( minus_minus_set_int @ B4 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 5.17/5.38 = A2 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % double_diff
% 5.17/5.38 thf(fact_1854_Diff__subset,axiom,
% 5.17/5.38 ! [A2: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ A2 ) ).
% 5.17/5.38
% 5.17/5.38 % Diff_subset
% 5.17/5.38 thf(fact_1855_Diff__subset,axiom,
% 5.17/5.38 ! [A2: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B4 ) @ A2 ) ).
% 5.17/5.38
% 5.17/5.38 % Diff_subset
% 5.17/5.38 thf(fact_1856_Diff__mono,axiom,
% 5.17/5.38 ! [A2: set_nat,C2: set_nat,D3: set_nat,B4: set_nat] :
% 5.17/5.38 ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 5.17/5.38 => ( ( ord_less_eq_set_nat @ D3 @ B4 )
% 5.17/5.38 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ ( minus_minus_set_nat @ C2 @ D3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Diff_mono
% 5.17/5.38 thf(fact_1857_Diff__mono,axiom,
% 5.17/5.38 ! [A2: set_int,C2: set_int,D3: set_int,B4: set_int] :
% 5.17/5.38 ( ( ord_less_eq_set_int @ A2 @ C2 )
% 5.17/5.38 => ( ( ord_less_eq_set_int @ D3 @ B4 )
% 5.17/5.38 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B4 ) @ ( minus_minus_set_int @ C2 @ D3 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Diff_mono
% 5.17/5.38 thf(fact_1858_le__numeral__extra_I4_J,axiom,
% 5.17/5.38 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.17/5.38
% 5.17/5.38 % le_numeral_extra(4)
% 5.17/5.38 thf(fact_1859_le__numeral__extra_I4_J,axiom,
% 5.17/5.38 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.17/5.38
% 5.17/5.38 % le_numeral_extra(4)
% 5.17/5.38 thf(fact_1860_le__numeral__extra_I4_J,axiom,
% 5.17/5.38 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.17/5.38
% 5.17/5.38 % le_numeral_extra(4)
% 5.17/5.38 thf(fact_1861_le__numeral__extra_I4_J,axiom,
% 5.17/5.38 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.17/5.38
% 5.17/5.38 % le_numeral_extra(4)
% 5.17/5.38 thf(fact_1862_Nat_OlessE,axiom,
% 5.17/5.38 ! [I: nat,K: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I @ K )
% 5.17/5.38 => ( ( K
% 5.17/5.38 != ( suc @ I ) )
% 5.17/5.38 => ~ ! [J2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I @ J2 )
% 5.17/5.38 => ( K
% 5.17/5.38 != ( suc @ J2 ) ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Nat.lessE
% 5.17/5.38 thf(fact_1863_Suc__lessD,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % Suc_lessD
% 5.17/5.38 thf(fact_1864_Suc__lessE,axiom,
% 5.17/5.38 ! [I: nat,K: nat] :
% 5.17/5.38 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.17/5.38 => ~ ! [J2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I @ J2 )
% 5.17/5.38 => ( K
% 5.17/5.38 != ( suc @ J2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Suc_lessE
% 5.17/5.38 thf(fact_1865_Suc__lessI,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ( ( suc @ M )
% 5.17/5.38 != N )
% 5.17/5.38 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Suc_lessI
% 5.17/5.38 thf(fact_1866_less__SucE,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.17/5.38 => ( ~ ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( M = N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_SucE
% 5.17/5.38 thf(fact_1867_less__SucI,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_SucI
% 5.17/5.38 thf(fact_1868_Ex__less__Suc,axiom,
% 5.17/5.38 ! [N: nat,P: nat > $o] :
% 5.17/5.38 ( ( ? [I2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.17/5.38 & ( P @ I2 ) ) )
% 5.17/5.38 = ( ( P @ N )
% 5.17/5.38 | ? [I2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I2 @ N )
% 5.17/5.38 & ( P @ I2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Ex_less_Suc
% 5.17/5.38 thf(fact_1869_less__Suc__eq,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.17/5.38 = ( ( ord_less_nat @ M @ N )
% 5.17/5.38 | ( M = N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_Suc_eq
% 5.17/5.38 thf(fact_1870_not__less__eq,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.17/5.38 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_less_eq
% 5.17/5.38 thf(fact_1871_All__less__Suc,axiom,
% 5.17/5.38 ! [N: nat,P: nat > $o] :
% 5.17/5.38 ( ( ! [I2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.17/5.38 => ( P @ I2 ) ) )
% 5.17/5.38 = ( ( P @ N )
% 5.17/5.38 & ! [I2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I2 @ N )
% 5.17/5.38 => ( P @ I2 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % All_less_Suc
% 5.17/5.38 thf(fact_1872_Suc__less__eq2,axiom,
% 5.17/5.38 ! [N: nat,M: nat] :
% 5.17/5.38 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.17/5.38 = ( ? [M6: nat] :
% 5.17/5.38 ( ( M
% 5.17/5.38 = ( suc @ M6 ) )
% 5.17/5.38 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % Suc_less_eq2
% 5.17/5.38 thf(fact_1873_less__antisym,axiom,
% 5.17/5.38 ! [N: nat,M: nat] :
% 5.17/5.38 ( ~ ( ord_less_nat @ N @ M )
% 5.17/5.38 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.17/5.38 => ( M = N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_antisym
% 5.17/5.38 thf(fact_1874_Suc__less__SucD,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % Suc_less_SucD
% 5.17/5.38 thf(fact_1875_less__trans__Suc,axiom,
% 5.17/5.38 ! [I: nat,J: nat,K: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I @ J )
% 5.17/5.38 => ( ( ord_less_nat @ J @ K )
% 5.17/5.38 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_trans_Suc
% 5.17/5.38 thf(fact_1876_less__Suc__induct,axiom,
% 5.17/5.38 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.17/5.38 ( ( ord_less_nat @ I @ J )
% 5.17/5.38 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.17/5.38 => ( ! [I3: nat,J2: nat,K2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I3 @ J2 )
% 5.17/5.38 => ( ( ord_less_nat @ J2 @ K2 )
% 5.17/5.38 => ( ( P @ I3 @ J2 )
% 5.17/5.38 => ( ( P @ J2 @ K2 )
% 5.17/5.38 => ( P @ I3 @ K2 ) ) ) ) )
% 5.17/5.38 => ( P @ I @ J ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_Suc_induct
% 5.17/5.38 thf(fact_1877_strict__inc__induct,axiom,
% 5.17/5.38 ! [I: nat,J: nat,P: nat > $o] :
% 5.17/5.38 ( ( ord_less_nat @ I @ J )
% 5.17/5.38 => ( ! [I3: nat] :
% 5.17/5.38 ( ( J
% 5.17/5.38 = ( suc @ I3 ) )
% 5.17/5.38 => ( P @ I3 ) )
% 5.17/5.38 => ( ! [I3: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I3 @ J )
% 5.17/5.38 => ( ( P @ ( suc @ I3 ) )
% 5.17/5.38 => ( P @ I3 ) ) )
% 5.17/5.38 => ( P @ I ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % strict_inc_induct
% 5.17/5.38 thf(fact_1878_not__less__less__Suc__eq,axiom,
% 5.17/5.38 ! [N: nat,M: nat] :
% 5.17/5.38 ( ~ ( ord_less_nat @ N @ M )
% 5.17/5.38 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.17/5.38 = ( N = M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_less_less_Suc_eq
% 5.17/5.38 thf(fact_1879_zero__neq__one,axiom,
% 5.17/5.38 zero_zero_complex != one_one_complex ).
% 5.17/5.38
% 5.17/5.38 % zero_neq_one
% 5.17/5.38 thf(fact_1880_zero__neq__one,axiom,
% 5.17/5.38 zero_zero_real != one_one_real ).
% 5.17/5.38
% 5.17/5.38 % zero_neq_one
% 5.17/5.38 thf(fact_1881_zero__neq__one,axiom,
% 5.17/5.38 zero_zero_rat != one_one_rat ).
% 5.17/5.38
% 5.17/5.38 % zero_neq_one
% 5.17/5.38 thf(fact_1882_zero__neq__one,axiom,
% 5.17/5.38 zero_zero_nat != one_one_nat ).
% 5.17/5.38
% 5.17/5.38 % zero_neq_one
% 5.17/5.38 thf(fact_1883_zero__neq__one,axiom,
% 5.17/5.38 zero_zero_int != one_one_int ).
% 5.17/5.38
% 5.17/5.38 % zero_neq_one
% 5.17/5.38 thf(fact_1884_bot__nat__0_Oextremum__strict,axiom,
% 5.17/5.38 ! [A: nat] :
% 5.17/5.38 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.17/5.38
% 5.17/5.38 % bot_nat_0.extremum_strict
% 5.17/5.38 thf(fact_1885_gr0I,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ( ( N != zero_zero_nat )
% 5.17/5.38 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % gr0I
% 5.17/5.38 thf(fact_1886_not__gr0,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.17/5.38 = ( N = zero_zero_nat ) ) ).
% 5.17/5.38
% 5.17/5.38 % not_gr0
% 5.17/5.38 thf(fact_1887_not__less0,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.17/5.38
% 5.17/5.38 % not_less0
% 5.17/5.38 thf(fact_1888_less__zeroE,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.17/5.38
% 5.17/5.38 % less_zeroE
% 5.17/5.38 thf(fact_1889_gr__implies__not0,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( N != zero_zero_nat ) ) ).
% 5.17/5.38
% 5.17/5.38 % gr_implies_not0
% 5.17/5.38 thf(fact_1890_infinite__descent0,axiom,
% 5.17/5.38 ! [P: nat > $o,N: nat] :
% 5.17/5.38 ( ( P @ zero_zero_nat )
% 5.17/5.38 => ( ! [N2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.38 => ( ~ ( P @ N2 )
% 5.17/5.38 => ? [M2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M2 @ N2 )
% 5.17/5.38 & ~ ( P @ M2 ) ) ) )
% 5.17/5.38 => ( P @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % infinite_descent0
% 5.17/5.38 thf(fact_1891_comm__monoid__mult__class_Omult__1,axiom,
% 5.17/5.38 ! [A: complex] :
% 5.17/5.38 ( ( times_times_complex @ one_one_complex @ A )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % comm_monoid_mult_class.mult_1
% 5.17/5.38 thf(fact_1892_comm__monoid__mult__class_Omult__1,axiom,
% 5.17/5.38 ! [A: real] :
% 5.17/5.38 ( ( times_times_real @ one_one_real @ A )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % comm_monoid_mult_class.mult_1
% 5.17/5.38 thf(fact_1893_comm__monoid__mult__class_Omult__1,axiom,
% 5.17/5.38 ! [A: rat] :
% 5.17/5.38 ( ( times_times_rat @ one_one_rat @ A )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % comm_monoid_mult_class.mult_1
% 5.17/5.38 thf(fact_1894_comm__monoid__mult__class_Omult__1,axiom,
% 5.17/5.38 ! [A: nat] :
% 5.17/5.38 ( ( times_times_nat @ one_one_nat @ A )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % comm_monoid_mult_class.mult_1
% 5.17/5.38 thf(fact_1895_comm__monoid__mult__class_Omult__1,axiom,
% 5.17/5.38 ! [A: int] :
% 5.17/5.38 ( ( times_times_int @ one_one_int @ A )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % comm_monoid_mult_class.mult_1
% 5.17/5.38 thf(fact_1896_mult_Ocomm__neutral,axiom,
% 5.17/5.38 ! [A: complex] :
% 5.17/5.38 ( ( times_times_complex @ A @ one_one_complex )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % mult.comm_neutral
% 5.17/5.38 thf(fact_1897_mult_Ocomm__neutral,axiom,
% 5.17/5.38 ! [A: real] :
% 5.17/5.38 ( ( times_times_real @ A @ one_one_real )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % mult.comm_neutral
% 5.17/5.38 thf(fact_1898_mult_Ocomm__neutral,axiom,
% 5.17/5.38 ! [A: rat] :
% 5.17/5.38 ( ( times_times_rat @ A @ one_one_rat )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % mult.comm_neutral
% 5.17/5.38 thf(fact_1899_mult_Ocomm__neutral,axiom,
% 5.17/5.38 ! [A: nat] :
% 5.17/5.38 ( ( times_times_nat @ A @ one_one_nat )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % mult.comm_neutral
% 5.17/5.38 thf(fact_1900_mult_Ocomm__neutral,axiom,
% 5.17/5.38 ! [A: int] :
% 5.17/5.38 ( ( times_times_int @ A @ one_one_int )
% 5.17/5.38 = A ) ).
% 5.17/5.38
% 5.17/5.38 % mult.comm_neutral
% 5.17/5.38 thf(fact_1901_int__distrib_I4_J,axiom,
% 5.17/5.38 ! [W: int,Z1: int,Z22: int] :
% 5.17/5.38 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.17/5.38 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % int_distrib(4)
% 5.17/5.38 thf(fact_1902_int__distrib_I3_J,axiom,
% 5.17/5.38 ! [Z1: int,Z22: int,W: int] :
% 5.17/5.38 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.17/5.38 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % int_distrib(3)
% 5.17/5.38 thf(fact_1903_less__mono__imp__le__mono,axiom,
% 5.17/5.38 ! [F: nat > nat,I: nat,J: nat] :
% 5.17/5.38 ( ! [I3: nat,J2: nat] :
% 5.17/5.38 ( ( ord_less_nat @ I3 @ J2 )
% 5.17/5.38 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 5.17/5.38 => ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.38 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_mono_imp_le_mono
% 5.17/5.38 thf(fact_1904_le__neq__implies__less,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.38 => ( ( M != N )
% 5.17/5.38 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % le_neq_implies_less
% 5.17/5.38 thf(fact_1905_less__or__eq__imp__le,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ( ord_less_nat @ M @ N )
% 5.17/5.38 | ( M = N ) )
% 5.17/5.38 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_or_eq_imp_le
% 5.17/5.38 thf(fact_1906_le__eq__less__or__eq,axiom,
% 5.17/5.38 ( ord_less_eq_nat
% 5.17/5.38 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M5 @ N4 )
% 5.17/5.38 | ( M5 = N4 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % le_eq_less_or_eq
% 5.17/5.38 thf(fact_1907_less__imp__le__nat,axiom,
% 5.17/5.38 ! [M: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_imp_le_nat
% 5.17/5.38 thf(fact_1908_nat__less__le,axiom,
% 5.17/5.38 ( ord_less_nat
% 5.17/5.38 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.38 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.17/5.38 & ( M5 != N4 ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % nat_less_le
% 5.17/5.38 thf(fact_1909_int__diff__cases,axiom,
% 5.17/5.38 ! [Z: int] :
% 5.17/5.38 ~ ! [M4: nat,N2: nat] :
% 5.17/5.38 ( Z
% 5.17/5.38 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % int_diff_cases
% 5.17/5.38 thf(fact_1910_diff__less__mono2,axiom,
% 5.17/5.38 ! [M: nat,N: nat,L: nat] :
% 5.17/5.38 ( ( ord_less_nat @ M @ N )
% 5.17/5.38 => ( ( ord_less_nat @ M @ L )
% 5.17/5.38 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % diff_less_mono2
% 5.17/5.38 thf(fact_1911_less__imp__diff__less,axiom,
% 5.17/5.38 ! [J: nat,K: nat,N: nat] :
% 5.17/5.38 ( ( ord_less_nat @ J @ K )
% 5.17/5.38 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.17/5.38
% 5.17/5.38 % less_imp_diff_less
% 5.17/5.38 thf(fact_1912_dvd__unit__imp__unit,axiom,
% 5.17/5.38 ! [A: code_integer,B: code_integer] :
% 5.17/5.38 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.38 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.38 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dvd_unit_imp_unit
% 5.17/5.38 thf(fact_1913_dvd__unit__imp__unit,axiom,
% 5.17/5.38 ! [A: nat,B: nat] :
% 5.17/5.38 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.38 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.38 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dvd_unit_imp_unit
% 5.17/5.38 thf(fact_1914_dvd__unit__imp__unit,axiom,
% 5.17/5.38 ! [A: int,B: int] :
% 5.17/5.38 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.38 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.38 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dvd_unit_imp_unit
% 5.17/5.38 thf(fact_1915_unit__imp__dvd,axiom,
% 5.17/5.38 ! [B: code_integer,A: code_integer] :
% 5.17/5.38 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.38 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % unit_imp_dvd
% 5.17/5.38 thf(fact_1916_unit__imp__dvd,axiom,
% 5.17/5.38 ! [B: nat,A: nat] :
% 5.17/5.38 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.38 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % unit_imp_dvd
% 5.17/5.38 thf(fact_1917_unit__imp__dvd,axiom,
% 5.17/5.38 ! [B: int,A: int] :
% 5.17/5.38 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.38 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.17/5.38
% 5.17/5.38 % unit_imp_dvd
% 5.17/5.38 thf(fact_1918_one__dvd,axiom,
% 5.17/5.38 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.17/5.38
% 5.17/5.38 % one_dvd
% 5.17/5.38 thf(fact_1919_one__dvd,axiom,
% 5.17/5.38 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.17/5.38
% 5.17/5.38 % one_dvd
% 5.17/5.38 thf(fact_1920_one__dvd,axiom,
% 5.17/5.38 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.17/5.38
% 5.17/5.38 % one_dvd
% 5.17/5.38 thf(fact_1921_one__dvd,axiom,
% 5.17/5.38 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.17/5.38
% 5.17/5.38 % one_dvd
% 5.17/5.38 thf(fact_1922_one__dvd,axiom,
% 5.17/5.38 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.17/5.38
% 5.17/5.38 % one_dvd
% 5.17/5.38 thf(fact_1923_one__dvd,axiom,
% 5.17/5.38 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.17/5.38
% 5.17/5.38 % one_dvd
% 5.17/5.38 thf(fact_1924_zdvd__zdiffD,axiom,
% 5.17/5.38 ! [K: int,M: int,N: int] :
% 5.17/5.38 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 5.17/5.38 => ( ( dvd_dvd_int @ K @ N )
% 5.17/5.38 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % zdvd_zdiffD
% 5.17/5.38 thf(fact_1925_nat__mult__1__right,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ( ( times_times_nat @ N @ one_one_nat )
% 5.17/5.38 = N ) ).
% 5.17/5.38
% 5.17/5.38 % nat_mult_1_right
% 5.17/5.38 thf(fact_1926_nat__mult__1,axiom,
% 5.17/5.38 ! [N: nat] :
% 5.17/5.38 ( ( times_times_nat @ one_one_nat @ N )
% 5.17/5.38 = N ) ).
% 5.17/5.38
% 5.17/5.38 % nat_mult_1
% 5.17/5.38 thf(fact_1927_dvd__pos__nat,axiom,
% 5.17/5.38 ! [N: nat,M: nat] :
% 5.17/5.38 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.38 => ( ( dvd_dvd_nat @ M @ N )
% 5.17/5.38 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % dvd_pos_nat
% 5.17/5.38 thf(fact_1928_mult__le__cancel__left1,axiom,
% 5.17/5.38 ! [C: rat,B: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.17/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.17/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_left1
% 5.17/5.38 thf(fact_1929_mult__le__cancel__left1,axiom,
% 5.17/5.38 ! [C: int,B: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.17/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.17/5.38 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_left1
% 5.17/5.38 thf(fact_1930_mult__le__cancel__left1,axiom,
% 5.17/5.38 ! [C: real,B: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.17/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.17/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_left1
% 5.17/5.38 thf(fact_1931_mult__le__cancel__left2,axiom,
% 5.17/5.38 ! [C: rat,A: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.17/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.17/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_left2
% 5.17/5.38 thf(fact_1932_mult__le__cancel__left2,axiom,
% 5.17/5.38 ! [C: int,A: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.17/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.17/5.38 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_left2
% 5.17/5.38 thf(fact_1933_mult__le__cancel__left2,axiom,
% 5.17/5.38 ! [C: real,A: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.17/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.17/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_left2
% 5.17/5.38 thf(fact_1934_mult__le__cancel__right1,axiom,
% 5.17/5.38 ! [C: rat,B: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.17/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.17/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_right1
% 5.17/5.38 thf(fact_1935_mult__le__cancel__right1,axiom,
% 5.17/5.38 ! [C: int,B: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.17/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.17/5.38 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_right1
% 5.17/5.38 thf(fact_1936_mult__le__cancel__right1,axiom,
% 5.17/5.38 ! [C: real,B: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.17/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.17/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_right1
% 5.17/5.38 thf(fact_1937_mult__le__cancel__right2,axiom,
% 5.17/5.38 ! [A: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.17/5.38 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.17/5.38 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_right2
% 5.17/5.38 thf(fact_1938_mult__le__cancel__right2,axiom,
% 5.17/5.38 ! [A: int,C: int] :
% 5.17/5.38 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.17/5.38 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.17/5.38 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_right2
% 5.17/5.38 thf(fact_1939_mult__le__cancel__right2,axiom,
% 5.17/5.38 ! [A: real,C: real] :
% 5.17/5.38 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.17/5.38 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.17/5.38 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_le_cancel_right2
% 5.17/5.38 thf(fact_1940_mult__less__cancel__left1,axiom,
% 5.17/5.38 ! [C: rat,B: rat] :
% 5.17/5.38 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.17/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.17/5.38 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_left1
% 5.17/5.38 thf(fact_1941_mult__less__cancel__left1,axiom,
% 5.17/5.38 ! [C: int,B: int] :
% 5.17/5.38 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.17/5.38 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_int @ one_one_int @ B ) )
% 5.17/5.38 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_left1
% 5.17/5.38 thf(fact_1942_mult__less__cancel__left1,axiom,
% 5.17/5.38 ! [C: real,B: real] :
% 5.17/5.38 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.17/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_real @ one_one_real @ B ) )
% 5.17/5.38 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_left1
% 5.17/5.38 thf(fact_1943_mult__less__cancel__left2,axiom,
% 5.17/5.38 ! [C: rat,A: rat] :
% 5.17/5.38 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.17/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.17/5.38 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_left2
% 5.17/5.38 thf(fact_1944_mult__less__cancel__left2,axiom,
% 5.17/5.38 ! [C: int,A: int] :
% 5.17/5.38 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.17/5.38 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_int @ A @ one_one_int ) )
% 5.17/5.38 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_left2
% 5.17/5.38 thf(fact_1945_mult__less__cancel__left2,axiom,
% 5.17/5.38 ! [C: real,A: real] :
% 5.17/5.38 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.17/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_real @ A @ one_one_real ) )
% 5.17/5.38 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_left2
% 5.17/5.38 thf(fact_1946_mult__less__cancel__right1,axiom,
% 5.17/5.38 ! [C: rat,B: rat] :
% 5.17/5.38 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.17/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.17/5.38 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.38 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_right1
% 5.17/5.38 thf(fact_1947_mult__less__cancel__right1,axiom,
% 5.17/5.38 ! [C: int,B: int] :
% 5.17/5.38 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.17/5.38 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.38 => ( ord_less_int @ one_one_int @ B ) )
% 5.17/5.38 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.38 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_right1
% 5.17/5.38 thf(fact_1948_mult__less__cancel__right1,axiom,
% 5.17/5.38 ! [C: real,B: real] :
% 5.17/5.38 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.17/5.38 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.38 => ( ord_less_real @ one_one_real @ B ) )
% 5.17/5.38 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.38 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.17/5.38
% 5.17/5.38 % mult_less_cancel_right1
% 5.17/5.38 thf(fact_1949_mult__less__cancel__right2,axiom,
% 5.17/5.38 ! [A: rat,C: rat] :
% 5.17/5.38 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.17/5.38 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.38 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.17/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right2
% 5.17/5.39 thf(fact_1950_mult__less__cancel__right2,axiom,
% 5.17/5.39 ! [A: int,C: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.17/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ A @ one_one_int ) )
% 5.17/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right2
% 5.17/5.39 thf(fact_1951_mult__less__cancel__right2,axiom,
% 5.17/5.39 ! [A: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.17/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ A @ one_one_real ) )
% 5.17/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right2
% 5.17/5.39 thf(fact_1952_field__le__mult__one__interval,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ! [Z2: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.17/5.39 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y4 ) ) )
% 5.17/5.39 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.17/5.39
% 5.17/5.39 % field_le_mult_one_interval
% 5.17/5.39 thf(fact_1953_field__le__mult__one__interval,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ! [Z2: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.17/5.39 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X ) @ Y4 ) ) )
% 5.17/5.39 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.39
% 5.17/5.39 % field_le_mult_one_interval
% 5.17/5.39 thf(fact_1954_divide__le__eq__1,axiom,
% 5.17/5.39 ! [B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 & ( ord_less_eq_rat @ B @ A ) )
% 5.17/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_eq_rat @ A @ B ) )
% 5.17/5.39 | ( A = zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_le_eq_1
% 5.17/5.39 thf(fact_1955_divide__le__eq__1,axiom,
% 5.17/5.39 ! [B: real,A: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 & ( ord_less_eq_real @ B @ A ) )
% 5.17/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 & ( ord_less_eq_real @ A @ B ) )
% 5.17/5.39 | ( A = zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_le_eq_1
% 5.17/5.39 thf(fact_1956_le__divide__eq__1,axiom,
% 5.17/5.39 ! [B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 & ( ord_less_eq_rat @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % le_divide_eq_1
% 5.17/5.39 thf(fact_1957_le__divide__eq__1,axiom,
% 5.17/5.39 ! [B: real,A: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 & ( ord_less_eq_real @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % le_divide_eq_1
% 5.17/5.39 thf(fact_1958_Suc__pred_H,axiom,
% 5.17/5.39 ! [N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( N
% 5.17/5.39 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_pred'
% 5.17/5.39 thf(fact_1959_Suc__diff__eq__diff__pred,axiom,
% 5.17/5.39 ! [N: nat,M: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.17/5.39 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_diff_eq_diff_pred
% 5.17/5.39 thf(fact_1960_dvd__mult__cancel2,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.39 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.17/5.39 = ( N = one_one_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_cancel2
% 5.17/5.39 thf(fact_1961_dvd__mult__cancel1,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.39 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.17/5.39 = ( N = one_one_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_cancel1
% 5.17/5.39 thf(fact_1962_of__nat__less__two__power,axiom,
% 5.17/5.39 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_two_power
% 5.17/5.39 thf(fact_1963_of__nat__less__two__power,axiom,
% 5.17/5.39 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_two_power
% 5.17/5.39 thf(fact_1964_of__nat__less__two__power,axiom,
% 5.17/5.39 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_two_power
% 5.17/5.39 thf(fact_1965_power__diff__power__eq,axiom,
% 5.17/5.39 ! [A: nat,N: nat,M: nat] :
% 5.17/5.39 ( ( A != zero_zero_nat )
% 5.17/5.39 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.39 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.17/5.39 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.17/5.39 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.39 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.17/5.39 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % power_diff_power_eq
% 5.17/5.39 thf(fact_1966_power__diff__power__eq,axiom,
% 5.17/5.39 ! [A: int,N: nat,M: nat] :
% 5.17/5.39 ( ( A != zero_zero_int )
% 5.17/5.39 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.39 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.17/5.39 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.17/5.39 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.39 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.17/5.39 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % power_diff_power_eq
% 5.17/5.39 thf(fact_1967_not__numeral__less__zero,axiom,
% 5.17/5.39 ! [N: num] :
% 5.17/5.39 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.17/5.39
% 5.17/5.39 % not_numeral_less_zero
% 5.17/5.39 thf(fact_1968_not__numeral__less__zero,axiom,
% 5.17/5.39 ! [N: num] :
% 5.17/5.39 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.17/5.39
% 5.17/5.39 % not_numeral_less_zero
% 5.17/5.39 thf(fact_1969_not__numeral__less__zero,axiom,
% 5.17/5.39 ! [N: num] :
% 5.17/5.39 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.17/5.39
% 5.17/5.39 % not_numeral_less_zero
% 5.17/5.39 thf(fact_1970_not__numeral__less__zero,axiom,
% 5.17/5.39 ! [N: num] :
% 5.17/5.39 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.17/5.39
% 5.17/5.39 % not_numeral_less_zero
% 5.17/5.39 thf(fact_1971_zero__less__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_numeral
% 5.17/5.39 thf(fact_1972_zero__less__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_numeral
% 5.17/5.39 thf(fact_1973_zero__less__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_numeral
% 5.17/5.39 thf(fact_1974_zero__less__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_numeral
% 5.17/5.39 thf(fact_1975_mult__neg__neg,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_neg
% 5.17/5.39 thf(fact_1976_mult__neg__neg,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_neg
% 5.17/5.39 thf(fact_1977_mult__neg__neg,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.39 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_neg
% 5.17/5.39 thf(fact_1978_not__square__less__zero,axiom,
% 5.17/5.39 ! [A: real] :
% 5.17/5.39 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.17/5.39
% 5.17/5.39 % not_square_less_zero
% 5.17/5.39 thf(fact_1979_not__square__less__zero,axiom,
% 5.17/5.39 ! [A: rat] :
% 5.17/5.39 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.17/5.39
% 5.17/5.39 % not_square_less_zero
% 5.17/5.39 thf(fact_1980_not__square__less__zero,axiom,
% 5.17/5.39 ! [A: int] :
% 5.17/5.39 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.17/5.39
% 5.17/5.39 % not_square_less_zero
% 5.17/5.39 thf(fact_1981_mult__less__0__iff,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.17/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_0_iff
% 5.17/5.39 thf(fact_1982_mult__less__0__iff,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.17/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_0_iff
% 5.17/5.39 thf(fact_1983_mult__less__0__iff,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.17/5.39 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.17/5.39 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.39 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_0_iff
% 5.17/5.39 thf(fact_1984_mult__neg__pos,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_pos
% 5.17/5.39 thf(fact_1985_mult__neg__pos,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_pos
% 5.17/5.39 thf(fact_1986_mult__neg__pos,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_pos
% 5.17/5.39 thf(fact_1987_mult__neg__pos,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_neg_pos
% 5.17/5.39 thf(fact_1988_mult__pos__neg,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg
% 5.17/5.39 thf(fact_1989_mult__pos__neg,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg
% 5.17/5.39 thf(fact_1990_mult__pos__neg,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg
% 5.17/5.39 thf(fact_1991_mult__pos__neg,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg
% 5.17/5.39 thf(fact_1992_mult__pos__pos,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_pos
% 5.17/5.39 thf(fact_1993_mult__pos__pos,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_pos
% 5.17/5.39 thf(fact_1994_mult__pos__pos,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.39 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_pos
% 5.17/5.39 thf(fact_1995_mult__pos__pos,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.39 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_pos
% 5.17/5.39 thf(fact_1996_mult__pos__neg2,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg2
% 5.17/5.39 thf(fact_1997_mult__pos__neg2,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg2
% 5.17/5.39 thf(fact_1998_mult__pos__neg2,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg2
% 5.17/5.39 thf(fact_1999_mult__pos__neg2,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_pos_neg2
% 5.17/5.39 thf(fact_2000_zero__less__mult__iff,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.17/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_iff
% 5.17/5.39 thf(fact_2001_zero__less__mult__iff,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.17/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_iff
% 5.17/5.39 thf(fact_2002_zero__less__mult__iff,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.17/5.39 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.17/5.39 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.39 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_iff
% 5.17/5.39 thf(fact_2003_zero__less__mult__pos,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos
% 5.17/5.39 thf(fact_2004_zero__less__mult__pos,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos
% 5.17/5.39 thf(fact_2005_zero__less__mult__pos,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos
% 5.17/5.39 thf(fact_2006_zero__less__mult__pos,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos
% 5.17/5.39 thf(fact_2007_zero__less__mult__pos2,axiom,
% 5.17/5.39 ! [B: real,A: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos2
% 5.17/5.39 thf(fact_2008_zero__less__mult__pos2,axiom,
% 5.17/5.39 ! [B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos2
% 5.17/5.39 thf(fact_2009_zero__less__mult__pos2,axiom,
% 5.17/5.39 ! [B: nat,A: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos2
% 5.17/5.39 thf(fact_2010_zero__less__mult__pos2,axiom,
% 5.17/5.39 ! [B: int,A: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_mult_pos2
% 5.17/5.39 thf(fact_2011_mult__less__cancel__left__neg,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ord_less_real @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_neg
% 5.17/5.39 thf(fact_2012_mult__less__cancel__left__neg,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_neg
% 5.17/5.39 thf(fact_2013_mult__less__cancel__left__neg,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ord_less_int @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_neg
% 5.17/5.39 thf(fact_2014_mult__less__cancel__left__pos,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_pos
% 5.17/5.39 thf(fact_2015_mult__less__cancel__left__pos,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_pos
% 5.17/5.39 thf(fact_2016_mult__less__cancel__left__pos,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_pos
% 5.17/5.39 thf(fact_2017_mult__strict__left__mono__neg,axiom,
% 5.17/5.39 ! [B: real,A: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ B @ A )
% 5.17/5.39 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono_neg
% 5.17/5.39 thf(fact_2018_mult__strict__left__mono__neg,axiom,
% 5.17/5.39 ! [B: rat,A: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ B @ A )
% 5.17/5.39 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono_neg
% 5.17/5.39 thf(fact_2019_mult__strict__left__mono__neg,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( ord_less_int @ B @ A )
% 5.17/5.39 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono_neg
% 5.17/5.39 thf(fact_2020_mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono
% 5.17/5.39 thf(fact_2021_mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono
% 5.17/5.39 thf(fact_2022_mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono
% 5.17/5.39 thf(fact_2023_mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_left_mono
% 5.17/5.39 thf(fact_2024_mult__less__cancel__left__disj,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 & ( ord_less_real @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_disj
% 5.17/5.39 thf(fact_2025_mult__less__cancel__left__disj,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 & ( ord_less_rat @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_disj
% 5.17/5.39 thf(fact_2026_mult__less__cancel__left__disj,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 & ( ord_less_int @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left_disj
% 5.17/5.39 thf(fact_2027_mult__strict__right__mono__neg,axiom,
% 5.17/5.39 ! [B: real,A: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ B @ A )
% 5.17/5.39 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono_neg
% 5.17/5.39 thf(fact_2028_mult__strict__right__mono__neg,axiom,
% 5.17/5.39 ! [B: rat,A: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ B @ A )
% 5.17/5.39 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono_neg
% 5.17/5.39 thf(fact_2029_mult__strict__right__mono__neg,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( ord_less_int @ B @ A )
% 5.17/5.39 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono_neg
% 5.17/5.39 thf(fact_2030_mult__strict__right__mono,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono
% 5.17/5.39 thf(fact_2031_mult__strict__right__mono,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono
% 5.17/5.39 thf(fact_2032_mult__strict__right__mono,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono
% 5.17/5.39 thf(fact_2033_mult__strict__right__mono,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_right_mono
% 5.17/5.39 thf(fact_2034_mult__less__cancel__right__disj,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 & ( ord_less_real @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right_disj
% 5.17/5.39 thf(fact_2035_mult__less__cancel__right__disj,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 & ( ord_less_rat @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right_disj
% 5.17/5.39 thf(fact_2036_mult__less__cancel__right__disj,axiom,
% 5.17/5.39 ! [A: int,C: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 & ( ord_less_int @ A @ B ) )
% 5.17/5.39 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right_disj
% 5.17/5.39 thf(fact_2037_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.17/5.39 thf(fact_2038_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.17/5.39 thf(fact_2039_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.17/5.39 thf(fact_2040_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.17/5.39 thf(fact_2041_less__iff__diff__less__0,axiom,
% 5.17/5.39 ( ord_less_real
% 5.17/5.39 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_iff_diff_less_0
% 5.17/5.39 thf(fact_2042_less__iff__diff__less__0,axiom,
% 5.17/5.39 ( ord_less_rat
% 5.17/5.39 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_iff_diff_less_0
% 5.17/5.39 thf(fact_2043_less__iff__diff__less__0,axiom,
% 5.17/5.39 ( ord_less_int
% 5.17/5.39 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_iff_diff_less_0
% 5.17/5.39 thf(fact_2044_divide__neg__neg,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_neg_neg
% 5.17/5.39 thf(fact_2045_divide__neg__neg,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_neg_neg
% 5.17/5.39 thf(fact_2046_divide__neg__pos,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_neg_pos
% 5.17/5.39 thf(fact_2047_divide__neg__pos,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_neg_pos
% 5.17/5.39 thf(fact_2048_divide__pos__neg,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_pos_neg
% 5.17/5.39 thf(fact_2049_divide__pos__neg,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_pos_neg
% 5.17/5.39 thf(fact_2050_divide__pos__pos,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_pos_pos
% 5.17/5.39 thf(fact_2051_divide__pos__pos,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_pos_pos
% 5.17/5.39 thf(fact_2052_divide__less__0__iff,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.17/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_0_iff
% 5.17/5.39 thf(fact_2053_divide__less__0__iff,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.17/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_0_iff
% 5.17/5.39 thf(fact_2054_divide__less__cancel,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ B @ A ) )
% 5.17/5.39 & ( C != zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_cancel
% 5.17/5.39 thf(fact_2055_divide__less__cancel,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ B @ A ) )
% 5.17/5.39 & ( C != zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_cancel
% 5.17/5.39 thf(fact_2056_zero__less__divide__iff,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.17/5.39 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.39 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_divide_iff
% 5.17/5.39 thf(fact_2057_zero__less__divide__iff,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.17/5.39 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.39 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_divide_iff
% 5.17/5.39 thf(fact_2058_divide__strict__right__mono,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_right_mono
% 5.17/5.39 thf(fact_2059_divide__strict__right__mono,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_right_mono
% 5.17/5.39 thf(fact_2060_divide__strict__right__mono__neg,axiom,
% 5.17/5.39 ! [B: real,A: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ B @ A )
% 5.17/5.39 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_right_mono_neg
% 5.17/5.39 thf(fact_2061_divide__strict__right__mono__neg,axiom,
% 5.17/5.39 ! [B: rat,A: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ B @ A )
% 5.17/5.39 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_right_mono_neg
% 5.17/5.39 thf(fact_2062_of__nat__less__0__iff,axiom,
% 5.17/5.39 ! [M: nat] :
% 5.17/5.39 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_0_iff
% 5.17/5.39 thf(fact_2063_of__nat__less__0__iff,axiom,
% 5.17/5.39 ! [M: nat] :
% 5.17/5.39 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_0_iff
% 5.17/5.39 thf(fact_2064_of__nat__less__0__iff,axiom,
% 5.17/5.39 ! [M: nat] :
% 5.17/5.39 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_0_iff
% 5.17/5.39 thf(fact_2065_of__nat__less__0__iff,axiom,
% 5.17/5.39 ! [M: nat] :
% 5.17/5.39 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.17/5.39
% 5.17/5.39 % of_nat_less_0_iff
% 5.17/5.39 thf(fact_2066_zero__less__one__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.17/5.39
% 5.17/5.39 % zero_less_one_class.zero_le_one
% 5.17/5.39 thf(fact_2067_zero__less__one__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.17/5.39
% 5.17/5.39 % zero_less_one_class.zero_le_one
% 5.17/5.39 thf(fact_2068_zero__less__one__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.17/5.39
% 5.17/5.39 % zero_less_one_class.zero_le_one
% 5.17/5.39 thf(fact_2069_zero__less__one__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.17/5.39
% 5.17/5.39 % zero_less_one_class.zero_le_one
% 5.17/5.39 thf(fact_2070_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.17/5.39
% 5.17/5.39 % linordered_nonzero_semiring_class.zero_le_one
% 5.17/5.39 thf(fact_2071_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.17/5.39
% 5.17/5.39 % linordered_nonzero_semiring_class.zero_le_one
% 5.17/5.39 thf(fact_2072_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.17/5.39
% 5.17/5.39 % linordered_nonzero_semiring_class.zero_le_one
% 5.17/5.39 thf(fact_2073_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.17/5.39 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.17/5.39
% 5.17/5.39 % linordered_nonzero_semiring_class.zero_le_one
% 5.17/5.39 thf(fact_2074_not__one__le__zero,axiom,
% 5.17/5.39 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.17/5.39
% 5.17/5.39 % not_one_le_zero
% 5.17/5.39 thf(fact_2075_not__one__le__zero,axiom,
% 5.17/5.39 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.17/5.39
% 5.17/5.39 % not_one_le_zero
% 5.17/5.39 thf(fact_2076_not__one__le__zero,axiom,
% 5.17/5.39 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.17/5.39
% 5.17/5.39 % not_one_le_zero
% 5.17/5.39 thf(fact_2077_not__one__le__zero,axiom,
% 5.17/5.39 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.17/5.39
% 5.17/5.39 % not_one_le_zero
% 5.17/5.39 thf(fact_2078_one__le__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % one_le_numeral
% 5.17/5.39 thf(fact_2079_one__le__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % one_le_numeral
% 5.17/5.39 thf(fact_2080_one__le__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % one_le_numeral
% 5.17/5.39 thf(fact_2081_one__le__numeral,axiom,
% 5.17/5.39 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % one_le_numeral
% 5.17/5.39 thf(fact_2082_less__Suc__eq__0__disj,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.17/5.39 = ( ( M = zero_zero_nat )
% 5.17/5.39 | ? [J3: nat] :
% 5.17/5.39 ( ( M
% 5.17/5.39 = ( suc @ J3 ) )
% 5.17/5.39 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_Suc_eq_0_disj
% 5.17/5.39 thf(fact_2083_gr0__implies__Suc,axiom,
% 5.17/5.39 ! [N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ? [M4: nat] :
% 5.17/5.39 ( N
% 5.17/5.39 = ( suc @ M4 ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gr0_implies_Suc
% 5.17/5.39 thf(fact_2084_All__less__Suc2,axiom,
% 5.17/5.39 ! [N: nat,P: nat > $o] :
% 5.17/5.39 ( ( ! [I2: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.17/5.39 => ( P @ I2 ) ) )
% 5.17/5.39 = ( ( P @ zero_zero_nat )
% 5.17/5.39 & ! [I2: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I2 @ N )
% 5.17/5.39 => ( P @ ( suc @ I2 ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % All_less_Suc2
% 5.17/5.39 thf(fact_2085_gr0__conv__Suc,axiom,
% 5.17/5.39 ! [N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 = ( ? [M5: nat] :
% 5.17/5.39 ( N
% 5.17/5.39 = ( suc @ M5 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gr0_conv_Suc
% 5.17/5.39 thf(fact_2086_Ex__less__Suc2,axiom,
% 5.17/5.39 ! [N: nat,P: nat > $o] :
% 5.17/5.39 ( ( ? [I2: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 5.17/5.39 & ( P @ I2 ) ) )
% 5.17/5.39 = ( ( P @ zero_zero_nat )
% 5.17/5.39 | ? [I2: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I2 @ N )
% 5.17/5.39 & ( P @ ( suc @ I2 ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % Ex_less_Suc2
% 5.17/5.39 thf(fact_2087_le__imp__less__Suc,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.39 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % le_imp_less_Suc
% 5.17/5.39 thf(fact_2088_less__eq__Suc__le,axiom,
% 5.17/5.39 ( ord_less_nat
% 5.17/5.39 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_eq_Suc_le
% 5.17/5.39 thf(fact_2089_less__Suc__eq__le,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.17/5.39 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_Suc_eq_le
% 5.17/5.39 thf(fact_2090_le__less__Suc__eq,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.39 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.17/5.39 = ( N = M ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % le_less_Suc_eq
% 5.17/5.39 thf(fact_2091_Suc__le__lessD,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.17/5.39 => ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_le_lessD
% 5.17/5.39 thf(fact_2092_inc__induct,axiom,
% 5.17/5.39 ! [I: nat,J: nat,P: nat > $o] :
% 5.17/5.39 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.39 => ( ( P @ J )
% 5.17/5.39 => ( ! [N2: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ I @ N2 )
% 5.17/5.39 => ( ( ord_less_nat @ N2 @ J )
% 5.17/5.39 => ( ( P @ ( suc @ N2 ) )
% 5.17/5.39 => ( P @ N2 ) ) ) )
% 5.17/5.39 => ( P @ I ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % inc_induct
% 5.17/5.39 thf(fact_2093_dec__induct,axiom,
% 5.17/5.39 ! [I: nat,J: nat,P: nat > $o] :
% 5.17/5.39 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.39 => ( ( P @ I )
% 5.17/5.39 => ( ! [N2: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ I @ N2 )
% 5.17/5.39 => ( ( ord_less_nat @ N2 @ J )
% 5.17/5.39 => ( ( P @ N2 )
% 5.17/5.39 => ( P @ ( suc @ N2 ) ) ) ) )
% 5.17/5.39 => ( P @ J ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dec_induct
% 5.17/5.39 thf(fact_2094_Suc__le__eq,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.17/5.39 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_le_eq
% 5.17/5.39 thf(fact_2095_Suc__leI,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ M @ N )
% 5.17/5.39 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_leI
% 5.17/5.39 thf(fact_2096_right__inverse__eq,axiom,
% 5.17/5.39 ! [B: complex,A: complex] :
% 5.17/5.39 ( ( B != zero_zero_complex )
% 5.17/5.39 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.17/5.39 = one_one_complex )
% 5.17/5.39 = ( A = B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % right_inverse_eq
% 5.17/5.39 thf(fact_2097_right__inverse__eq,axiom,
% 5.17/5.39 ! [B: real,A: real] :
% 5.17/5.39 ( ( B != zero_zero_real )
% 5.17/5.39 => ( ( ( divide_divide_real @ A @ B )
% 5.17/5.39 = one_one_real )
% 5.17/5.39 = ( A = B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % right_inverse_eq
% 5.17/5.39 thf(fact_2098_right__inverse__eq,axiom,
% 5.17/5.39 ! [B: rat,A: rat] :
% 5.17/5.39 ( ( B != zero_zero_rat )
% 5.17/5.39 => ( ( ( divide_divide_rat @ A @ B )
% 5.17/5.39 = one_one_rat )
% 5.17/5.39 = ( A = B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % right_inverse_eq
% 5.17/5.39 thf(fact_2099_numeral__One,axiom,
% 5.17/5.39 ( ( numera6690914467698888265omplex @ one )
% 5.17/5.39 = one_one_complex ) ).
% 5.17/5.39
% 5.17/5.39 % numeral_One
% 5.17/5.39 thf(fact_2100_numeral__One,axiom,
% 5.17/5.39 ( ( numeral_numeral_real @ one )
% 5.17/5.39 = one_one_real ) ).
% 5.17/5.39
% 5.17/5.39 % numeral_One
% 5.17/5.39 thf(fact_2101_numeral__One,axiom,
% 5.17/5.39 ( ( numeral_numeral_rat @ one )
% 5.17/5.39 = one_one_rat ) ).
% 5.17/5.39
% 5.17/5.39 % numeral_One
% 5.17/5.39 thf(fact_2102_numeral__One,axiom,
% 5.17/5.39 ( ( numeral_numeral_nat @ one )
% 5.17/5.39 = one_one_nat ) ).
% 5.17/5.39
% 5.17/5.39 % numeral_One
% 5.17/5.39 thf(fact_2103_numeral__One,axiom,
% 5.17/5.39 ( ( numeral_numeral_int @ one )
% 5.17/5.39 = one_one_int ) ).
% 5.17/5.39
% 5.17/5.39 % numeral_One
% 5.17/5.39 thf(fact_2104_ex__least__nat__le,axiom,
% 5.17/5.39 ! [P: nat > $o,N: nat] :
% 5.17/5.39 ( ( P @ N )
% 5.17/5.39 => ( ~ ( P @ zero_zero_nat )
% 5.17/5.39 => ? [K2: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ K2 @ N )
% 5.17/5.39 & ! [I4: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I4 @ K2 )
% 5.17/5.39 => ~ ( P @ I4 ) )
% 5.17/5.39 & ( P @ K2 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % ex_least_nat_le
% 5.17/5.39 thf(fact_2105_not__is__unit__0,axiom,
% 5.17/5.39 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.17/5.39
% 5.17/5.39 % not_is_unit_0
% 5.17/5.39 thf(fact_2106_not__is__unit__0,axiom,
% 5.17/5.39 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.17/5.39
% 5.17/5.39 % not_is_unit_0
% 5.17/5.39 thf(fact_2107_not__is__unit__0,axiom,
% 5.17/5.39 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.17/5.39
% 5.17/5.39 % not_is_unit_0
% 5.17/5.39 thf(fact_2108_diff__less__Suc,axiom,
% 5.17/5.39 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.17/5.39
% 5.17/5.39 % diff_less_Suc
% 5.17/5.39 thf(fact_2109_Suc__diff__Suc,axiom,
% 5.17/5.39 ! [N: nat,M: nat] :
% 5.17/5.39 ( ( ord_less_nat @ N @ M )
% 5.17/5.39 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.17/5.39 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_diff_Suc
% 5.17/5.39 thf(fact_2110_Suc__mult__less__cancel1,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.17/5.39 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % Suc_mult_less_cancel1
% 5.17/5.39 thf(fact_2111_diff__less,axiom,
% 5.17/5.39 ! [N: nat,M: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.39 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % diff_less
% 5.17/5.39 thf(fact_2112_nat__mult__less__cancel1,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.39 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % nat_mult_less_cancel1
% 5.17/5.39 thf(fact_2113_nat__mult__eq__cancel1,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ( ( times_times_nat @ K @ M )
% 5.17/5.39 = ( times_times_nat @ K @ N ) )
% 5.17/5.39 = ( M = N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % nat_mult_eq_cancel1
% 5.17/5.39 thf(fact_2114_mult__less__mono2,axiom,
% 5.17/5.39 ! [I: nat,J: nat,K: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I @ J )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_mono2
% 5.17/5.39 thf(fact_2115_mult__less__mono1,axiom,
% 5.17/5.39 ! [I: nat,J: nat,K: nat] :
% 5.17/5.39 ( ( ord_less_nat @ I @ J )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_mono1
% 5.17/5.39 thf(fact_2116_is__unit__mult__iff,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.17/5.39 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unit_mult_iff
% 5.17/5.39 thf(fact_2117_is__unit__mult__iff,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.17/5.39 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unit_mult_iff
% 5.17/5.39 thf(fact_2118_is__unit__mult__iff,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.17/5.39 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unit_mult_iff
% 5.17/5.39 thf(fact_2119_dvd__mult__unit__iff,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.17/5.39 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_unit_iff
% 5.17/5.39 thf(fact_2120_dvd__mult__unit__iff,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.17/5.39 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_unit_iff
% 5.17/5.39 thf(fact_2121_dvd__mult__unit__iff,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_unit_iff
% 5.17/5.39 thf(fact_2122_mult__unit__dvd__iff,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_unit_dvd_iff
% 5.17/5.39 thf(fact_2123_mult__unit__dvd__iff,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_unit_dvd_iff
% 5.17/5.39 thf(fact_2124_mult__unit__dvd__iff,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_unit_dvd_iff
% 5.17/5.39 thf(fact_2125_dvd__mult__unit__iff_H,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.39 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_unit_iff'
% 5.17/5.39 thf(fact_2126_dvd__mult__unit__iff_H,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.39 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_unit_iff'
% 5.17/5.39 thf(fact_2127_dvd__mult__unit__iff_H,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.39 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_unit_iff'
% 5.17/5.39 thf(fact_2128_mult__unit__dvd__iff_H,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_unit_dvd_iff'
% 5.17/5.39 thf(fact_2129_mult__unit__dvd__iff_H,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_unit_dvd_iff'
% 5.17/5.39 thf(fact_2130_mult__unit__dvd__iff_H,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_unit_dvd_iff'
% 5.17/5.39 thf(fact_2131_unit__mult__left__cancel,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.17/5.39 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_mult_left_cancel
% 5.17/5.39 thf(fact_2132_unit__mult__left__cancel,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 => ( ( ( times_times_nat @ A @ B )
% 5.17/5.39 = ( times_times_nat @ A @ C ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_mult_left_cancel
% 5.17/5.39 thf(fact_2133_unit__mult__left__cancel,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 => ( ( ( times_times_int @ A @ B )
% 5.17/5.39 = ( times_times_int @ A @ C ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_mult_left_cancel
% 5.17/5.39 thf(fact_2134_unit__mult__right__cancel,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.17/5.39 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_mult_right_cancel
% 5.17/5.39 thf(fact_2135_unit__mult__right__cancel,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 => ( ( ( times_times_nat @ B @ A )
% 5.17/5.39 = ( times_times_nat @ C @ A ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_mult_right_cancel
% 5.17/5.39 thf(fact_2136_unit__mult__right__cancel,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 => ( ( ( times_times_int @ B @ A )
% 5.17/5.39 = ( times_times_int @ C @ A ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_mult_right_cancel
% 5.17/5.39 thf(fact_2137_diff__less__mono,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_nat @ C @ A )
% 5.17/5.39 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % diff_less_mono
% 5.17/5.39 thf(fact_2138_less__diff__iff,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.39 => ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.39 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.17/5.39 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_diff_iff
% 5.17/5.39 thf(fact_2139_nat__dvd__not__less,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.39 => ( ( ord_less_nat @ M @ N )
% 5.17/5.39 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % nat_dvd_not_less
% 5.17/5.39 thf(fact_2140_unit__div__cancel,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.17/5.39 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_cancel
% 5.17/5.39 thf(fact_2141_unit__div__cancel,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 => ( ( ( divide_divide_nat @ B @ A )
% 5.17/5.39 = ( divide_divide_nat @ C @ A ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_cancel
% 5.17/5.39 thf(fact_2142_unit__div__cancel,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 => ( ( ( divide_divide_int @ B @ A )
% 5.17/5.39 = ( divide_divide_int @ C @ A ) )
% 5.17/5.39 = ( B = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_cancel
% 5.17/5.39 thf(fact_2143_div__unit__dvd__iff,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_unit_dvd_iff
% 5.17/5.39 thf(fact_2144_div__unit__dvd__iff,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_unit_dvd_iff
% 5.17/5.39 thf(fact_2145_div__unit__dvd__iff,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.17/5.39 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_unit_dvd_iff
% 5.17/5.39 thf(fact_2146_dvd__div__unit__iff,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.17/5.39 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_div_unit_iff
% 5.17/5.39 thf(fact_2147_dvd__div__unit__iff,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.17/5.39 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_div_unit_iff
% 5.17/5.39 thf(fact_2148_dvd__div__unit__iff,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.17/5.39 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_div_unit_iff
% 5.17/5.39 thf(fact_2149_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ( divide_divide_nat @ M @ N )
% 5.17/5.39 = zero_zero_nat )
% 5.17/5.39 = ( ( ord_less_nat @ M @ N )
% 5.17/5.39 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % Euclidean_Division.div_eq_0_iff
% 5.17/5.39 thf(fact_2150_numerals_I1_J,axiom,
% 5.17/5.39 ( ( numeral_numeral_nat @ one )
% 5.17/5.39 = one_one_nat ) ).
% 5.17/5.39
% 5.17/5.39 % numerals(1)
% 5.17/5.39 thf(fact_2151_One__nat__def,axiom,
% 5.17/5.39 ( one_one_nat
% 5.17/5.39 = ( suc @ zero_zero_nat ) ) ).
% 5.17/5.39
% 5.17/5.39 % One_nat_def
% 5.17/5.39 thf(fact_2152_dvd__minus__self,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.39 = ( ( ord_less_nat @ N @ M )
% 5.17/5.39 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_minus_self
% 5.17/5.39 thf(fact_2153_less__mult__imp__div__less,axiom,
% 5.17/5.39 ! [M: nat,I: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.17/5.39 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_mult_imp_div_less
% 5.17/5.39 thf(fact_2154_diff__Suc__eq__diff__pred,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.17/5.39 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % diff_Suc_eq_diff_pred
% 5.17/5.39 thf(fact_2155_mult__eq__self__implies__10,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( M
% 5.17/5.39 = ( times_times_nat @ M @ N ) )
% 5.17/5.39 => ( ( N = one_one_nat )
% 5.17/5.39 | ( M = zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_eq_self_implies_10
% 5.17/5.39 thf(fact_2156_zero__less__power__eq,axiom,
% 5.17/5.39 ! [A: real,N: nat] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.17/5.39 = ( ( N = zero_zero_nat )
% 5.17/5.39 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( A != zero_zero_real ) )
% 5.17/5.39 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_power_eq
% 5.17/5.39 thf(fact_2157_zero__less__power__eq,axiom,
% 5.17/5.39 ! [A: rat,N: nat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.17/5.39 = ( ( N = zero_zero_nat )
% 5.17/5.39 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( A != zero_zero_rat ) )
% 5.17/5.39 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_power_eq
% 5.17/5.39 thf(fact_2158_zero__less__power__eq,axiom,
% 5.17/5.39 ! [A: int,N: nat] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.17/5.39 = ( ( N = zero_zero_nat )
% 5.17/5.39 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( A != zero_zero_int ) )
% 5.17/5.39 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % zero_less_power_eq
% 5.17/5.39 thf(fact_2159_mult__le__cancel__left,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left
% 5.17/5.39 thf(fact_2160_mult__le__cancel__left,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_eq_int @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left
% 5.17/5.39 thf(fact_2161_mult__le__cancel__left,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left
% 5.17/5.39 thf(fact_2162_mult__le__cancel__right,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_right
% 5.17/5.39 thf(fact_2163_mult__le__cancel__right,axiom,
% 5.17/5.39 ! [A: int,C: int,B: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_eq_int @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_right
% 5.17/5.39 thf(fact_2164_mult__le__cancel__right,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_right
% 5.17/5.39 thf(fact_2165_mult__left__less__imp__less,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_less_imp_less
% 5.17/5.39 thf(fact_2166_mult__left__less__imp__less,axiom,
% 5.17/5.39 ! [C: nat,A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_less_imp_less
% 5.17/5.39 thf(fact_2167_mult__left__less__imp__less,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_less_imp_less
% 5.17/5.39 thf(fact_2168_mult__left__less__imp__less,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_less_imp_less
% 5.17/5.39 thf(fact_2169_mult__strict__mono,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ C @ D )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono
% 5.17/5.39 thf(fact_2170_mult__strict__mono,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_nat @ C @ D )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono
% 5.17/5.39 thf(fact_2171_mult__strict__mono,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_int @ C @ D )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono
% 5.17/5.39 thf(fact_2172_mult__strict__mono,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ C @ D )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono
% 5.17/5.39 thf(fact_2173_mult__less__cancel__left,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left
% 5.17/5.39 thf(fact_2174_mult__less__cancel__left,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left
% 5.17/5.39 thf(fact_2175_mult__less__cancel__left,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_left
% 5.17/5.39 thf(fact_2176_mult__right__less__imp__less,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_less_imp_less
% 5.17/5.39 thf(fact_2177_mult__right__less__imp__less,axiom,
% 5.17/5.39 ! [A: nat,C: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_less_imp_less
% 5.17/5.39 thf(fact_2178_mult__right__less__imp__less,axiom,
% 5.17/5.39 ! [A: int,C: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_less_imp_less
% 5.17/5.39 thf(fact_2179_mult__right__less__imp__less,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_less_imp_less
% 5.17/5.39 thf(fact_2180_mult__strict__mono_H,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono'
% 5.17/5.39 thf(fact_2181_mult__strict__mono_H,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_nat @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono'
% 5.17/5.39 thf(fact_2182_mult__strict__mono_H,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_int @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono'
% 5.17/5.39 thf(fact_2183_mult__strict__mono_H,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_strict_mono'
% 5.17/5.39 thf(fact_2184_mult__less__cancel__right,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right
% 5.17/5.39 thf(fact_2185_mult__less__cancel__right,axiom,
% 5.17/5.39 ! [A: int,C: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right
% 5.17/5.39 thf(fact_2186_mult__less__cancel__right,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_cancel_right
% 5.17/5.39 thf(fact_2187_mult__le__cancel__left__neg,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left_neg
% 5.17/5.39 thf(fact_2188_mult__le__cancel__left__neg,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ C @ zero_zero_int )
% 5.17/5.39 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left_neg
% 5.17/5.39 thf(fact_2189_mult__le__cancel__left__neg,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left_neg
% 5.17/5.39 thf(fact_2190_mult__le__cancel__left__pos,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left_pos
% 5.17/5.39 thf(fact_2191_mult__le__cancel__left__pos,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left_pos
% 5.17/5.39 thf(fact_2192_mult__le__cancel__left__pos,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_cancel_left_pos
% 5.17/5.39 thf(fact_2193_mult__left__le__imp__le,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_imp_le
% 5.17/5.39 thf(fact_2194_mult__left__le__imp__le,axiom,
% 5.17/5.39 ! [C: nat,A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_imp_le
% 5.17/5.39 thf(fact_2195_mult__left__le__imp__le,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_imp_le
% 5.17/5.39 thf(fact_2196_mult__left__le__imp__le,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_imp_le
% 5.17/5.39 thf(fact_2197_mult__right__le__imp__le,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_imp_le
% 5.17/5.39 thf(fact_2198_mult__right__le__imp__le,axiom,
% 5.17/5.39 ! [A: nat,C: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_imp_le
% 5.17/5.39 thf(fact_2199_mult__right__le__imp__le,axiom,
% 5.17/5.39 ! [A: int,C: int,B: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_imp_le
% 5.17/5.39 thf(fact_2200_mult__right__le__imp__le,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_imp_le
% 5.17/5.39 thf(fact_2201_mult__le__less__imp__less,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ C @ D )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_less_imp_less
% 5.17/5.39 thf(fact_2202_mult__le__less__imp__less,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_nat @ C @ D )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_less_imp_less
% 5.17/5.39 thf(fact_2203_mult__le__less__imp__less,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_int @ C @ D )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_less_imp_less
% 5.17/5.39 thf(fact_2204_mult__le__less__imp__less,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ C @ D )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_less_imp_less
% 5.17/5.39 thf(fact_2205_mult__less__le__imp__less,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_rat @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_le_imp_less
% 5.17/5.39 thf(fact_2206_mult__less__le__imp__less,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.39 ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_nat @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.39 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_le_imp_less
% 5.17/5.39 thf(fact_2207_mult__less__le__imp__less,axiom,
% 5.17/5.39 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.39 ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_int @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.17/5.39 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_le_imp_less
% 5.17/5.39 thf(fact_2208_mult__less__le__imp__less,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_real @ C @ D )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_less_le_imp_less
% 5.17/5.39 thf(fact_2209_frac__le,axiom,
% 5.17/5.39 ! [Y4: rat,X: rat,W: rat,Z: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.17/5.39 => ( ( ord_less_eq_rat @ W @ Z )
% 5.17/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y4 @ W ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_le
% 5.17/5.39 thf(fact_2210_frac__le,axiom,
% 5.17/5.39 ! [Y4: real,X: real,W: real,Z: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.17/5.39 => ( ( ord_less_eq_real @ W @ Z )
% 5.17/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y4 @ W ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_le
% 5.17/5.39 thf(fact_2211_frac__less,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat,W: rat,Z: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.17/5.39 => ( ( ord_less_eq_rat @ W @ Z )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y4 @ W ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_less
% 5.17/5.39 thf(fact_2212_frac__less,axiom,
% 5.17/5.39 ! [X: real,Y4: real,W: real,Z: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.17/5.39 => ( ( ord_less_eq_real @ W @ Z )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y4 @ W ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_less
% 5.17/5.39 thf(fact_2213_frac__less2,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat,W: rat,Z: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.17/5.39 => ( ( ord_less_rat @ W @ Z )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y4 @ W ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_less2
% 5.17/5.39 thf(fact_2214_frac__less2,axiom,
% 5.17/5.39 ! [X: real,Y4: real,W: real,Z: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.17/5.39 => ( ( ord_less_real @ W @ Z )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y4 @ W ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_less2
% 5.17/5.39 thf(fact_2215_divide__le__cancel,axiom,
% 5.17/5.39 ! [A: rat,C: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_le_cancel
% 5.17/5.39 thf(fact_2216_divide__le__cancel,axiom,
% 5.17/5.39 ! [A: real,C: real,B: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ A @ B ) )
% 5.17/5.39 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_le_cancel
% 5.17/5.39 thf(fact_2217_divide__nonneg__neg,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonneg_neg
% 5.17/5.39 thf(fact_2218_divide__nonneg__neg,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonneg_neg
% 5.17/5.39 thf(fact_2219_divide__nonneg__pos,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonneg_pos
% 5.17/5.39 thf(fact_2220_divide__nonneg__pos,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonneg_pos
% 5.17/5.39 thf(fact_2221_divide__nonpos__neg,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonpos_neg
% 5.17/5.39 thf(fact_2222_divide__nonpos__neg,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonpos_neg
% 5.17/5.39 thf(fact_2223_divide__nonpos__pos,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonpos_pos
% 5.17/5.39 thf(fact_2224_divide__nonpos__pos,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_nonpos_pos
% 5.17/5.39 thf(fact_2225_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ( ord_less_nat @ A @ B )
% 5.17/5.39 => ( ( divide_divide_nat @ A @ B )
% 5.17/5.39 = zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unique_euclidean_semiring_numeral_class.div_less
% 5.17/5.39 thf(fact_2226_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ( ord_less_int @ A @ B )
% 5.17/5.39 => ( ( divide_divide_int @ A @ B )
% 5.17/5.39 = zero_zero_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unique_euclidean_semiring_numeral_class.div_less
% 5.17/5.39 thf(fact_2227_div__positive,axiom,
% 5.17/5.39 ! [B: nat,A: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.39 => ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.39 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_positive
% 5.17/5.39 thf(fact_2228_div__positive,axiom,
% 5.17/5.39 ! [B: int,A: int] :
% 5.17/5.39 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.39 => ( ( ord_less_eq_int @ B @ A )
% 5.17/5.39 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_positive
% 5.17/5.39 thf(fact_2229_divide__less__eq,axiom,
% 5.17/5.39 ! [B: real,C: real,A: real] :
% 5.17/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_eq
% 5.17/5.39 thf(fact_2230_divide__less__eq,axiom,
% 5.17/5.39 ! [B: rat,C: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_eq
% 5.17/5.39 thf(fact_2231_less__divide__eq,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_divide_eq
% 5.17/5.39 thf(fact_2232_less__divide__eq,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_divide_eq
% 5.17/5.39 thf(fact_2233_neg__divide__less__eq,axiom,
% 5.17/5.39 ! [C: real,B: real,A: real] :
% 5.17/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_divide_less_eq
% 5.17/5.39 thf(fact_2234_neg__divide__less__eq,axiom,
% 5.17/5.39 ! [C: rat,B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_divide_less_eq
% 5.17/5.39 thf(fact_2235_neg__less__divide__eq,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_less_divide_eq
% 5.17/5.39 thf(fact_2236_neg__less__divide__eq,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_less_divide_eq
% 5.17/5.39 thf(fact_2237_pos__divide__less__eq,axiom,
% 5.17/5.39 ! [C: real,B: real,A: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_divide_less_eq
% 5.17/5.39 thf(fact_2238_pos__divide__less__eq,axiom,
% 5.17/5.39 ! [C: rat,B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_divide_less_eq
% 5.17/5.39 thf(fact_2239_pos__less__divide__eq,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_less_divide_eq
% 5.17/5.39 thf(fact_2240_pos__less__divide__eq,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_less_divide_eq
% 5.17/5.39 thf(fact_2241_mult__imp__div__pos__less,axiom,
% 5.17/5.39 ! [Y4: real,X: real,Z: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y4 ) )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_div_pos_less
% 5.17/5.39 thf(fact_2242_mult__imp__div__pos__less,axiom,
% 5.17/5.39 ! [Y4: rat,X: rat,Z: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y4 ) )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_div_pos_less
% 5.17/5.39 thf(fact_2243_mult__imp__less__div__pos,axiom,
% 5.17/5.39 ! [Y4: real,Z: real,X: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_real @ ( times_times_real @ Z @ Y4 ) @ X )
% 5.17/5.39 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_less_div_pos
% 5.17/5.39 thf(fact_2244_mult__imp__less__div__pos,axiom,
% 5.17/5.39 ! [Y4: rat,Z: rat,X: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y4 ) @ X )
% 5.17/5.39 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_less_div_pos
% 5.17/5.39 thf(fact_2245_divide__strict__left__mono,axiom,
% 5.17/5.39 ! [B: real,A: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ B @ A )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_left_mono
% 5.17/5.39 thf(fact_2246_divide__strict__left__mono,axiom,
% 5.17/5.39 ! [B: rat,A: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ B @ A )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_left_mono
% 5.17/5.39 thf(fact_2247_divide__strict__left__mono__neg,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.39 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_left_mono_neg
% 5.17/5.39 thf(fact_2248_divide__strict__left__mono__neg,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.39 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_strict_left_mono_neg
% 5.17/5.39 thf(fact_2249_mult__left__le__one__le,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_rat @ Y4 @ one_one_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ Y4 @ X ) @ X ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_one_le
% 5.17/5.39 thf(fact_2250_mult__left__le__one__le,axiom,
% 5.17/5.39 ! [X: int,Y4: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_int @ Y4 @ one_one_int )
% 5.17/5.39 => ( ord_less_eq_int @ ( times_times_int @ Y4 @ X ) @ X ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_one_le
% 5.17/5.39 thf(fact_2251_mult__left__le__one__le,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ Y4 @ X ) @ X ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le_one_le
% 5.17/5.39 thf(fact_2252_mult__right__le__one__le,axiom,
% 5.17/5.39 ! [X: rat,Y4: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_rat @ Y4 @ one_one_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y4 ) @ X ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_one_le
% 5.17/5.39 thf(fact_2253_mult__right__le__one__le,axiom,
% 5.17/5.39 ! [X: int,Y4: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_int @ Y4 @ one_one_int )
% 5.17/5.39 => ( ord_less_eq_int @ ( times_times_int @ X @ Y4 ) @ X ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_one_le
% 5.17/5.39 thf(fact_2254_mult__right__le__one__le,axiom,
% 5.17/5.39 ! [X: real,Y4: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ X @ Y4 ) @ X ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_right_le_one_le
% 5.17/5.39 thf(fact_2255_mult__le__one,axiom,
% 5.17/5.39 ! [A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.39 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_one
% 5.17/5.39 thf(fact_2256_mult__le__one,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.39 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_one
% 5.17/5.39 thf(fact_2257_mult__le__one,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.39 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.17/5.39 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_one
% 5.17/5.39 thf(fact_2258_mult__le__one,axiom,
% 5.17/5.39 ! [A: real,B: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.39 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_le_one
% 5.17/5.39 thf(fact_2259_mult__left__le,axiom,
% 5.17/5.39 ! [C: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le
% 5.17/5.39 thf(fact_2260_mult__left__le,axiom,
% 5.17/5.39 ! [C: nat,A: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.17/5.39 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.39 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le
% 5.17/5.39 thf(fact_2261_mult__left__le,axiom,
% 5.17/5.39 ! [C: int,A: int] :
% 5.17/5.39 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.17/5.39 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.39 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le
% 5.17/5.39 thf(fact_2262_mult__left__le,axiom,
% 5.17/5.39 ! [C: real,A: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_left_le
% 5.17/5.39 thf(fact_2263_ex__least__nat__less,axiom,
% 5.17/5.39 ! [P: nat > $o,N: nat] :
% 5.17/5.39 ( ( P @ N )
% 5.17/5.39 => ( ~ ( P @ zero_zero_nat )
% 5.17/5.39 => ? [K2: nat] :
% 5.17/5.39 ( ( ord_less_nat @ K2 @ N )
% 5.17/5.39 & ! [I4: nat] :
% 5.17/5.39 ( ( ord_less_eq_nat @ I4 @ K2 )
% 5.17/5.39 => ~ ( P @ I4 ) )
% 5.17/5.39 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % ex_least_nat_less
% 5.17/5.39 thf(fact_2264_unit__dvdE,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.39 => ! [C3: code_integer] :
% 5.17/5.39 ( B
% 5.17/5.39 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_dvdE
% 5.17/5.39 thf(fact_2265_unit__dvdE,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 => ~ ( ( A != zero_zero_nat )
% 5.17/5.39 => ! [C3: nat] :
% 5.17/5.39 ( B
% 5.17/5.39 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_dvdE
% 5.17/5.39 thf(fact_2266_unit__dvdE,axiom,
% 5.17/5.39 ! [A: int,B: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 => ~ ( ( A != zero_zero_int )
% 5.17/5.39 => ! [C3: int] :
% 5.17/5.39 ( B
% 5.17/5.39 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_dvdE
% 5.17/5.39 thf(fact_2267_diff__Suc__less,axiom,
% 5.17/5.39 ! [N: nat,I: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % diff_Suc_less
% 5.17/5.39 thf(fact_2268_n__less__n__mult__m,axiom,
% 5.17/5.39 ! [N: nat,M: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.17/5.39 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % n_less_n_mult_m
% 5.17/5.39 thf(fact_2269_n__less__m__mult__n,axiom,
% 5.17/5.39 ! [N: nat,M: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.17/5.39 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % n_less_m_mult_n
% 5.17/5.39 thf(fact_2270_one__less__mult,axiom,
% 5.17/5.39 ! [N: nat,M: nat] :
% 5.17/5.39 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.39 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.17/5.39 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % one_less_mult
% 5.17/5.39 thf(fact_2271_unit__div__eq__0__iff,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.17/5.39 = zero_z3403309356797280102nteger )
% 5.17/5.39 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_eq_0_iff
% 5.17/5.39 thf(fact_2272_unit__div__eq__0__iff,axiom,
% 5.17/5.39 ! [B: nat,A: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( ( divide_divide_nat @ A @ B )
% 5.17/5.39 = zero_zero_nat )
% 5.17/5.39 = ( A = zero_zero_nat ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_eq_0_iff
% 5.17/5.39 thf(fact_2273_unit__div__eq__0__iff,axiom,
% 5.17/5.39 ! [B: int,A: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( ( divide_divide_int @ A @ B )
% 5.17/5.39 = zero_zero_int )
% 5.17/5.39 = ( A = zero_zero_int ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_eq_0_iff
% 5.17/5.39 thf(fact_2274_nat__mult__le__cancel1,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.39 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % nat_mult_le_cancel1
% 5.17/5.39 thf(fact_2275_unit__eq__div1,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.17/5.39 = C )
% 5.17/5.39 = ( A
% 5.17/5.39 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_eq_div1
% 5.17/5.39 thf(fact_2276_unit__eq__div1,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( ( divide_divide_nat @ A @ B )
% 5.17/5.39 = C )
% 5.17/5.39 = ( A
% 5.17/5.39 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_eq_div1
% 5.17/5.39 thf(fact_2277_unit__eq__div1,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( ( divide_divide_int @ A @ B )
% 5.17/5.39 = C )
% 5.17/5.39 = ( A
% 5.17/5.39 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_eq_div1
% 5.17/5.39 thf(fact_2278_unit__eq__div2,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( A
% 5.17/5.39 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.17/5.39 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.17/5.39 = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_eq_div2
% 5.17/5.39 thf(fact_2279_unit__eq__div2,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( A
% 5.17/5.39 = ( divide_divide_nat @ C @ B ) )
% 5.17/5.39 = ( ( times_times_nat @ A @ B )
% 5.17/5.39 = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_eq_div2
% 5.17/5.39 thf(fact_2280_unit__eq__div2,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( A
% 5.17/5.39 = ( divide_divide_int @ C @ B ) )
% 5.17/5.39 = ( ( times_times_int @ A @ B )
% 5.17/5.39 = C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_eq_div2
% 5.17/5.39 thf(fact_2281_div__mult__unit2,axiom,
% 5.17/5.39 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.39 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.39 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_mult_unit2
% 5.17/5.39 thf(fact_2282_div__mult__unit2,axiom,
% 5.17/5.39 ! [C: nat,B: nat,A: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.39 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.39 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_mult_unit2
% 5.17/5.39 thf(fact_2283_div__mult__unit2,axiom,
% 5.17/5.39 ! [C: int,B: int,A: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ B @ A )
% 5.17/5.39 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.39 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_mult_unit2
% 5.17/5.39 thf(fact_2284_unit__div__commute,axiom,
% 5.17/5.39 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.17/5.39 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_commute
% 5.17/5.39 thf(fact_2285_unit__div__commute,axiom,
% 5.17/5.39 ! [B: nat,A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.17/5.39 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_commute
% 5.17/5.39 thf(fact_2286_unit__div__commute,axiom,
% 5.17/5.39 ! [B: int,A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.17/5.39 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_commute
% 5.17/5.39 thf(fact_2287_unit__div__mult__swap,axiom,
% 5.17/5.39 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.17/5.39 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.17/5.39 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_mult_swap
% 5.17/5.39 thf(fact_2288_unit__div__mult__swap,axiom,
% 5.17/5.39 ! [C: nat,A: nat,B: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.17/5.39 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.17/5.39 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_mult_swap
% 5.17/5.39 thf(fact_2289_unit__div__mult__swap,axiom,
% 5.17/5.39 ! [C: int,A: int,B: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.17/5.39 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.17/5.39 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % unit_div_mult_swap
% 5.17/5.39 thf(fact_2290_is__unit__div__mult2__eq,axiom,
% 5.17/5.39 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.17/5.39 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.39 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unit_div_mult2_eq
% 5.17/5.39 thf(fact_2291_is__unit__div__mult2__eq,axiom,
% 5.17/5.39 ! [B: nat,C: nat,A: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.17/5.39 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.39 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unit_div_mult2_eq
% 5.17/5.39 thf(fact_2292_is__unit__div__mult2__eq,axiom,
% 5.17/5.39 ! [B: int,C: int,A: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.17/5.39 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.39 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unit_div_mult2_eq
% 5.17/5.39 thf(fact_2293_dvd__imp__le,axiom,
% 5.17/5.39 ! [K: nat,N: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ K @ N )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_imp_le
% 5.17/5.39 thf(fact_2294_div__greater__zero__iff,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.39 = ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.39 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_greater_zero_iff
% 5.17/5.39 thf(fact_2295_div__le__mono2,axiom,
% 5.17/5.39 ! [M: nat,N: nat,K: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.39 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.39 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_le_mono2
% 5.17/5.39 thf(fact_2296_nat__mult__dvd__cancel1,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.39 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % nat_mult_dvd_cancel1
% 5.17/5.39 thf(fact_2297_dvd__mult__cancel,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.39 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % dvd_mult_cancel
% 5.17/5.39 thf(fact_2298_div__less__iff__less__mult,axiom,
% 5.17/5.39 ! [Q2: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.17/5.39 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.17/5.39 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % div_less_iff_less_mult
% 5.17/5.39 thf(fact_2299_nat__mult__div__cancel1,axiom,
% 5.17/5.39 ! [K: nat,M: nat,N: nat] :
% 5.17/5.39 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.39 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.17/5.39 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % nat_mult_div_cancel1
% 5.17/5.39 thf(fact_2300_power__le__zero__eq,axiom,
% 5.17/5.39 ! [A: rat,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.17/5.39 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.17/5.39 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % power_le_zero_eq
% 5.17/5.39 thf(fact_2301_power__le__zero__eq,axiom,
% 5.17/5.39 ! [A: int,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.17/5.39 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.17/5.39 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % power_le_zero_eq
% 5.17/5.39 thf(fact_2302_power__le__zero__eq,axiom,
% 5.17/5.39 ! [A: real,N: nat] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.17/5.39 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.39 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.17/5.39 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % power_le_zero_eq
% 5.17/5.39 thf(fact_2303_even__mask__div__iff_H,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( 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 ) ) )
% 5.17/5.39 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % even_mask_div_iff'
% 5.17/5.39 thf(fact_2304_even__mask__div__iff_H,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( 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 ) ) )
% 5.17/5.39 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % even_mask_div_iff'
% 5.17/5.39 thf(fact_2305_even__mask__div__iff_H,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( 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 ) ) )
% 5.17/5.39 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.39
% 5.17/5.39 % even_mask_div_iff'
% 5.17/5.39 thf(fact_2306_conj__le__cong,axiom,
% 5.17/5.39 ! [X: int,X7: int,P: $o,P4: $o] :
% 5.17/5.39 ( ( X = X7 )
% 5.17/5.39 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.17/5.39 => ( P = P4 ) )
% 5.17/5.39 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.39 & P )
% 5.17/5.39 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.17/5.39 & P4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % conj_le_cong
% 5.17/5.39 thf(fact_2307_imp__le__cong,axiom,
% 5.17/5.39 ! [X: int,X7: int,P: $o,P4: $o] :
% 5.17/5.39 ( ( X = X7 )
% 5.17/5.39 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.17/5.39 => ( P = P4 ) )
% 5.17/5.39 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.39 => P )
% 5.17/5.39 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.17/5.39 => P4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % imp_le_cong
% 5.17/5.39 thf(fact_2308_gcd__nat_Onot__eq__order__implies__strict,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( A != B )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.not_eq_order_implies_strict
% 5.17/5.39 thf(fact_2309_gcd__nat_Ostrict__implies__not__eq,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 => ( A != B ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_implies_not_eq
% 5.17/5.39 thf(fact_2310_gcd__nat_Ostrict__implies__order,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 => ( dvd_dvd_nat @ A @ B ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_implies_order
% 5.17/5.39 thf(fact_2311_gcd__nat_Ostrict__iff__order,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 = ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_iff_order
% 5.17/5.39 thf(fact_2312_gcd__nat_Oorder__iff__strict,axiom,
% 5.17/5.39 ( dvd_dvd_nat
% 5.17/5.39 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A3 @ B2 )
% 5.17/5.39 & ( A3 != B2 ) )
% 5.17/5.39 | ( A3 = B2 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.order_iff_strict
% 5.17/5.39 thf(fact_2313_gcd__nat_Ostrict__iff__not,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 = ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_iff_not
% 5.17/5.39 thf(fact_2314_gcd__nat_Ostrict__trans2,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 => ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.39 & ( A != C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_trans2
% 5.17/5.39 thf(fact_2315_gcd__nat_Ostrict__trans1,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 => ( ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.39 & ( B != C ) )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.39 & ( A != C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_trans1
% 5.17/5.39 thf(fact_2316_gcd__nat_Ostrict__trans,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 => ( ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.39 & ( B != C ) )
% 5.17/5.39 => ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.39 & ( A != C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.strict_trans
% 5.17/5.39 thf(fact_2317_gcd__nat_Oantisym,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 => ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.39 => ( A = B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.antisym
% 5.17/5.39 thf(fact_2318_gcd__nat_Oirrefl,axiom,
% 5.17/5.39 ! [A: nat] :
% 5.17/5.39 ~ ( ( dvd_dvd_nat @ A @ A )
% 5.17/5.39 & ( A != A ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.irrefl
% 5.17/5.39 thf(fact_2319_gcd__nat_Oeq__iff,axiom,
% 5.17/5.39 ( ( ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.39 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A3 @ B2 )
% 5.17/5.39 & ( dvd_dvd_nat @ B2 @ A3 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.eq_iff
% 5.17/5.39 thf(fact_2320_gcd__nat_Otrans,axiom,
% 5.17/5.39 ! [A: nat,B: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 => ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.39 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.trans
% 5.17/5.39 thf(fact_2321_gcd__nat_Orefl,axiom,
% 5.17/5.39 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.refl
% 5.17/5.39 thf(fact_2322_gcd__nat_Oasym,axiom,
% 5.17/5.39 ! [A: nat,B: nat] :
% 5.17/5.39 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.39 & ( A != B ) )
% 5.17/5.39 => ~ ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.39 & ( B != A ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % gcd_nat.asym
% 5.17/5.39 thf(fact_2323_even__mask__div__iff,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( 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 ) ) )
% 5.17/5.39 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 = zero_z3403309356797280102nteger )
% 5.17/5.39 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % even_mask_div_iff
% 5.17/5.39 thf(fact_2324_even__mask__div__iff,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( 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 ) ) )
% 5.17/5.39 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 = zero_zero_nat )
% 5.17/5.39 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % even_mask_div_iff
% 5.17/5.39 thf(fact_2325_even__mask__div__iff,axiom,
% 5.17/5.39 ! [M: nat,N: nat] :
% 5.17/5.39 ( ( 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 ) ) )
% 5.17/5.39 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.39 = zero_zero_int )
% 5.17/5.39 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % even_mask_div_iff
% 5.17/5.39 thf(fact_2326_divide__le__eq,axiom,
% 5.17/5.39 ! [B: rat,C: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_le_eq
% 5.17/5.39 thf(fact_2327_divide__le__eq,axiom,
% 5.17/5.39 ! [B: real,C: real,A: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_le_eq
% 5.17/5.39 thf(fact_2328_le__divide__eq,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % le_divide_eq
% 5.17/5.39 thf(fact_2329_le__divide__eq,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % le_divide_eq
% 5.17/5.39 thf(fact_2330_divide__left__mono,axiom,
% 5.17/5.39 ! [B: rat,A: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.39 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_left_mono
% 5.17/5.39 thf(fact_2331_divide__left__mono,axiom,
% 5.17/5.39 ! [B: real,A: real,C: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.39 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_left_mono
% 5.17/5.39 thf(fact_2332_neg__divide__le__eq,axiom,
% 5.17/5.39 ! [C: rat,B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_divide_le_eq
% 5.17/5.39 thf(fact_2333_neg__divide__le__eq,axiom,
% 5.17/5.39 ! [C: real,B: real,A: real] :
% 5.17/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_divide_le_eq
% 5.17/5.39 thf(fact_2334_neg__le__divide__eq,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_le_divide_eq
% 5.17/5.39 thf(fact_2335_neg__le__divide__eq,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % neg_le_divide_eq
% 5.17/5.39 thf(fact_2336_pos__divide__le__eq,axiom,
% 5.17/5.39 ! [C: rat,B: rat,A: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_divide_le_eq
% 5.17/5.39 thf(fact_2337_pos__divide__le__eq,axiom,
% 5.17/5.39 ! [C: real,B: real,A: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.17/5.39 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_divide_le_eq
% 5.17/5.39 thf(fact_2338_pos__le__divide__eq,axiom,
% 5.17/5.39 ! [C: rat,A: rat,B: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_le_divide_eq
% 5.17/5.39 thf(fact_2339_pos__le__divide__eq,axiom,
% 5.17/5.39 ! [C: real,A: real,B: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos_le_divide_eq
% 5.17/5.39 thf(fact_2340_mult__imp__div__pos__le,axiom,
% 5.17/5.39 ! [Y4: rat,X: rat,Z: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y4 ) )
% 5.17/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_div_pos_le
% 5.17/5.39 thf(fact_2341_mult__imp__div__pos__le,axiom,
% 5.17/5.39 ! [Y4: real,X: real,Z: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y4 ) )
% 5.17/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_div_pos_le
% 5.17/5.39 thf(fact_2342_mult__imp__le__div__pos,axiom,
% 5.17/5.39 ! [Y4: rat,Z: rat,X: rat] :
% 5.17/5.39 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y4 ) @ X )
% 5.17/5.39 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_le_div_pos
% 5.17/5.39 thf(fact_2343_mult__imp__le__div__pos,axiom,
% 5.17/5.39 ! [Y4: real,Z: real,X: real] :
% 5.17/5.39 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.39 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y4 ) @ X )
% 5.17/5.39 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % mult_imp_le_div_pos
% 5.17/5.39 thf(fact_2344_divide__left__mono__neg,axiom,
% 5.17/5.39 ! [A: rat,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.39 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_left_mono_neg
% 5.17/5.39 thf(fact_2345_divide__left__mono__neg,axiom,
% 5.17/5.39 ! [A: real,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.39 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.39 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_left_mono_neg
% 5.17/5.39 thf(fact_2346_divide__less__eq__numeral_I1_J,axiom,
% 5.17/5.39 ! [B: real,C: real,W: num] :
% 5.17/5.39 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_eq_numeral(1)
% 5.17/5.39 thf(fact_2347_divide__less__eq__numeral_I1_J,axiom,
% 5.17/5.39 ! [B: rat,C: rat,W: num] :
% 5.17/5.39 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % divide_less_eq_numeral(1)
% 5.17/5.39 thf(fact_2348_less__divide__eq__numeral_I1_J,axiom,
% 5.17/5.39 ! [W: num,B: real,C: real] :
% 5.17/5.39 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.39 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.39 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_divide_eq_numeral(1)
% 5.17/5.39 thf(fact_2349_less__divide__eq__numeral_I1_J,axiom,
% 5.17/5.39 ! [W: num,B: rat,C: rat] :
% 5.17/5.39 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.39 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.39 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.17/5.39 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.39 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % less_divide_eq_numeral(1)
% 5.17/5.39 thf(fact_2350_frac__less__eq,axiom,
% 5.17/5.39 ! [Y4: real,Z: real,X: real,W: real] :
% 5.17/5.39 ( ( Y4 != zero_zero_real )
% 5.17/5.39 => ( ( Z != zero_zero_real )
% 5.17/5.39 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.17/5.39 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_less_eq
% 5.17/5.39 thf(fact_2351_frac__less__eq,axiom,
% 5.17/5.39 ! [Y4: rat,Z: rat,X: rat,W: rat] :
% 5.17/5.39 ( ( Y4 != zero_zero_rat )
% 5.17/5.39 => ( ( Z != zero_zero_rat )
% 5.17/5.39 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.17/5.39 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % frac_less_eq
% 5.17/5.39 thf(fact_2352_not__exp__less__eq__0__int,axiom,
% 5.17/5.39 ! [N: nat] :
% 5.17/5.39 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.17/5.39
% 5.17/5.39 % not_exp_less_eq_0_int
% 5.17/5.39 thf(fact_2353_pos2,axiom,
% 5.17/5.39 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.17/5.39
% 5.17/5.39 % pos2
% 5.17/5.39 thf(fact_2354_is__unitE,axiom,
% 5.17/5.39 ! [A: code_integer,C: code_integer] :
% 5.17/5.39 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.39 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.39 => ! [B3: code_integer] :
% 5.17/5.39 ( ( B3 != zero_z3403309356797280102nteger )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 5.17/5.39 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.17/5.39 = B3 )
% 5.17/5.39 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 5.17/5.39 = A )
% 5.17/5.39 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 5.17/5.39 = one_one_Code_integer )
% 5.17/5.39 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.17/5.39 != ( times_3573771949741848930nteger @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unitE
% 5.17/5.39 thf(fact_2355_is__unitE,axiom,
% 5.17/5.39 ! [A: nat,C: nat] :
% 5.17/5.39 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.39 => ~ ( ( A != zero_zero_nat )
% 5.17/5.39 => ! [B3: nat] :
% 5.17/5.39 ( ( B3 != zero_zero_nat )
% 5.17/5.39 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 5.17/5.39 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.17/5.39 = B3 )
% 5.17/5.39 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 5.17/5.39 = A )
% 5.17/5.39 => ( ( ( times_times_nat @ A @ B3 )
% 5.17/5.39 = one_one_nat )
% 5.17/5.39 => ( ( divide_divide_nat @ C @ A )
% 5.17/5.39 != ( times_times_nat @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unitE
% 5.17/5.39 thf(fact_2356_is__unitE,axiom,
% 5.17/5.39 ! [A: int,C: int] :
% 5.17/5.39 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.39 => ~ ( ( A != zero_zero_int )
% 5.17/5.39 => ! [B3: int] :
% 5.17/5.39 ( ( B3 != zero_zero_int )
% 5.17/5.39 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 5.17/5.39 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.17/5.39 = B3 )
% 5.17/5.39 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 5.17/5.39 = A )
% 5.17/5.39 => ( ( ( times_times_int @ A @ B3 )
% 5.17/5.39 = one_one_int )
% 5.17/5.39 => ( ( divide_divide_int @ C @ A )
% 5.17/5.39 != ( times_times_int @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.39
% 5.17/5.39 % is_unitE
% 5.17/5.39 thf(fact_2357_is__unit__div__mult__cancel__left,axiom,
% 5.17/5.39 ! [A: code_integer,B: code_integer] :
% 5.17/5.39 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.39 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.39 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.17/5.40 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_div_mult_cancel_left
% 5.17/5.40 thf(fact_2358_is__unit__div__mult__cancel__left,axiom,
% 5.17/5.40 ! [A: nat,B: nat] :
% 5.17/5.40 ( ( A != zero_zero_nat )
% 5.17/5.40 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.40 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.17/5.40 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_div_mult_cancel_left
% 5.17/5.40 thf(fact_2359_is__unit__div__mult__cancel__left,axiom,
% 5.17/5.40 ! [A: int,B: int] :
% 5.17/5.40 ( ( A != zero_zero_int )
% 5.17/5.40 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.40 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.17/5.40 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_div_mult_cancel_left
% 5.17/5.40 thf(fact_2360_is__unit__div__mult__cancel__right,axiom,
% 5.17/5.40 ! [A: code_integer,B: code_integer] :
% 5.17/5.40 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.40 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.40 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.17/5.40 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_div_mult_cancel_right
% 5.17/5.40 thf(fact_2361_is__unit__div__mult__cancel__right,axiom,
% 5.17/5.40 ! [A: nat,B: nat] :
% 5.17/5.40 ( ( A != zero_zero_nat )
% 5.17/5.40 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.40 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.17/5.40 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_div_mult_cancel_right
% 5.17/5.40 thf(fact_2362_is__unit__div__mult__cancel__right,axiom,
% 5.17/5.40 ! [A: int,B: int] :
% 5.17/5.40 ( ( A != zero_zero_int )
% 5.17/5.40 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.40 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.17/5.40 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_div_mult_cancel_right
% 5.17/5.40 thf(fact_2363_odd__one,axiom,
% 5.17/5.40 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.17/5.40
% 5.17/5.40 % odd_one
% 5.17/5.40 thf(fact_2364_odd__one,axiom,
% 5.17/5.40 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.17/5.40
% 5.17/5.40 % odd_one
% 5.17/5.40 thf(fact_2365_odd__one,axiom,
% 5.17/5.40 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.17/5.40
% 5.17/5.40 % odd_one
% 5.17/5.40 thf(fact_2366_div__if,axiom,
% 5.17/5.40 ( divide_divide_nat
% 5.17/5.40 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.40 ( if_nat
% 5.17/5.40 @ ( ( ord_less_nat @ M5 @ N4 )
% 5.17/5.40 | ( N4 = zero_zero_nat ) )
% 5.17/5.40 @ zero_zero_nat
% 5.17/5.40 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_if
% 5.17/5.40 thf(fact_2367_div__geq,axiom,
% 5.17/5.40 ! [N: nat,M: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ~ ( ord_less_nat @ M @ N )
% 5.17/5.40 => ( ( divide_divide_nat @ M @ N )
% 5.17/5.40 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_geq
% 5.17/5.40 thf(fact_2368_div__nat__eqI,axiom,
% 5.17/5.40 ! [N: nat,Q2: nat,M: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.17/5.40 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.17/5.40 => ( ( divide_divide_nat @ M @ N )
% 5.17/5.40 = Q2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_nat_eqI
% 5.17/5.40 thf(fact_2369_less__eq__div__iff__mult__less__eq,axiom,
% 5.17/5.40 ! [Q2: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % less_eq_div_iff_mult_less_eq
% 5.17/5.40 thf(fact_2370_even__mult__exp__div__exp__iff,axiom,
% 5.17/5.40 ! [A: code_integer,M: nat,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.40 = ( ( ord_less_nat @ N @ M )
% 5.17/5.40 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 = zero_z3403309356797280102nteger )
% 5.17/5.40 | ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % even_mult_exp_div_exp_iff
% 5.17/5.40 thf(fact_2371_even__mult__exp__div__exp__iff,axiom,
% 5.17/5.40 ! [A: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( 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 ) ) )
% 5.17/5.40 = ( ( ord_less_nat @ N @ M )
% 5.17/5.40 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 = zero_zero_nat )
% 5.17/5.40 | ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 & ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % even_mult_exp_div_exp_iff
% 5.17/5.40 thf(fact_2372_even__mult__exp__div__exp__iff,axiom,
% 5.17/5.40 ! [A: int,M: nat,N: nat] :
% 5.17/5.40 ( ( 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 ) ) )
% 5.17/5.40 = ( ( ord_less_nat @ N @ M )
% 5.17/5.40 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 = zero_zero_int )
% 5.17/5.40 | ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 & ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % even_mult_exp_div_exp_iff
% 5.17/5.40 thf(fact_2373_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.17/5.40 ! [N: nat,M: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.40 != zero_zero_nat ) ) ).
% 5.17/5.40
% 5.17/5.40 % exp_not_zero_imp_exp_diff_not_zero
% 5.17/5.40 thf(fact_2374_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.17/5.40 ! [N: nat,M: nat] :
% 5.17/5.40 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 != zero_zero_int )
% 5.17/5.40 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.40 != zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % exp_not_zero_imp_exp_diff_not_zero
% 5.17/5.40 thf(fact_2375_power__mono__odd,axiom,
% 5.17/5.40 ! [N: nat,A: rat,B: rat] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.40 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_odd
% 5.17/5.40 thf(fact_2376_power__mono__odd,axiom,
% 5.17/5.40 ! [N: nat,A: int,B: int] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ( ord_less_eq_int @ A @ B )
% 5.17/5.40 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_odd
% 5.17/5.40 thf(fact_2377_power__mono__odd,axiom,
% 5.17/5.40 ! [N: nat,A: real,B: real] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.40 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_odd
% 5.17/5.40 thf(fact_2378_divide__le__eq__numeral_I1_J,axiom,
% 5.17/5.40 ! [B: rat,C: rat,W: num] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.17/5.40 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.40 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.17/5.40 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.40 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.40 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.17/5.40 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % divide_le_eq_numeral(1)
% 5.17/5.40 thf(fact_2379_divide__le__eq__numeral_I1_J,axiom,
% 5.17/5.40 ! [B: real,C: real,W: num] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.17/5.40 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.40 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.17/5.40 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.40 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.40 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.17/5.40 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.40 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % divide_le_eq_numeral(1)
% 5.17/5.40 thf(fact_2380_le__divide__eq__numeral_I1_J,axiom,
% 5.17/5.40 ! [W: num,B: rat,C: rat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.40 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.40 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.17/5.40 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.40 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.40 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.17/5.40 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.40 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_divide_eq_numeral(1)
% 5.17/5.40 thf(fact_2381_le__divide__eq__numeral_I1_J,axiom,
% 5.17/5.40 ! [W: num,B: real,C: real] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.17/5.40 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.40 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.17/5.40 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.40 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.40 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.17/5.40 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.40 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_divide_eq_numeral(1)
% 5.17/5.40 thf(fact_2382_half__gt__zero,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % half_gt_zero
% 5.17/5.40 thf(fact_2383_half__gt__zero,axiom,
% 5.17/5.40 ! [A: rat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % half_gt_zero
% 5.17/5.40 thf(fact_2384_half__gt__zero__iff,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % half_gt_zero_iff
% 5.17/5.40 thf(fact_2385_half__gt__zero__iff,axiom,
% 5.17/5.40 ! [A: rat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % half_gt_zero_iff
% 5.17/5.40 thf(fact_2386_four__x__squared,axiom,
% 5.17/5.40 ! [X: real] :
% 5.17/5.40 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % four_x_squared
% 5.17/5.40 thf(fact_2387_less__2__cases,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 => ( ( N = zero_zero_nat )
% 5.17/5.40 | ( N
% 5.17/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % less_2_cases
% 5.17/5.40 thf(fact_2388_less__2__cases__iff,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = ( ( N = zero_zero_nat )
% 5.17/5.40 | ( N
% 5.17/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % less_2_cases_iff
% 5.17/5.40 thf(fact_2389_real__of__nat__div2,axiom,
% 5.17/5.40 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_div2
% 5.17/5.40 thf(fact_2390_odd__pos,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % odd_pos
% 5.17/5.40 thf(fact_2391_le__div__geq,axiom,
% 5.17/5.40 ! [N: nat,M: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( ( divide_divide_nat @ M @ N )
% 5.17/5.40 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_div_geq
% 5.17/5.40 thf(fact_2392_split__div_H,axiom,
% 5.17/5.40 ! [P: nat > $o,M: nat,N: nat] :
% 5.17/5.40 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.40 = ( ( ( N = zero_zero_nat )
% 5.17/5.40 & ( P @ zero_zero_nat ) )
% 5.17/5.40 | ? [Q3: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 5.17/5.40 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 5.17/5.40 & ( P @ Q3 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % split_div'
% 5.17/5.40 thf(fact_2393_inverse__of__nat__le,axiom,
% 5.17/5.40 ! [N: nat,M: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inverse_of_nat_le
% 5.17/5.40 thf(fact_2394_inverse__of__nat__le,axiom,
% 5.17/5.40 ! [N: nat,M: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inverse_of_nat_le
% 5.17/5.40 thf(fact_2395_real__archimedian__rdiv__eq__0,axiom,
% 5.17/5.40 ! [X: real,C: real] :
% 5.17/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.40 => ( ! [M4: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.17/5.40 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 5.17/5.40 => ( X = zero_zero_real ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_archimedian_rdiv_eq_0
% 5.17/5.40 thf(fact_2396_zero__le__power__eq,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.17/5.40 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power_eq
% 5.17/5.40 thf(fact_2397_zero__le__power__eq,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.17/5.40 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power_eq
% 5.17/5.40 thf(fact_2398_zero__le__power__eq,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.17/5.40 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power_eq
% 5.17/5.40 thf(fact_2399_zero__le__odd__power,axiom,
% 5.17/5.40 ! [N: nat,A: rat] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.17/5.40 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_odd_power
% 5.17/5.40 thf(fact_2400_zero__le__odd__power,axiom,
% 5.17/5.40 ! [N: nat,A: int] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.17/5.40 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_odd_power
% 5.17/5.40 thf(fact_2401_zero__le__odd__power,axiom,
% 5.17/5.40 ! [N: nat,A: real] :
% 5.17/5.40 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.17/5.40 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_odd_power
% 5.17/5.40 thf(fact_2402_zero__le__even__power,axiom,
% 5.17/5.40 ! [N: nat,A: rat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_even_power
% 5.17/5.40 thf(fact_2403_zero__le__even__power,axiom,
% 5.17/5.40 ! [N: nat,A: int] :
% 5.17/5.40 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_even_power
% 5.17/5.40 thf(fact_2404_zero__le__even__power,axiom,
% 5.17/5.40 ! [N: nat,A: real] :
% 5.17/5.40 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.40 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_even_power
% 5.17/5.40 thf(fact_2405_nat__bit__induct,axiom,
% 5.17/5.40 ! [P: nat > $o,N: nat] :
% 5.17/5.40 ( ( P @ zero_zero_nat )
% 5.17/5.40 => ( ! [N2: nat] :
% 5.17/5.40 ( ( P @ N2 )
% 5.17/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.40 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.17/5.40 => ( ! [N2: nat] :
% 5.17/5.40 ( ( P @ N2 )
% 5.17/5.40 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.17/5.40 => ( P @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nat_bit_induct
% 5.17/5.40 thf(fact_2406_div__2__gt__zero,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.40 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_2_gt_zero
% 5.17/5.40 thf(fact_2407_Suc__n__div__2__gt__zero,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % Suc_n_div_2_gt_zero
% 5.17/5.40 thf(fact_2408_inf__period_I2_J,axiom,
% 5.17/5.40 ! [P: real > $o,D3: real,Q: real > $o] :
% 5.17/5.40 ( ! [X4: real,K2: real] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ( ! [X4: real,K2: real] :
% 5.17/5.40 ( ( Q @ X4 )
% 5.17/5.40 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ! [X5: real,K4: real] :
% 5.17/5.40 ( ( ( P @ X5 )
% 5.17/5.40 | ( Q @ X5 ) )
% 5.17/5.40 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 5.17/5.40 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inf_period(2)
% 5.17/5.40 thf(fact_2409_inf__period_I2_J,axiom,
% 5.17/5.40 ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 5.17/5.40 ( ! [X4: rat,K2: rat] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ( ! [X4: rat,K2: rat] :
% 5.17/5.40 ( ( Q @ X4 )
% 5.17/5.40 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ! [X5: rat,K4: rat] :
% 5.17/5.40 ( ( ( P @ X5 )
% 5.17/5.40 | ( Q @ X5 ) )
% 5.17/5.40 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.17/5.40 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inf_period(2)
% 5.17/5.40 thf(fact_2410_inf__period_I2_J,axiom,
% 5.17/5.40 ! [P: int > $o,D3: int,Q: int > $o] :
% 5.17/5.40 ( ! [X4: int,K2: int] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ( ! [X4: int,K2: int] :
% 5.17/5.40 ( ( Q @ X4 )
% 5.17/5.40 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ! [X5: int,K4: int] :
% 5.17/5.40 ( ( ( P @ X5 )
% 5.17/5.40 | ( Q @ X5 ) )
% 5.17/5.40 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.17/5.40 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inf_period(2)
% 5.17/5.40 thf(fact_2411_inf__period_I1_J,axiom,
% 5.17/5.40 ! [P: real > $o,D3: real,Q: real > $o] :
% 5.17/5.40 ( ! [X4: real,K2: real] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ( ! [X4: real,K2: real] :
% 5.17/5.40 ( ( Q @ X4 )
% 5.17/5.40 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ! [X5: real,K4: real] :
% 5.17/5.40 ( ( ( P @ X5 )
% 5.17/5.40 & ( Q @ X5 ) )
% 5.17/5.40 = ( ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 5.17/5.40 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inf_period(1)
% 5.17/5.40 thf(fact_2412_inf__period_I1_J,axiom,
% 5.17/5.40 ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 5.17/5.40 ( ! [X4: rat,K2: rat] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ( ! [X4: rat,K2: rat] :
% 5.17/5.40 ( ( Q @ X4 )
% 5.17/5.40 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ! [X5: rat,K4: rat] :
% 5.17/5.40 ( ( ( P @ X5 )
% 5.17/5.40 & ( Q @ X5 ) )
% 5.17/5.40 = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.17/5.40 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inf_period(1)
% 5.17/5.40 thf(fact_2413_inf__period_I1_J,axiom,
% 5.17/5.40 ! [P: int > $o,D3: int,Q: int > $o] :
% 5.17/5.40 ( ! [X4: int,K2: int] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ( ! [X4: int,K2: int] :
% 5.17/5.40 ( ( Q @ X4 )
% 5.17/5.40 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.17/5.40 => ! [X5: int,K4: int] :
% 5.17/5.40 ( ( ( P @ X5 )
% 5.17/5.40 & ( Q @ X5 ) )
% 5.17/5.40 = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.17/5.40 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % inf_period(1)
% 5.17/5.40 thf(fact_2414_dvd__productE,axiom,
% 5.17/5.40 ! [P5: nat,A: nat,B: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 5.17/5.40 => ~ ! [X4: nat,Y: nat] :
% 5.17/5.40 ( ( P5
% 5.17/5.40 = ( times_times_nat @ X4 @ Y ) )
% 5.17/5.40 => ( ( dvd_dvd_nat @ X4 @ A )
% 5.17/5.40 => ~ ( dvd_dvd_nat @ Y @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_productE
% 5.17/5.40 thf(fact_2415_dvd__productE,axiom,
% 5.17/5.40 ! [P5: int,A: int,B: int] :
% 5.17/5.40 ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 5.17/5.40 => ~ ! [X4: int,Y: int] :
% 5.17/5.40 ( ( P5
% 5.17/5.40 = ( times_times_int @ X4 @ Y ) )
% 5.17/5.40 => ( ( dvd_dvd_int @ X4 @ A )
% 5.17/5.40 => ~ ( dvd_dvd_int @ Y @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_productE
% 5.17/5.40 thf(fact_2416_division__decomp,axiom,
% 5.17/5.40 ! [A: nat,B: nat,C: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.40 => ? [B7: nat,C4: nat] :
% 5.17/5.40 ( ( A
% 5.17/5.40 = ( times_times_nat @ B7 @ C4 ) )
% 5.17/5.40 & ( dvd_dvd_nat @ B7 @ B )
% 5.17/5.40 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % division_decomp
% 5.17/5.40 thf(fact_2417_division__decomp,axiom,
% 5.17/5.40 ! [A: int,B: int,C: int] :
% 5.17/5.40 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.40 => ? [B7: int,C4: int] :
% 5.17/5.40 ( ( A
% 5.17/5.40 = ( times_times_int @ B7 @ C4 ) )
% 5.17/5.40 & ( dvd_dvd_int @ B7 @ B )
% 5.17/5.40 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % division_decomp
% 5.17/5.40 thf(fact_2418_space__space_H,axiom,
% 5.17/5.40 ! [T: vEBT_VEBT] : ( ord_less_nat @ ( vEBT_VEBT_space @ T ) @ ( vEBT_VEBT_space2 @ T ) ) ).
% 5.17/5.40
% 5.17/5.40 % space_space'
% 5.17/5.40 thf(fact_2419_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2420_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2421_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2422_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2423_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2424_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2425_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2426_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2427_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2428_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2429_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2430_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [I: num,N: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2431_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2432_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2433_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2434_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,I: num,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2435_of__nat__zero__less__power__iff,axiom,
% 5.17/5.40 ! [X: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 5.17/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_zero_less_power_iff
% 5.17/5.40 thf(fact_2436_of__nat__zero__less__power__iff,axiom,
% 5.17/5.40 ! [X: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 5.17/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_zero_less_power_iff
% 5.17/5.40 thf(fact_2437_of__nat__zero__less__power__iff,axiom,
% 5.17/5.40 ! [X: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 5.17/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_zero_less_power_iff
% 5.17/5.40 thf(fact_2438_of__nat__zero__less__power__iff,axiom,
% 5.17/5.40 ! [X: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 5.17/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_zero_less_power_iff
% 5.17/5.40 thf(fact_2439_zero__less__power2,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( A != zero_zero_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power2
% 5.17/5.40 thf(fact_2440_zero__less__power2,axiom,
% 5.17/5.40 ! [A: rat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( A != zero_zero_rat ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power2
% 5.17/5.40 thf(fact_2441_zero__less__power2,axiom,
% 5.17/5.40 ! [A: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( A != zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power2
% 5.17/5.40 thf(fact_2442_power2__less__eq__zero__iff,axiom,
% 5.17/5.40 ! [A: rat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.17/5.40 = ( A = zero_zero_rat ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_less_eq_zero_iff
% 5.17/5.40 thf(fact_2443_power2__less__eq__zero__iff,axiom,
% 5.17/5.40 ! [A: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.17/5.40 = ( A = zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_less_eq_zero_iff
% 5.17/5.40 thf(fact_2444_power2__less__eq__zero__iff,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.17/5.40 = ( A = zero_zero_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_less_eq_zero_iff
% 5.17/5.40 thf(fact_2445_power2__eq__iff__nonneg,axiom,
% 5.17/5.40 ! [X: rat,Y4: rat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.40 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( X = Y4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_eq_iff_nonneg
% 5.17/5.40 thf(fact_2446_power2__eq__iff__nonneg,axiom,
% 5.17/5.40 ! [X: nat,Y4: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.17/5.40 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( X = Y4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_eq_iff_nonneg
% 5.17/5.40 thf(fact_2447_power2__eq__iff__nonneg,axiom,
% 5.17/5.40 ! [X: int,Y4: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.40 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( X = Y4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_eq_iff_nonneg
% 5.17/5.40 thf(fact_2448_power2__eq__iff__nonneg,axiom,
% 5.17/5.40 ! [X: real,Y4: real] :
% 5.17/5.40 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.40 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( X = Y4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_eq_iff_nonneg
% 5.17/5.40 thf(fact_2449_power__decreasing__iff,axiom,
% 5.17/5.40 ! [B: rat,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.40 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.17/5.40 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_decreasing_iff
% 5.17/5.40 thf(fact_2450_power__decreasing__iff,axiom,
% 5.17/5.40 ! [B: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.40 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.17/5.40 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_decreasing_iff
% 5.17/5.40 thf(fact_2451_power__decreasing__iff,axiom,
% 5.17/5.40 ! [B: int,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ( ord_less_int @ B @ one_one_int )
% 5.17/5.40 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_decreasing_iff
% 5.17/5.40 thf(fact_2452_power__decreasing__iff,axiom,
% 5.17/5.40 ! [B: real,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.40 => ( ( ord_less_real @ B @ one_one_real )
% 5.17/5.40 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_decreasing_iff
% 5.17/5.40 thf(fact_2453_power__mono__iff,axiom,
% 5.17/5.40 ! [A: rat,B: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_iff
% 5.17/5.40 thf(fact_2454_power__mono__iff,axiom,
% 5.17/5.40 ! [A: nat,B: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_iff
% 5.17/5.40 thf(fact_2455_power__mono__iff,axiom,
% 5.17/5.40 ! [A: int,B: int,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_iff
% 5.17/5.40 thf(fact_2456_power__mono__iff,axiom,
% 5.17/5.40 ! [A: real,B: real,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.40 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.17/5.40 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono_iff
% 5.17/5.40 thf(fact_2457_psubsetI,axiom,
% 5.17/5.40 ! [A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.40 => ( ( A2 != B4 )
% 5.17/5.40 => ( ord_less_set_int @ A2 @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubsetI
% 5.17/5.40 thf(fact_2458_DiffI,axiom,
% 5.17/5.40 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.17/5.40 ( ( member_complex @ C @ A2 )
% 5.17/5.40 => ( ~ ( member_complex @ C @ B4 )
% 5.17/5.40 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffI
% 5.17/5.40 thf(fact_2459_DiffI,axiom,
% 5.17/5.40 ! [C: real,A2: set_real,B4: set_real] :
% 5.17/5.40 ( ( member_real @ C @ A2 )
% 5.17/5.40 => ( ~ ( member_real @ C @ B4 )
% 5.17/5.40 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffI
% 5.17/5.40 thf(fact_2460_DiffI,axiom,
% 5.17/5.40 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.40 ( ( member_set_nat @ C @ A2 )
% 5.17/5.40 => ( ~ ( member_set_nat @ C @ B4 )
% 5.17/5.40 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffI
% 5.17/5.40 thf(fact_2461_DiffI,axiom,
% 5.17/5.40 ! [C: int,A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( member_int @ C @ A2 )
% 5.17/5.40 => ( ~ ( member_int @ C @ B4 )
% 5.17/5.40 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffI
% 5.17/5.40 thf(fact_2462_DiffI,axiom,
% 5.17/5.40 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( member_nat @ C @ A2 )
% 5.17/5.40 => ( ~ ( member_nat @ C @ B4 )
% 5.17/5.40 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffI
% 5.17/5.40 thf(fact_2463_Diff__iff,axiom,
% 5.17/5.40 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.17/5.40 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.17/5.40 = ( ( member_complex @ C @ A2 )
% 5.17/5.40 & ~ ( member_complex @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % Diff_iff
% 5.17/5.40 thf(fact_2464_Diff__iff,axiom,
% 5.17/5.40 ! [C: real,A2: set_real,B4: set_real] :
% 5.17/5.40 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.17/5.40 = ( ( member_real @ C @ A2 )
% 5.17/5.40 & ~ ( member_real @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % Diff_iff
% 5.17/5.40 thf(fact_2465_Diff__iff,axiom,
% 5.17/5.40 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.40 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.17/5.40 = ( ( member_set_nat @ C @ A2 )
% 5.17/5.40 & ~ ( member_set_nat @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % Diff_iff
% 5.17/5.40 thf(fact_2466_Diff__iff,axiom,
% 5.17/5.40 ! [C: int,A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.17/5.40 = ( ( member_int @ C @ A2 )
% 5.17/5.40 & ~ ( member_int @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % Diff_iff
% 5.17/5.40 thf(fact_2467_Diff__iff,axiom,
% 5.17/5.40 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.17/5.40 = ( ( member_nat @ C @ A2 )
% 5.17/5.40 & ~ ( member_nat @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % Diff_iff
% 5.17/5.40 thf(fact_2468_Diff__idemp,axiom,
% 5.17/5.40 ! [A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B4 ) @ B4 )
% 5.17/5.40 = ( minus_minus_set_nat @ A2 @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % Diff_idemp
% 5.17/5.40 thf(fact_2469_i0__less,axiom,
% 5.17/5.40 ! [N: extended_enat] :
% 5.17/5.40 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.17/5.40 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.17/5.40
% 5.17/5.40 % i0_less
% 5.17/5.40 thf(fact_2470_two__realpow__ge__two,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.40 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % two_realpow_ge_two
% 5.17/5.40 thf(fact_2471_not__real__square__gt__zero,axiom,
% 5.17/5.40 ! [X: real] :
% 5.17/5.40 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.17/5.40 = ( X = zero_zero_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % not_real_square_gt_zero
% 5.17/5.40 thf(fact_2472_zle__diff1__eq,axiom,
% 5.17/5.40 ! [W: int,Z: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.17/5.40 = ( ord_less_int @ W @ Z ) ) ).
% 5.17/5.40
% 5.17/5.40 % zle_diff1_eq
% 5.17/5.40 thf(fact_2473_semiring__norm_I78_J,axiom,
% 5.17/5.40 ! [M: num,N: num] :
% 5.17/5.40 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.40 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(78)
% 5.17/5.40 thf(fact_2474_semiring__norm_I75_J,axiom,
% 5.17/5.40 ! [M: num] :
% 5.17/5.40 ~ ( ord_less_num @ M @ one ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(75)
% 5.17/5.40 thf(fact_2475_semiring__norm_I80_J,axiom,
% 5.17/5.40 ! [M: num,N: num] :
% 5.17/5.40 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.40 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(80)
% 5.17/5.40 thf(fact_2476_unset__bit__negative__int__iff,axiom,
% 5.17/5.40 ! [N: nat,K: int] :
% 5.17/5.40 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.17/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % unset_bit_negative_int_iff
% 5.17/5.40 thf(fact_2477_set__bit__negative__int__iff,axiom,
% 5.17/5.40 ! [N: nat,K: int] :
% 5.17/5.40 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.17/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % set_bit_negative_int_iff
% 5.17/5.40 thf(fact_2478_flip__bit__negative__int__iff,axiom,
% 5.17/5.40 ! [N: nat,K: int] :
% 5.17/5.40 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.17/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % flip_bit_negative_int_iff
% 5.17/5.40 thf(fact_2479_power__0__Suc,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.17/5.40 = zero_zero_rat ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_Suc
% 5.17/5.40 thf(fact_2480_power__0__Suc,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.17/5.40 = zero_zero_int ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_Suc
% 5.17/5.40 thf(fact_2481_power__0__Suc,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.17/5.40 = zero_zero_real ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_Suc
% 5.17/5.40 thf(fact_2482_power__0__Suc,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.17/5.40 = zero_zero_nat ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_Suc
% 5.17/5.40 thf(fact_2483_power__0__Suc,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.17/5.40 = zero_zero_complex ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_Suc
% 5.17/5.40 thf(fact_2484_power__zero__numeral,axiom,
% 5.17/5.40 ! [K: num] :
% 5.17/5.40 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.17/5.40 = zero_zero_rat ) ).
% 5.17/5.40
% 5.17/5.40 % power_zero_numeral
% 5.17/5.40 thf(fact_2485_power__zero__numeral,axiom,
% 5.17/5.40 ! [K: num] :
% 5.17/5.40 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.17/5.40 = zero_zero_int ) ).
% 5.17/5.40
% 5.17/5.40 % power_zero_numeral
% 5.17/5.40 thf(fact_2486_power__zero__numeral,axiom,
% 5.17/5.40 ! [K: num] :
% 5.17/5.40 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.17/5.40 = zero_zero_real ) ).
% 5.17/5.40
% 5.17/5.40 % power_zero_numeral
% 5.17/5.40 thf(fact_2487_power__zero__numeral,axiom,
% 5.17/5.40 ! [K: num] :
% 5.17/5.40 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.17/5.40 = zero_zero_nat ) ).
% 5.17/5.40
% 5.17/5.40 % power_zero_numeral
% 5.17/5.40 thf(fact_2488_power__zero__numeral,axiom,
% 5.17/5.40 ! [K: num] :
% 5.17/5.40 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.17/5.40 = zero_zero_complex ) ).
% 5.17/5.40
% 5.17/5.40 % power_zero_numeral
% 5.17/5.40 thf(fact_2489_power__Suc0__right,axiom,
% 5.17/5.40 ! [A: int] :
% 5.17/5.40 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.17/5.40 = A ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc0_right
% 5.17/5.40 thf(fact_2490_power__Suc0__right,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.17/5.40 = A ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc0_right
% 5.17/5.40 thf(fact_2491_power__Suc0__right,axiom,
% 5.17/5.40 ! [A: nat] :
% 5.17/5.40 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.17/5.40 = A ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc0_right
% 5.17/5.40 thf(fact_2492_power__Suc0__right,axiom,
% 5.17/5.40 ! [A: complex] :
% 5.17/5.40 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.17/5.40 = A ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc0_right
% 5.17/5.40 thf(fact_2493_power__Suc__0,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.40 = ( suc @ zero_zero_nat ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc_0
% 5.17/5.40 thf(fact_2494_nat__power__eq__Suc__0__iff,axiom,
% 5.17/5.40 ! [X: nat,M: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ X @ M )
% 5.17/5.40 = ( suc @ zero_zero_nat ) )
% 5.17/5.40 = ( ( M = zero_zero_nat )
% 5.17/5.40 | ( X
% 5.17/5.40 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nat_power_eq_Suc_0_iff
% 5.17/5.40 thf(fact_2495_nat__zero__less__power__iff,axiom,
% 5.17/5.40 ! [X: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 5.17/5.40 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nat_zero_less_power_iff
% 5.17/5.40 thf(fact_2496_of__nat__power,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power
% 5.17/5.40 thf(fact_2497_of__nat__power,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power
% 5.17/5.40 thf(fact_2498_of__nat__power,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power
% 5.17/5.40 thf(fact_2499_of__nat__power,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power
% 5.17/5.40 thf(fact_2500_of__nat__power,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power
% 5.17/5.40 thf(fact_2501_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.17/5.40 = ( semiri8010041392384452111omplex @ X ) )
% 5.17/5.40 = ( ( power_power_nat @ B @ W )
% 5.17/5.40 = X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_eq_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2502_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.17/5.40 = ( semiri5074537144036343181t_real @ X ) )
% 5.17/5.40 = ( ( power_power_nat @ B @ W )
% 5.17/5.40 = X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_eq_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2503_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.17/5.40 = ( semiri681578069525770553at_rat @ X ) )
% 5.17/5.40 = ( ( power_power_nat @ B @ W )
% 5.17/5.40 = X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_eq_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2504_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.17/5.40 = ( semiri1316708129612266289at_nat @ X ) )
% 5.17/5.40 = ( ( power_power_nat @ B @ W )
% 5.17/5.40 = X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_eq_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2505_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.17/5.40 = ( semiri1314217659103216013at_int @ X ) )
% 5.17/5.40 = ( ( power_power_nat @ B @ W )
% 5.17/5.40 = X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_eq_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2506_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ( semiri8010041392384452111omplex @ X )
% 5.17/5.40 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.17/5.40 = ( X
% 5.17/5.40 = ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2507_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ( semiri5074537144036343181t_real @ X )
% 5.17/5.40 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.17/5.40 = ( X
% 5.17/5.40 = ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2508_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ( semiri681578069525770553at_rat @ X )
% 5.17/5.40 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.17/5.40 = ( X
% 5.17/5.40 = ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2509_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.17/5.40 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.17/5.40 = ( X
% 5.17/5.40 = ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2510_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ( semiri1314217659103216013at_int @ X )
% 5.17/5.40 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.17/5.40 = ( X
% 5.17/5.40 = ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2511_div__neg__neg__trivial,axiom,
% 5.17/5.40 ! [K: int,L: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.17/5.40 => ( ( ord_less_int @ L @ K )
% 5.17/5.40 => ( ( divide_divide_int @ K @ L )
% 5.17/5.40 = zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_neg_neg_trivial
% 5.17/5.40 thf(fact_2512_div__pos__pos__trivial,axiom,
% 5.17/5.40 ! [K: int,L: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.40 => ( ( ord_less_int @ K @ L )
% 5.17/5.40 => ( ( divide_divide_int @ K @ L )
% 5.17/5.40 = zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_pos_pos_trivial
% 5.17/5.40 thf(fact_2513_power__mult__numeral,axiom,
% 5.17/5.40 ! [A: int,M: num,N: num] :
% 5.17/5.40 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.40 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_numeral
% 5.17/5.40 thf(fact_2514_power__mult__numeral,axiom,
% 5.17/5.40 ! [A: real,M: num,N: num] :
% 5.17/5.40 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.40 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_numeral
% 5.17/5.40 thf(fact_2515_power__mult__numeral,axiom,
% 5.17/5.40 ! [A: nat,M: num,N: num] :
% 5.17/5.40 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.40 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_numeral
% 5.17/5.40 thf(fact_2516_power__mult__numeral,axiom,
% 5.17/5.40 ! [A: complex,M: num,N: num] :
% 5.17/5.40 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.40 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_numeral
% 5.17/5.40 thf(fact_2517_semiring__norm_I76_J,axiom,
% 5.17/5.40 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(76)
% 5.17/5.40 thf(fact_2518_semiring__norm_I81_J,axiom,
% 5.17/5.40 ! [M: num,N: num] :
% 5.17/5.40 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.40 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(81)
% 5.17/5.40 thf(fact_2519_semiring__norm_I77_J,axiom,
% 5.17/5.40 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(77)
% 5.17/5.40 thf(fact_2520_enat__ord__number_I2_J,axiom,
% 5.17/5.40 ! [M: num,N: num] :
% 5.17/5.40 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.17/5.40 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % enat_ord_number(2)
% 5.17/5.40 thf(fact_2521_power__eq__0__iff,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ( power_power_rat @ A @ N )
% 5.17/5.40 = zero_zero_rat )
% 5.17/5.40 = ( ( A = zero_zero_rat )
% 5.17/5.40 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_eq_0_iff
% 5.17/5.40 thf(fact_2522_power__eq__0__iff,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ( power_power_int @ A @ N )
% 5.17/5.40 = zero_zero_int )
% 5.17/5.40 = ( ( A = zero_zero_int )
% 5.17/5.40 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_eq_0_iff
% 5.17/5.40 thf(fact_2523_power__eq__0__iff,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ( power_power_real @ A @ N )
% 5.17/5.40 = zero_zero_real )
% 5.17/5.40 = ( ( A = zero_zero_real )
% 5.17/5.40 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_eq_0_iff
% 5.17/5.40 thf(fact_2524_power__eq__0__iff,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ A @ N )
% 5.17/5.40 = zero_zero_nat )
% 5.17/5.40 = ( ( A = zero_zero_nat )
% 5.17/5.40 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_eq_0_iff
% 5.17/5.40 thf(fact_2525_power__eq__0__iff,axiom,
% 5.17/5.40 ! [A: complex,N: nat] :
% 5.17/5.40 ( ( ( power_power_complex @ A @ N )
% 5.17/5.40 = zero_zero_complex )
% 5.17/5.40 = ( ( A = zero_zero_complex )
% 5.17/5.40 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_eq_0_iff
% 5.17/5.40 thf(fact_2526_real__of__nat__less__numeral__iff,axiom,
% 5.17/5.40 ! [N: nat,W: num] :
% 5.17/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.17/5.40 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_less_numeral_iff
% 5.17/5.40 thf(fact_2527_numeral__less__real__of__nat__iff,axiom,
% 5.17/5.40 ! [W: num,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.40 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_less_real_of_nat_iff
% 5.17/5.40 thf(fact_2528_semiring__norm_I74_J,axiom,
% 5.17/5.40 ! [M: num,N: num] :
% 5.17/5.40 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.40 = ( ord_less_num @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(74)
% 5.17/5.40 thf(fact_2529_semiring__norm_I79_J,axiom,
% 5.17/5.40 ! [M: num,N: num] :
% 5.17/5.40 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.40 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % semiring_norm(79)
% 5.17/5.40 thf(fact_2530_power__strict__decreasing__iff,axiom,
% 5.17/5.40 ! [B: real,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.40 => ( ( ord_less_real @ B @ one_one_real )
% 5.17/5.40 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.17/5.40 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_strict_decreasing_iff
% 5.17/5.40 thf(fact_2531_power__strict__decreasing__iff,axiom,
% 5.17/5.40 ! [B: rat,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.40 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.17/5.40 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.17/5.40 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_strict_decreasing_iff
% 5.17/5.40 thf(fact_2532_power__strict__decreasing__iff,axiom,
% 5.17/5.40 ! [B: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.40 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.17/5.40 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.17/5.40 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_strict_decreasing_iff
% 5.17/5.40 thf(fact_2533_power__strict__decreasing__iff,axiom,
% 5.17/5.40 ! [B: int,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ( ord_less_int @ B @ one_one_int )
% 5.17/5.40 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.17/5.40 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_strict_decreasing_iff
% 5.17/5.40 thf(fact_2534_power__increasing__iff,axiom,
% 5.17/5.40 ! [B: rat,X: nat,Y4: nat] :
% 5.17/5.40 ( ( ord_less_rat @ one_one_rat @ B )
% 5.17/5.40 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y4 ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing_iff
% 5.17/5.40 thf(fact_2535_power__increasing__iff,axiom,
% 5.17/5.40 ! [B: nat,X: nat,Y4: nat] :
% 5.17/5.40 ( ( ord_less_nat @ one_one_nat @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y4 ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing_iff
% 5.17/5.40 thf(fact_2536_power__increasing__iff,axiom,
% 5.17/5.40 ! [B: int,X: nat,Y4: nat] :
% 5.17/5.40 ( ( ord_less_int @ one_one_int @ B )
% 5.17/5.40 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y4 ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing_iff
% 5.17/5.40 thf(fact_2537_power__increasing__iff,axiom,
% 5.17/5.40 ! [B: real,X: nat,Y4: nat] :
% 5.17/5.40 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.40 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y4 ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing_iff
% 5.17/5.40 thf(fact_2538_zero__eq__power2,axiom,
% 5.17/5.40 ! [A: rat] :
% 5.17/5.40 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = zero_zero_rat )
% 5.17/5.40 = ( A = zero_zero_rat ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_eq_power2
% 5.17/5.40 thf(fact_2539_zero__eq__power2,axiom,
% 5.17/5.40 ! [A: int] :
% 5.17/5.40 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = zero_zero_int )
% 5.17/5.40 = ( A = zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_eq_power2
% 5.17/5.40 thf(fact_2540_zero__eq__power2,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = zero_zero_real )
% 5.17/5.40 = ( A = zero_zero_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_eq_power2
% 5.17/5.40 thf(fact_2541_zero__eq__power2,axiom,
% 5.17/5.40 ! [A: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = zero_zero_nat )
% 5.17/5.40 = ( A = zero_zero_nat ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_eq_power2
% 5.17/5.40 thf(fact_2542_zero__eq__power2,axiom,
% 5.17/5.40 ! [A: complex] :
% 5.17/5.40 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.40 = zero_zero_complex )
% 5.17/5.40 = ( A = zero_zero_complex ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_eq_power2
% 5.17/5.40 thf(fact_2543_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2544_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2545_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2546_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.17/5.40 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_less_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2547_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2548_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2549_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2550_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_less_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2551_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2552_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2553_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2554_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: nat,B: nat,W: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.17/5.40 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_power_le_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2555_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2556_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2557_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2558_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.17/5.40 ! [B: nat,W: nat,X: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.17/5.40 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.17/5.40
% 5.17/5.40 % of_nat_le_of_nat_power_cancel_iff
% 5.17/5.40 thf(fact_2559_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [Y4: nat,X: num,N: nat] :
% 5.17/5.40 ( ( ( semiri8010041392384452111omplex @ Y4 )
% 5.17/5.40 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.17/5.40 = ( Y4
% 5.17/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2560_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [Y4: nat,X: num,N: nat] :
% 5.17/5.40 ( ( ( semiri5074537144036343181t_real @ Y4 )
% 5.17/5.40 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.17/5.40 = ( Y4
% 5.17/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2561_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [Y4: nat,X: num,N: nat] :
% 5.17/5.40 ( ( ( semiri681578069525770553at_rat @ Y4 )
% 5.17/5.40 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.17/5.40 = ( Y4
% 5.17/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2562_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [Y4: nat,X: num,N: nat] :
% 5.17/5.40 ( ( ( semiri1316708129612266289at_nat @ Y4 )
% 5.17/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.17/5.40 = ( Y4
% 5.17/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2563_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.40 ! [Y4: nat,X: num,N: nat] :
% 5.17/5.40 ( ( ( semiri1314217659103216013at_int @ Y4 )
% 5.17/5.40 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.17/5.40 = ( Y4
% 5.17/5.40 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_eq_numeral_power_cancel_iff
% 5.17/5.40 thf(fact_2564_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: num,N: nat,Y4: nat] :
% 5.17/5.40 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.17/5.40 = ( semiri8010041392384452111omplex @ Y4 ) )
% 5.17/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.40 = Y4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2565_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: num,N: nat,Y4: nat] :
% 5.17/5.40 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.17/5.40 = ( semiri5074537144036343181t_real @ Y4 ) )
% 5.17/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.40 = Y4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2566_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: num,N: nat,Y4: nat] :
% 5.17/5.40 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.17/5.40 = ( semiri681578069525770553at_rat @ Y4 ) )
% 5.17/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.40 = Y4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2567_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: num,N: nat,Y4: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.40 = ( semiri1316708129612266289at_nat @ Y4 ) )
% 5.17/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.40 = Y4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2568_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.17/5.40 ! [X: num,N: nat,Y4: nat] :
% 5.17/5.40 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.40 = ( semiri1314217659103216013at_int @ Y4 ) )
% 5.17/5.40 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.40 = Y4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % numeral_power_eq_of_nat_cancel_iff
% 5.17/5.40 thf(fact_2569_half__negative__int__iff,axiom,
% 5.17/5.40 ! [K: int] :
% 5.17/5.40 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.17/5.40 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % half_negative_int_iff
% 5.17/5.40 thf(fact_2570_DiffE,axiom,
% 5.17/5.40 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.17/5.40 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( ( member_complex @ C @ A2 )
% 5.17/5.40 => ( member_complex @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffE
% 5.17/5.40 thf(fact_2571_DiffE,axiom,
% 5.17/5.40 ! [C: real,A2: set_real,B4: set_real] :
% 5.17/5.40 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( ( member_real @ C @ A2 )
% 5.17/5.40 => ( member_real @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffE
% 5.17/5.40 thf(fact_2572_DiffE,axiom,
% 5.17/5.40 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.40 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( ( member_set_nat @ C @ A2 )
% 5.17/5.40 => ( member_set_nat @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffE
% 5.17/5.40 thf(fact_2573_DiffE,axiom,
% 5.17/5.40 ! [C: int,A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( ( member_int @ C @ A2 )
% 5.17/5.40 => ( member_int @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffE
% 5.17/5.40 thf(fact_2574_DiffE,axiom,
% 5.17/5.40 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( ( member_nat @ C @ A2 )
% 5.17/5.40 => ( member_nat @ C @ B4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffE
% 5.17/5.40 thf(fact_2575_DiffD1,axiom,
% 5.17/5.40 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.17/5.40 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.17/5.40 => ( member_complex @ C @ A2 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD1
% 5.17/5.40 thf(fact_2576_DiffD1,axiom,
% 5.17/5.40 ! [C: real,A2: set_real,B4: set_real] :
% 5.17/5.40 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.17/5.40 => ( member_real @ C @ A2 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD1
% 5.17/5.40 thf(fact_2577_DiffD1,axiom,
% 5.17/5.40 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.40 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.17/5.40 => ( member_set_nat @ C @ A2 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD1
% 5.17/5.40 thf(fact_2578_DiffD1,axiom,
% 5.17/5.40 ! [C: int,A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.17/5.40 => ( member_int @ C @ A2 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD1
% 5.17/5.40 thf(fact_2579_DiffD1,axiom,
% 5.17/5.40 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.17/5.40 => ( member_nat @ C @ A2 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD1
% 5.17/5.40 thf(fact_2580_DiffD2,axiom,
% 5.17/5.40 ! [C: complex,A2: set_complex,B4: set_complex] :
% 5.17/5.40 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( member_complex @ C @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD2
% 5.17/5.40 thf(fact_2581_DiffD2,axiom,
% 5.17/5.40 ! [C: real,A2: set_real,B4: set_real] :
% 5.17/5.40 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( member_real @ C @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD2
% 5.17/5.40 thf(fact_2582_DiffD2,axiom,
% 5.17/5.40 ! [C: set_nat,A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.40 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( member_set_nat @ C @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD2
% 5.17/5.40 thf(fact_2583_DiffD2,axiom,
% 5.17/5.40 ! [C: int,A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( member_int @ C @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD2
% 5.17/5.40 thf(fact_2584_DiffD2,axiom,
% 5.17/5.40 ! [C: nat,A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B4 ) )
% 5.17/5.40 => ~ ( member_nat @ C @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % DiffD2
% 5.17/5.40 thf(fact_2585_psubset__imp__ex__mem,axiom,
% 5.17/5.40 ! [A2: set_complex,B4: set_complex] :
% 5.17/5.40 ( ( ord_less_set_complex @ A2 @ B4 )
% 5.17/5.40 => ? [B3: complex] : ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B4 @ A2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_imp_ex_mem
% 5.17/5.40 thf(fact_2586_psubset__imp__ex__mem,axiom,
% 5.17/5.40 ! [A2: set_real,B4: set_real] :
% 5.17/5.40 ( ( ord_less_set_real @ A2 @ B4 )
% 5.17/5.40 => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_imp_ex_mem
% 5.17/5.40 thf(fact_2587_psubset__imp__ex__mem,axiom,
% 5.17/5.40 ! [A2: set_set_nat,B4: set_set_nat] :
% 5.17/5.40 ( ( ord_less_set_set_nat @ A2 @ B4 )
% 5.17/5.40 => ? [B3: set_nat] : ( member_set_nat @ B3 @ ( minus_2163939370556025621et_nat @ B4 @ A2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_imp_ex_mem
% 5.17/5.40 thf(fact_2588_psubset__imp__ex__mem,axiom,
% 5.17/5.40 ! [A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( ord_less_set_int @ A2 @ B4 )
% 5.17/5.40 => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B4 @ A2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_imp_ex_mem
% 5.17/5.40 thf(fact_2589_psubset__imp__ex__mem,axiom,
% 5.17/5.40 ! [A2: set_nat,B4: set_nat] :
% 5.17/5.40 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.17/5.40 => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B4 @ A2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_imp_ex_mem
% 5.17/5.40 thf(fact_2590_int__less__induct,axiom,
% 5.17/5.40 ! [I: int,K: int,P: int > $o] :
% 5.17/5.40 ( ( ord_less_int @ I @ K )
% 5.17/5.40 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.17/5.40 => ( ! [I3: int] :
% 5.17/5.40 ( ( ord_less_int @ I3 @ K )
% 5.17/5.40 => ( ( P @ I3 )
% 5.17/5.40 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.17/5.40 => ( P @ I ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % int_less_induct
% 5.17/5.40 thf(fact_2591_real__arch__pow,axiom,
% 5.17/5.40 ! [X: real,Y4: real] :
% 5.17/5.40 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.40 => ? [N2: nat] : ( ord_less_real @ Y4 @ ( power_power_real @ X @ N2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_arch_pow
% 5.17/5.40 thf(fact_2592_real__arch__pow__inv,axiom,
% 5.17/5.40 ! [Y4: real,X: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.40 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.40 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X @ N2 ) @ Y4 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % real_arch_pow_inv
% 5.17/5.40 thf(fact_2593_int__one__le__iff__zero__less,axiom,
% 5.17/5.40 ! [Z: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.17/5.40 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.40
% 5.17/5.40 % int_one_le_iff_zero_less
% 5.17/5.40 thf(fact_2594_pos__zmult__eq__1__iff,axiom,
% 5.17/5.40 ! [M: int,N: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ M )
% 5.17/5.40 => ( ( ( times_times_int @ M @ N )
% 5.17/5.40 = one_one_int )
% 5.17/5.40 = ( ( M = one_one_int )
% 5.17/5.40 & ( N = one_one_int ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % pos_zmult_eq_1_iff
% 5.17/5.40 thf(fact_2595_int__div__less__self,axiom,
% 5.17/5.40 ! [X: int,K: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ X )
% 5.17/5.40 => ( ( ord_less_int @ one_one_int @ K )
% 5.17/5.40 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % int_div_less_self
% 5.17/5.40 thf(fact_2596_psubsetE,axiom,
% 5.17/5.40 ! [A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( ord_less_set_int @ A2 @ B4 )
% 5.17/5.40 => ~ ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.40 => ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubsetE
% 5.17/5.40 thf(fact_2597_psubset__eq,axiom,
% 5.17/5.40 ( ord_less_set_int
% 5.17/5.40 = ( ^ [A5: set_int,B5: set_int] :
% 5.17/5.40 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.17/5.40 & ( A5 != B5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_eq
% 5.17/5.40 thf(fact_2598_psubset__imp__subset,axiom,
% 5.17/5.40 ! [A2: set_int,B4: set_int] :
% 5.17/5.40 ( ( ord_less_set_int @ A2 @ B4 )
% 5.17/5.40 => ( ord_less_eq_set_int @ A2 @ B4 ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_imp_subset
% 5.17/5.40 thf(fact_2599_psubset__subset__trans,axiom,
% 5.17/5.40 ! [A2: set_int,B4: set_int,C2: set_int] :
% 5.17/5.40 ( ( ord_less_set_int @ A2 @ B4 )
% 5.17/5.40 => ( ( ord_less_eq_set_int @ B4 @ C2 )
% 5.17/5.40 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % psubset_subset_trans
% 5.17/5.40 thf(fact_2600_subset__not__subset__eq,axiom,
% 5.17/5.40 ( ord_less_set_int
% 5.17/5.40 = ( ^ [A5: set_int,B5: set_int] :
% 5.17/5.40 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.17/5.40 & ~ ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % subset_not_subset_eq
% 5.17/5.40 thf(fact_2601_subset__psubset__trans,axiom,
% 5.17/5.40 ! [A2: set_int,B4: set_int,C2: set_int] :
% 5.17/5.40 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.40 => ( ( ord_less_set_int @ B4 @ C2 )
% 5.17/5.40 => ( ord_less_set_int @ A2 @ C2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % subset_psubset_trans
% 5.17/5.40 thf(fact_2602_subset__iff__psubset__eq,axiom,
% 5.17/5.40 ( ord_less_eq_set_int
% 5.17/5.40 = ( ^ [A5: set_int,B5: set_int] :
% 5.17/5.40 ( ( ord_less_set_int @ A5 @ B5 )
% 5.17/5.40 | ( A5 = B5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % subset_iff_psubset_eq
% 5.17/5.40 thf(fact_2603_less__int__code_I1_J,axiom,
% 5.17/5.40 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.17/5.40
% 5.17/5.40 % less_int_code(1)
% 5.17/5.40 thf(fact_2604_less__eq__real__def,axiom,
% 5.17/5.40 ( ord_less_eq_real
% 5.17/5.40 = ( ^ [X3: real,Y6: real] :
% 5.17/5.40 ( ( ord_less_real @ X3 @ Y6 )
% 5.17/5.40 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % less_eq_real_def
% 5.17/5.40 thf(fact_2605_int__le__induct,axiom,
% 5.17/5.40 ! [I: int,K: int,P: int > $o] :
% 5.17/5.40 ( ( ord_less_eq_int @ I @ K )
% 5.17/5.40 => ( ( P @ K )
% 5.17/5.40 => ( ! [I3: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ I3 @ K )
% 5.17/5.40 => ( ( P @ I3 )
% 5.17/5.40 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.17/5.40 => ( P @ I ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % int_le_induct
% 5.17/5.40 thf(fact_2606_enat__0__less__mult__iff,axiom,
% 5.17/5.40 ! [M: extended_enat,N: extended_enat] :
% 5.17/5.40 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.17/5.40 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.17/5.40 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % enat_0_less_mult_iff
% 5.17/5.40 thf(fact_2607_not__iless0,axiom,
% 5.17/5.40 ! [N: extended_enat] :
% 5.17/5.40 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.17/5.40
% 5.17/5.40 % not_iless0
% 5.17/5.40 thf(fact_2608_zero__one__enat__neq_I1_J,axiom,
% 5.17/5.40 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.17/5.40
% 5.17/5.40 % zero_one_enat_neq(1)
% 5.17/5.40 thf(fact_2609_realpow__pos__nth2,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.40 => ? [R3: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.17/5.40 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.17/5.40 = A ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % realpow_pos_nth2
% 5.17/5.40 thf(fact_2610_nat__int__comparison_I2_J,axiom,
% 5.17/5.40 ( ord_less_nat
% 5.17/5.40 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nat_int_comparison(2)
% 5.17/5.40 thf(fact_2611_zmult__zless__mono2,axiom,
% 5.17/5.40 ! [I: int,J: int,K: int] :
% 5.17/5.40 ( ( ord_less_int @ I @ J )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.40 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zmult_zless_mono2
% 5.17/5.40 thf(fact_2612_plusinfinity,axiom,
% 5.17/5.40 ! [D: int,P4: int > $o,P: int > $o] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.40 => ( ! [X4: int,K2: int] :
% 5.17/5.40 ( ( P4 @ X4 )
% 5.17/5.40 = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.17/5.40 => ( ? [Z3: int] :
% 5.17/5.40 ! [X4: int] :
% 5.17/5.40 ( ( ord_less_int @ Z3 @ X4 )
% 5.17/5.40 => ( ( P @ X4 )
% 5.17/5.40 = ( P4 @ X4 ) ) )
% 5.17/5.40 => ( ? [X_12: int] : ( P4 @ X_12 )
% 5.17/5.40 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % plusinfinity
% 5.17/5.40 thf(fact_2613_minusinfinity,axiom,
% 5.17/5.40 ! [D: int,P1: int > $o,P: int > $o] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.40 => ( ! [X4: int,K2: int] :
% 5.17/5.40 ( ( P1 @ X4 )
% 5.17/5.40 = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.17/5.40 => ( ? [Z3: int] :
% 5.17/5.40 ! [X4: int] :
% 5.17/5.40 ( ( ord_less_int @ X4 @ Z3 )
% 5.17/5.40 => ( ( P @ X4 )
% 5.17/5.40 = ( P1 @ X4 ) ) )
% 5.17/5.40 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.17/5.40 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % minusinfinity
% 5.17/5.40 thf(fact_2614_pos__imp__zdiv__neg__iff,axiom,
% 5.17/5.40 ! [B: int,A: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.17/5.40 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % pos_imp_zdiv_neg_iff
% 5.17/5.40 thf(fact_2615_neg__imp__zdiv__neg__iff,axiom,
% 5.17/5.40 ! [B: int,A: int] :
% 5.17/5.40 ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.40 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.17/5.40 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % neg_imp_zdiv_neg_iff
% 5.17/5.40 thf(fact_2616_div__neg__pos__less0,axiom,
% 5.17/5.40 ! [A: int,B: int] :
% 5.17/5.40 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_neg_pos_less0
% 5.17/5.40 thf(fact_2617_zdvd__not__zless,axiom,
% 5.17/5.40 ! [M: int,N: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ M )
% 5.17/5.40 => ( ( ord_less_int @ M @ N )
% 5.17/5.40 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdvd_not_zless
% 5.17/5.40 thf(fact_2618_int__ops_I2_J,axiom,
% 5.17/5.40 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.17/5.40 = one_one_int ) ).
% 5.17/5.40
% 5.17/5.40 % int_ops(2)
% 5.17/5.40 thf(fact_2619_realpow__pos__nth__unique,axiom,
% 5.17/5.40 ! [N: nat,A: real] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.40 => ? [X4: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.17/5.40 & ( ( power_power_real @ X4 @ N )
% 5.17/5.40 = A )
% 5.17/5.40 & ! [Y3: real] :
% 5.17/5.40 ( ( ( ord_less_real @ zero_zero_real @ Y3 )
% 5.17/5.40 & ( ( power_power_real @ Y3 @ N )
% 5.17/5.40 = A ) )
% 5.17/5.40 => ( Y3 = X4 ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % realpow_pos_nth_unique
% 5.17/5.40 thf(fact_2620_realpow__pos__nth,axiom,
% 5.17/5.40 ! [N: nat,A: real] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.40 => ? [R3: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.17/5.40 & ( ( power_power_real @ R3 @ N )
% 5.17/5.40 = A ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % realpow_pos_nth
% 5.17/5.40 thf(fact_2621_int__ops_I6_J,axiom,
% 5.17/5.40 ! [A: nat,B: nat] :
% 5.17/5.40 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.17/5.40 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.17/5.40 = zero_zero_int ) )
% 5.17/5.40 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.17/5.40 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.17/5.40 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % int_ops(6)
% 5.17/5.40 thf(fact_2622_decr__mult__lemma,axiom,
% 5.17/5.40 ! [D: int,P: int > $o,K: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.40 => ( ! [X4: int] :
% 5.17/5.40 ( ( P @ X4 )
% 5.17/5.40 => ( P @ ( minus_minus_int @ X4 @ D ) ) )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.40 => ! [X5: int] :
% 5.17/5.40 ( ( P @ X5 )
% 5.17/5.40 => ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % decr_mult_lemma
% 5.17/5.40 thf(fact_2623_reals__Archimedean3,axiom,
% 5.17/5.40 ! [X: real] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.40 => ! [Y3: real] :
% 5.17/5.40 ? [N2: nat] : ( ord_less_real @ Y3 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % reals_Archimedean3
% 5.17/5.40 thf(fact_2624_zdiv__mono1,axiom,
% 5.17/5.40 ! [A: int,A6: int,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ A @ A6 )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A6 @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdiv_mono1
% 5.17/5.40 thf(fact_2625_zdiv__mono2,axiom,
% 5.17/5.40 ! [A: int,B6: int,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.17/5.40 => ( ( ord_less_eq_int @ B6 @ B )
% 5.17/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B6 ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdiv_mono2
% 5.17/5.40 thf(fact_2626_zdiv__eq__0__iff,axiom,
% 5.17/5.40 ! [I: int,K: int] :
% 5.17/5.40 ( ( ( divide_divide_int @ I @ K )
% 5.17/5.40 = zero_zero_int )
% 5.17/5.40 = ( ( K = zero_zero_int )
% 5.17/5.40 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.17/5.40 & ( ord_less_int @ I @ K ) )
% 5.17/5.40 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.17/5.40 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdiv_eq_0_iff
% 5.17/5.40 thf(fact_2627_zdiv__mono1__neg,axiom,
% 5.17/5.40 ! [A: int,A6: int,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ A @ A6 )
% 5.17/5.40 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A6 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdiv_mono1_neg
% 5.17/5.40 thf(fact_2628_zdiv__mono2__neg,axiom,
% 5.17/5.40 ! [A: int,B6: int,B: int] :
% 5.17/5.40 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.17/5.40 => ( ( ord_less_eq_int @ B6 @ B )
% 5.17/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B6 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdiv_mono2_neg
% 5.17/5.40 thf(fact_2629_div__int__pos__iff,axiom,
% 5.17/5.40 ! [K: int,L: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.17/5.40 = ( ( K = zero_zero_int )
% 5.17/5.40 | ( L = zero_zero_int )
% 5.17/5.40 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.40 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.17/5.40 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.40 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_int_pos_iff
% 5.17/5.40 thf(fact_2630_div__positive__int,axiom,
% 5.17/5.40 ! [L: int,K: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ L @ K )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.40 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_positive_int
% 5.17/5.40 thf(fact_2631_div__nonneg__neg__le0,axiom,
% 5.17/5.40 ! [A: int,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_nonneg_neg_le0
% 5.17/5.40 thf(fact_2632_div__nonpos__pos__le0,axiom,
% 5.17/5.40 ! [A: int,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_nonpos_pos_le0
% 5.17/5.40 thf(fact_2633_pos__imp__zdiv__pos__iff,axiom,
% 5.17/5.40 ! [K: int,I: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.17/5.40 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % pos_imp_zdiv_pos_iff
% 5.17/5.40 thf(fact_2634_neg__imp__zdiv__nonneg__iff,axiom,
% 5.17/5.40 ! [B: int,A: int] :
% 5.17/5.40 ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.17/5.40 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % neg_imp_zdiv_nonneg_iff
% 5.17/5.40 thf(fact_2635_pos__imp__zdiv__nonneg__iff,axiom,
% 5.17/5.40 ! [B: int,A: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.17/5.40 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % pos_imp_zdiv_nonneg_iff
% 5.17/5.40 thf(fact_2636_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.17/5.40 ! [A: int,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.17/5.40 = ( ( ord_less_eq_int @ B @ A )
% 5.17/5.40 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nonneg1_imp_zdiv_pos_iff
% 5.17/5.40 thf(fact_2637_zdvd__imp__le,axiom,
% 5.17/5.40 ! [Z: int,N: int] :
% 5.17/5.40 ( ( dvd_dvd_int @ Z @ N )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.17/5.40 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zdvd_imp_le
% 5.17/5.40 thf(fact_2638_pos__int__cases,axiom,
% 5.17/5.40 ! [K: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.40 => ~ ! [N2: nat] :
% 5.17/5.40 ( ( K
% 5.17/5.40 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.17/5.40 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % pos_int_cases
% 5.17/5.40 thf(fact_2639_zero__less__imp__eq__int,axiom,
% 5.17/5.40 ! [K: int] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.40 => ? [N2: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.40 & ( K
% 5.17/5.40 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_imp_eq_int
% 5.17/5.40 thf(fact_2640_zmult__zless__mono2__lemma,axiom,
% 5.17/5.40 ! [I: int,J: int,K: nat] :
% 5.17/5.40 ( ( ord_less_int @ I @ J )
% 5.17/5.40 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.40 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zmult_zless_mono2_lemma
% 5.17/5.40 thf(fact_2641_two__realpow__ge__one,axiom,
% 5.17/5.40 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % two_realpow_ge_one
% 5.17/5.40 thf(fact_2642_real__of__nat__div3,axiom,
% 5.17/5.40 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 5.17/5.40
% 5.17/5.40 % real_of_nat_div3
% 5.17/5.40 thf(fact_2643_int__power__div__base,axiom,
% 5.17/5.40 ! [M: nat,K: int] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.40 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.40 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.17/5.40 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % int_power_div_base
% 5.17/5.40 thf(fact_2644_power__not__zero,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( A != zero_zero_rat )
% 5.17/5.40 => ( ( power_power_rat @ A @ N )
% 5.17/5.40 != zero_zero_rat ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_not_zero
% 5.17/5.40 thf(fact_2645_power__not__zero,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( A != zero_zero_int )
% 5.17/5.40 => ( ( power_power_int @ A @ N )
% 5.17/5.40 != zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_not_zero
% 5.17/5.40 thf(fact_2646_power__not__zero,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( A != zero_zero_real )
% 5.17/5.40 => ( ( power_power_real @ A @ N )
% 5.17/5.40 != zero_zero_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_not_zero
% 5.17/5.40 thf(fact_2647_power__not__zero,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( A != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_nat @ A @ N )
% 5.17/5.40 != zero_zero_nat ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_not_zero
% 5.17/5.40 thf(fact_2648_power__not__zero,axiom,
% 5.17/5.40 ! [A: complex,N: nat] :
% 5.17/5.40 ( ( A != zero_zero_complex )
% 5.17/5.40 => ( ( power_power_complex @ A @ N )
% 5.17/5.40 != zero_zero_complex ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_not_zero
% 5.17/5.40 thf(fact_2649_power__commuting__commutes,axiom,
% 5.17/5.40 ! [X: complex,Y4: complex,N: nat] :
% 5.17/5.40 ( ( ( times_times_complex @ X @ Y4 )
% 5.17/5.40 = ( times_times_complex @ Y4 @ X ) )
% 5.17/5.40 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y4 )
% 5.17/5.40 = ( times_times_complex @ Y4 @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commuting_commutes
% 5.17/5.40 thf(fact_2650_power__commuting__commutes,axiom,
% 5.17/5.40 ! [X: real,Y4: real,N: nat] :
% 5.17/5.40 ( ( ( times_times_real @ X @ Y4 )
% 5.17/5.40 = ( times_times_real @ Y4 @ X ) )
% 5.17/5.40 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y4 )
% 5.17/5.40 = ( times_times_real @ Y4 @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commuting_commutes
% 5.17/5.40 thf(fact_2651_power__commuting__commutes,axiom,
% 5.17/5.40 ! [X: rat,Y4: rat,N: nat] :
% 5.17/5.40 ( ( ( times_times_rat @ X @ Y4 )
% 5.17/5.40 = ( times_times_rat @ Y4 @ X ) )
% 5.17/5.40 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y4 )
% 5.17/5.40 = ( times_times_rat @ Y4 @ ( power_power_rat @ X @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commuting_commutes
% 5.17/5.40 thf(fact_2652_power__commuting__commutes,axiom,
% 5.17/5.40 ! [X: nat,Y4: nat,N: nat] :
% 5.17/5.40 ( ( ( times_times_nat @ X @ Y4 )
% 5.17/5.40 = ( times_times_nat @ Y4 @ X ) )
% 5.17/5.40 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y4 )
% 5.17/5.40 = ( times_times_nat @ Y4 @ ( power_power_nat @ X @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commuting_commutes
% 5.17/5.40 thf(fact_2653_power__commuting__commutes,axiom,
% 5.17/5.40 ! [X: int,Y4: int,N: nat] :
% 5.17/5.40 ( ( ( times_times_int @ X @ Y4 )
% 5.17/5.40 = ( times_times_int @ Y4 @ X ) )
% 5.17/5.40 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y4 )
% 5.17/5.40 = ( times_times_int @ Y4 @ ( power_power_int @ X @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commuting_commutes
% 5.17/5.40 thf(fact_2654_power__mult__distrib,axiom,
% 5.17/5.40 ! [A: complex,B: complex,N: nat] :
% 5.17/5.40 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.17/5.40 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_distrib
% 5.17/5.40 thf(fact_2655_power__mult__distrib,axiom,
% 5.17/5.40 ! [A: real,B: real,N: nat] :
% 5.17/5.40 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.17/5.40 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_distrib
% 5.17/5.40 thf(fact_2656_power__mult__distrib,axiom,
% 5.17/5.40 ! [A: rat,B: rat,N: nat] :
% 5.17/5.40 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.17/5.40 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_distrib
% 5.17/5.40 thf(fact_2657_power__mult__distrib,axiom,
% 5.17/5.40 ! [A: nat,B: nat,N: nat] :
% 5.17/5.40 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.17/5.40 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_distrib
% 5.17/5.40 thf(fact_2658_power__mult__distrib,axiom,
% 5.17/5.40 ! [A: int,B: int,N: nat] :
% 5.17/5.40 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.17/5.40 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult_distrib
% 5.17/5.40 thf(fact_2659_power__commutes,axiom,
% 5.17/5.40 ! [A: complex,N: nat] :
% 5.17/5.40 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.17/5.40 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commutes
% 5.17/5.40 thf(fact_2660_power__commutes,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.17/5.40 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commutes
% 5.17/5.40 thf(fact_2661_power__commutes,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.17/5.40 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commutes
% 5.17/5.40 thf(fact_2662_power__commutes,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.17/5.40 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commutes
% 5.17/5.40 thf(fact_2663_power__commutes,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.17/5.40 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_commutes
% 5.17/5.40 thf(fact_2664_power__divide,axiom,
% 5.17/5.40 ! [A: complex,B: complex,N: nat] :
% 5.17/5.40 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.17/5.40 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_divide
% 5.17/5.40 thf(fact_2665_power__divide,axiom,
% 5.17/5.40 ! [A: real,B: real,N: nat] :
% 5.17/5.40 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.17/5.40 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_divide
% 5.17/5.40 thf(fact_2666_power__divide,axiom,
% 5.17/5.40 ! [A: rat,B: rat,N: nat] :
% 5.17/5.40 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.17/5.40 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_divide
% 5.17/5.40 thf(fact_2667_dvd__power__same,axiom,
% 5.17/5.40 ! [X: code_integer,Y4: code_integer,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_Code_integer @ X @ Y4 )
% 5.17/5.40 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y4 @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_same
% 5.17/5.40 thf(fact_2668_dvd__power__same,axiom,
% 5.17/5.40 ! [X: int,Y4: int,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_int @ X @ Y4 )
% 5.17/5.40 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_same
% 5.17/5.40 thf(fact_2669_dvd__power__same,axiom,
% 5.17/5.40 ! [X: real,Y4: real,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_real @ X @ Y4 )
% 5.17/5.40 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_same
% 5.17/5.40 thf(fact_2670_dvd__power__same,axiom,
% 5.17/5.40 ! [X: nat,Y4: nat,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ X @ Y4 )
% 5.17/5.40 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y4 @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_same
% 5.17/5.40 thf(fact_2671_dvd__power__same,axiom,
% 5.17/5.40 ! [X: complex,Y4: complex,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_complex @ X @ Y4 )
% 5.17/5.40 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_same
% 5.17/5.40 thf(fact_2672_nat__power__less__imp__less,axiom,
% 5.17/5.40 ! [I: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.17/5.40 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.17/5.40 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nat_power_less_imp_less
% 5.17/5.40 thf(fact_2673_power__mult,axiom,
% 5.17/5.40 ! [A: int,M: nat,N: nat] :
% 5.17/5.40 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult
% 5.17/5.40 thf(fact_2674_power__mult,axiom,
% 5.17/5.40 ! [A: real,M: nat,N: nat] :
% 5.17/5.40 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult
% 5.17/5.40 thf(fact_2675_power__mult,axiom,
% 5.17/5.40 ! [A: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult
% 5.17/5.40 thf(fact_2676_power__mult,axiom,
% 5.17/5.40 ! [A: complex,M: nat,N: nat] :
% 5.17/5.40 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.17/5.40 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mult
% 5.17/5.40 thf(fact_2677_power__mono,axiom,
% 5.17/5.40 ! [A: rat,B: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono
% 5.17/5.40 thf(fact_2678_power__mono,axiom,
% 5.17/5.40 ! [A: nat,B: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono
% 5.17/5.40 thf(fact_2679_power__mono,axiom,
% 5.17/5.40 ! [A: int,B: int,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono
% 5.17/5.40 thf(fact_2680_power__mono,axiom,
% 5.17/5.40 ! [A: real,B: real,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_mono
% 5.17/5.40 thf(fact_2681_zero__le__power,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power
% 5.17/5.40 thf(fact_2682_zero__le__power,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power
% 5.17/5.40 thf(fact_2683_zero__le__power,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power
% 5.17/5.40 thf(fact_2684_zero__le__power,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_le_power
% 5.17/5.40 thf(fact_2685_zero__less__power,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power
% 5.17/5.40 thf(fact_2686_zero__less__power,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power
% 5.17/5.40 thf(fact_2687_zero__less__power,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power
% 5.17/5.40 thf(fact_2688_zero__less__power,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_less_power
% 5.17/5.40 thf(fact_2689_one__le__power,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.17/5.40 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % one_le_power
% 5.17/5.40 thf(fact_2690_one__le__power,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.17/5.40 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % one_le_power
% 5.17/5.40 thf(fact_2691_one__le__power,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.17/5.40 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % one_le_power
% 5.17/5.40 thf(fact_2692_one__le__power,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.17/5.40 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % one_le_power
% 5.17/5.40 thf(fact_2693_left__right__inverse__power,axiom,
% 5.17/5.40 ! [X: complex,Y4: complex,N: nat] :
% 5.17/5.40 ( ( ( times_times_complex @ X @ Y4 )
% 5.17/5.40 = one_one_complex )
% 5.17/5.40 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ N ) )
% 5.17/5.40 = one_one_complex ) ) ).
% 5.17/5.40
% 5.17/5.40 % left_right_inverse_power
% 5.17/5.40 thf(fact_2694_left__right__inverse__power,axiom,
% 5.17/5.40 ! [X: real,Y4: real,N: nat] :
% 5.17/5.40 ( ( ( times_times_real @ X @ Y4 )
% 5.17/5.40 = one_one_real )
% 5.17/5.40 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ N ) )
% 5.17/5.40 = one_one_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % left_right_inverse_power
% 5.17/5.40 thf(fact_2695_left__right__inverse__power,axiom,
% 5.17/5.40 ! [X: rat,Y4: rat,N: nat] :
% 5.17/5.40 ( ( ( times_times_rat @ X @ Y4 )
% 5.17/5.40 = one_one_rat )
% 5.17/5.40 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y4 @ N ) )
% 5.17/5.40 = one_one_rat ) ) ).
% 5.17/5.40
% 5.17/5.40 % left_right_inverse_power
% 5.17/5.40 thf(fact_2696_left__right__inverse__power,axiom,
% 5.17/5.40 ! [X: nat,Y4: nat,N: nat] :
% 5.17/5.40 ( ( ( times_times_nat @ X @ Y4 )
% 5.17/5.40 = one_one_nat )
% 5.17/5.40 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y4 @ N ) )
% 5.17/5.40 = one_one_nat ) ) ).
% 5.17/5.40
% 5.17/5.40 % left_right_inverse_power
% 5.17/5.40 thf(fact_2697_left__right__inverse__power,axiom,
% 5.17/5.40 ! [X: int,Y4: int,N: nat] :
% 5.17/5.40 ( ( ( times_times_int @ X @ Y4 )
% 5.17/5.40 = one_one_int )
% 5.17/5.40 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ N ) )
% 5.17/5.40 = one_one_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % left_right_inverse_power
% 5.17/5.40 thf(fact_2698_power__Suc2,axiom,
% 5.17/5.40 ! [A: complex,N: nat] :
% 5.17/5.40 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc2
% 5.17/5.40 thf(fact_2699_power__Suc2,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc2
% 5.17/5.40 thf(fact_2700_power__Suc2,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc2
% 5.17/5.40 thf(fact_2701_power__Suc2,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc2
% 5.17/5.40 thf(fact_2702_power__Suc2,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc2
% 5.17/5.40 thf(fact_2703_power__Suc,axiom,
% 5.17/5.40 ! [A: complex,N: nat] :
% 5.17/5.40 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc
% 5.17/5.40 thf(fact_2704_power__Suc,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc
% 5.17/5.40 thf(fact_2705_power__Suc,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc
% 5.17/5.40 thf(fact_2706_power__Suc,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc
% 5.17/5.40 thf(fact_2707_power__Suc,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.17/5.40 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc
% 5.17/5.40 thf(fact_2708_power__one__over,axiom,
% 5.17/5.40 ! [A: complex,N: nat] :
% 5.17/5.40 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.17/5.40 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_one_over
% 5.17/5.40 thf(fact_2709_power__one__over,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.17/5.40 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_one_over
% 5.17/5.40 thf(fact_2710_power__one__over,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.17/5.40 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_one_over
% 5.17/5.40 thf(fact_2711_power__0,axiom,
% 5.17/5.40 ! [A: rat] :
% 5.17/5.40 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.17/5.40 = one_one_rat ) ).
% 5.17/5.40
% 5.17/5.40 % power_0
% 5.17/5.40 thf(fact_2712_power__0,axiom,
% 5.17/5.40 ! [A: int] :
% 5.17/5.40 ( ( power_power_int @ A @ zero_zero_nat )
% 5.17/5.40 = one_one_int ) ).
% 5.17/5.40
% 5.17/5.40 % power_0
% 5.17/5.40 thf(fact_2713_power__0,axiom,
% 5.17/5.40 ! [A: real] :
% 5.17/5.40 ( ( power_power_real @ A @ zero_zero_nat )
% 5.17/5.40 = one_one_real ) ).
% 5.17/5.40
% 5.17/5.40 % power_0
% 5.17/5.40 thf(fact_2714_power__0,axiom,
% 5.17/5.40 ! [A: nat] :
% 5.17/5.40 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.17/5.40 = one_one_nat ) ).
% 5.17/5.40
% 5.17/5.40 % power_0
% 5.17/5.40 thf(fact_2715_power__0,axiom,
% 5.17/5.40 ! [A: complex] :
% 5.17/5.40 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.17/5.40 = one_one_complex ) ).
% 5.17/5.40
% 5.17/5.40 % power_0
% 5.17/5.40 thf(fact_2716_div__power,axiom,
% 5.17/5.40 ! [B: code_integer,A: code_integer,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.40 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.17/5.40 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_power
% 5.17/5.40 thf(fact_2717_div__power,axiom,
% 5.17/5.40 ! [B: nat,A: nat,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.40 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.17/5.40 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_power
% 5.17/5.40 thf(fact_2718_div__power,axiom,
% 5.17/5.40 ! [B: int,A: int,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.40 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.17/5.40 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % div_power
% 5.17/5.40 thf(fact_2719_power__gt__expt,axiom,
% 5.17/5.40 ! [N: nat,K: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.40 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt_expt
% 5.17/5.40 thf(fact_2720_nat__one__le__power,axiom,
% 5.17/5.40 ! [I: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.17/5.40 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % nat_one_le_power
% 5.17/5.40 thf(fact_2721_dvd__power__le,axiom,
% 5.17/5.40 ! [X: code_integer,Y4: code_integer,N: nat,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_Code_integer @ X @ Y4 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y4 @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_le
% 5.17/5.40 thf(fact_2722_dvd__power__le,axiom,
% 5.17/5.40 ! [X: int,Y4: int,N: nat,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_int @ X @ Y4 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y4 @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_le
% 5.17/5.40 thf(fact_2723_dvd__power__le,axiom,
% 5.17/5.40 ! [X: real,Y4: real,N: nat,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_real @ X @ Y4 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y4 @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_le
% 5.17/5.40 thf(fact_2724_dvd__power__le,axiom,
% 5.17/5.40 ! [X: nat,Y4: nat,N: nat,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ X @ Y4 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y4 @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_le
% 5.17/5.40 thf(fact_2725_dvd__power__le,axiom,
% 5.17/5.40 ! [X: complex,Y4: complex,N: nat,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_complex @ X @ Y4 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.40 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y4 @ M ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % dvd_power_le
% 5.17/5.40 thf(fact_2726_power__le__dvd,axiom,
% 5.17/5.40 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_dvd
% 5.17/5.40 thf(fact_2727_power__le__dvd,axiom,
% 5.17/5.40 ! [A: int,N: nat,B: int,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_dvd
% 5.17/5.40 thf(fact_2728_power__le__dvd,axiom,
% 5.17/5.40 ! [A: real,N: nat,B: real,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_dvd
% 5.17/5.40 thf(fact_2729_power__le__dvd,axiom,
% 5.17/5.40 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_dvd
% 5.17/5.40 thf(fact_2730_power__le__dvd,axiom,
% 5.17/5.40 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.17/5.40 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.17/5.40 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_dvd
% 5.17/5.40 thf(fact_2731_le__imp__power__dvd,axiom,
% 5.17/5.40 ! [M: nat,N: nat,A: code_integer] :
% 5.17/5.40 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_imp_power_dvd
% 5.17/5.40 thf(fact_2732_le__imp__power__dvd,axiom,
% 5.17/5.40 ! [M: nat,N: nat,A: int] :
% 5.17/5.40 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_imp_power_dvd
% 5.17/5.40 thf(fact_2733_le__imp__power__dvd,axiom,
% 5.17/5.40 ! [M: nat,N: nat,A: real] :
% 5.17/5.40 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_imp_power_dvd
% 5.17/5.40 thf(fact_2734_le__imp__power__dvd,axiom,
% 5.17/5.40 ! [M: nat,N: nat,A: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_imp_power_dvd
% 5.17/5.40 thf(fact_2735_le__imp__power__dvd,axiom,
% 5.17/5.40 ! [M: nat,N: nat,A: complex] :
% 5.17/5.40 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.40 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % le_imp_power_dvd
% 5.17/5.40 thf(fact_2736_power__less__imp__less__base,axiom,
% 5.17/5.40 ! [A: rat,N: nat,B: rat] :
% 5.17/5.40 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.40 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_imp_less_base
% 5.17/5.40 thf(fact_2737_power__less__imp__less__base,axiom,
% 5.17/5.40 ! [A: nat,N: nat,B: nat] :
% 5.17/5.40 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.40 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_imp_less_base
% 5.17/5.40 thf(fact_2738_power__less__imp__less__base,axiom,
% 5.17/5.40 ! [A: int,N: nat,B: int] :
% 5.17/5.40 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_imp_less_base
% 5.17/5.40 thf(fact_2739_power__less__imp__less__base,axiom,
% 5.17/5.40 ! [A: real,N: nat,B: real] :
% 5.17/5.40 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.40 => ( ord_less_real @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_imp_less_base
% 5.17/5.40 thf(fact_2740_power__le__one,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.17/5.40 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_one
% 5.17/5.40 thf(fact_2741_power__le__one,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.17/5.40 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_one
% 5.17/5.40 thf(fact_2742_power__le__one,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.17/5.40 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_one
% 5.17/5.40 thf(fact_2743_power__le__one,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.17/5.40 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_one
% 5.17/5.40 thf(fact_2744_power__le__imp__le__base,axiom,
% 5.17/5.40 ! [A: rat,N: nat,B: rat] :
% 5.17/5.40 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.40 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_imp_le_base
% 5.17/5.40 thf(fact_2745_power__le__imp__le__base,axiom,
% 5.17/5.40 ! [A: nat,N: nat,B: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.40 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_imp_le_base
% 5.17/5.40 thf(fact_2746_power__le__imp__le__base,axiom,
% 5.17/5.40 ! [A: int,N: nat,B: int] :
% 5.17/5.40 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.40 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_imp_le_base
% 5.17/5.40 thf(fact_2747_power__le__imp__le__base,axiom,
% 5.17/5.40 ! [A: real,N: nat,B: real] :
% 5.17/5.40 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.40 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_le_imp_le_base
% 5.17/5.40 thf(fact_2748_power__inject__base,axiom,
% 5.17/5.40 ! [A: rat,N: nat,B: rat] :
% 5.17/5.40 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.17/5.40 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.40 => ( A = B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_inject_base
% 5.17/5.40 thf(fact_2749_power__inject__base,axiom,
% 5.17/5.40 ! [A: nat,N: nat,B: nat] :
% 5.17/5.40 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.17/5.40 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.40 => ( A = B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_inject_base
% 5.17/5.40 thf(fact_2750_power__inject__base,axiom,
% 5.17/5.40 ! [A: int,N: nat,B: int] :
% 5.17/5.40 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.17/5.40 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.40 => ( A = B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_inject_base
% 5.17/5.40 thf(fact_2751_power__inject__base,axiom,
% 5.17/5.40 ! [A: real,N: nat,B: real] :
% 5.17/5.40 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.17/5.40 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.40 => ( A = B ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_inject_base
% 5.17/5.40 thf(fact_2752_power__less__power__Suc,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.40 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_power_Suc
% 5.17/5.40 thf(fact_2753_power__less__power__Suc,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ one_one_rat @ A )
% 5.17/5.40 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_power_Suc
% 5.17/5.40 thf(fact_2754_power__less__power__Suc,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ one_one_nat @ A )
% 5.17/5.40 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_power_Suc
% 5.17/5.40 thf(fact_2755_power__less__power__Suc,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ one_one_int @ A )
% 5.17/5.40 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_less_power_Suc
% 5.17/5.40 thf(fact_2756_power__gt1__lemma,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.40 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1_lemma
% 5.17/5.40 thf(fact_2757_power__gt1__lemma,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ one_one_rat @ A )
% 5.17/5.40 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1_lemma
% 5.17/5.40 thf(fact_2758_power__gt1__lemma,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ one_one_nat @ A )
% 5.17/5.40 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1_lemma
% 5.17/5.40 thf(fact_2759_power__gt1__lemma,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ one_one_int @ A )
% 5.17/5.40 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1_lemma
% 5.17/5.40 thf(fact_2760_power__0__left,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ( N = zero_zero_nat )
% 5.17/5.40 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.17/5.40 = one_one_rat ) )
% 5.17/5.40 & ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.17/5.40 = zero_zero_rat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_left
% 5.17/5.40 thf(fact_2761_power__0__left,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ( N = zero_zero_nat )
% 5.17/5.40 => ( ( power_power_int @ zero_zero_int @ N )
% 5.17/5.40 = one_one_int ) )
% 5.17/5.40 & ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_int @ zero_zero_int @ N )
% 5.17/5.40 = zero_zero_int ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_left
% 5.17/5.40 thf(fact_2762_power__0__left,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ( N = zero_zero_nat )
% 5.17/5.40 => ( ( power_power_real @ zero_zero_real @ N )
% 5.17/5.40 = one_one_real ) )
% 5.17/5.40 & ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_real @ zero_zero_real @ N )
% 5.17/5.40 = zero_zero_real ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_left
% 5.17/5.40 thf(fact_2763_power__0__left,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ( N = zero_zero_nat )
% 5.17/5.40 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.17/5.40 = one_one_nat ) )
% 5.17/5.40 & ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.17/5.40 = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_left
% 5.17/5.40 thf(fact_2764_power__0__left,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ( N = zero_zero_nat )
% 5.17/5.40 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.17/5.40 = one_one_complex ) )
% 5.17/5.40 & ( ( N != zero_zero_nat )
% 5.17/5.40 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.17/5.40 = zero_zero_complex ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_0_left
% 5.17/5.40 thf(fact_2765_power__gt1,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.40 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1
% 5.17/5.40 thf(fact_2766_power__gt1,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ one_one_rat @ A )
% 5.17/5.40 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1
% 5.17/5.40 thf(fact_2767_power__gt1,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ one_one_nat @ A )
% 5.17/5.40 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1
% 5.17/5.40 thf(fact_2768_power__gt1,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ one_one_int @ A )
% 5.17/5.40 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_gt1
% 5.17/5.40 thf(fact_2769_power__increasing,axiom,
% 5.17/5.40 ! [N: nat,N5: nat,A: rat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.40 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.17/5.40 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing
% 5.17/5.40 thf(fact_2770_power__increasing,axiom,
% 5.17/5.40 ! [N: nat,N5: nat,A: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.40 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.17/5.40 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing
% 5.17/5.40 thf(fact_2771_power__increasing,axiom,
% 5.17/5.40 ! [N: nat,N5: nat,A: int] :
% 5.17/5.40 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.40 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.17/5.40 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing
% 5.17/5.40 thf(fact_2772_power__increasing,axiom,
% 5.17/5.40 ! [N: nat,N5: nat,A: real] :
% 5.17/5.40 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.40 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.17/5.40 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_increasing
% 5.17/5.40 thf(fact_2773_zero__power,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.17/5.40 = zero_zero_rat ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_power
% 5.17/5.40 thf(fact_2774_zero__power,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( power_power_int @ zero_zero_int @ N )
% 5.17/5.40 = zero_zero_int ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_power
% 5.17/5.40 thf(fact_2775_zero__power,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( power_power_real @ zero_zero_real @ N )
% 5.17/5.40 = zero_zero_real ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_power
% 5.17/5.40 thf(fact_2776_zero__power,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.17/5.40 = zero_zero_nat ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_power
% 5.17/5.40 thf(fact_2777_zero__power,axiom,
% 5.17/5.40 ! [N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.40 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.17/5.40 = zero_zero_complex ) ) ).
% 5.17/5.40
% 5.17/5.40 % zero_power
% 5.17/5.40 thf(fact_2778_less__exp,axiom,
% 5.17/5.40 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % less_exp
% 5.17/5.40 thf(fact_2779_power2__nat__le__imp__le,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.17/5.40 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_nat_le_imp_le
% 5.17/5.40 thf(fact_2780_power2__nat__le__eq__le,axiom,
% 5.17/5.40 ! [M: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.40 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.40
% 5.17/5.40 % power2_nat_le_eq_le
% 5.17/5.40 thf(fact_2781_self__le__ge2__pow,axiom,
% 5.17/5.40 ! [K: nat,M: nat] :
% 5.17/5.40 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.17/5.40 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % self_le_ge2_pow
% 5.17/5.40 thf(fact_2782_is__unit__power__iff,axiom,
% 5.17/5.40 ! [A: code_integer,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.17/5.40 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_power_iff
% 5.17/5.40 thf(fact_2783_is__unit__power__iff,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.17/5.40 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_power_iff
% 5.17/5.40 thf(fact_2784_is__unit__power__iff,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.17/5.40 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.17/5.40 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % is_unit_power_iff
% 5.17/5.40 thf(fact_2785_power__dvd__imp__le,axiom,
% 5.17/5.40 ! [I: nat,M: nat,N: nat] :
% 5.17/5.40 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.17/5.40 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.17/5.40 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_dvd_imp_le
% 5.17/5.40 thf(fact_2786_power__Suc__less,axiom,
% 5.17/5.40 ! [A: real,N: nat] :
% 5.17/5.40 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.40 => ( ( ord_less_real @ A @ one_one_real )
% 5.17/5.40 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc_less
% 5.17/5.40 thf(fact_2787_power__Suc__less,axiom,
% 5.17/5.40 ! [A: rat,N: nat] :
% 5.17/5.40 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.40 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.17/5.40 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc_less
% 5.17/5.40 thf(fact_2788_power__Suc__less,axiom,
% 5.17/5.40 ! [A: nat,N: nat] :
% 5.17/5.40 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.40 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.17/5.40 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.17/5.40
% 5.17/5.40 % power_Suc_less
% 5.17/5.40 thf(fact_2789_power__Suc__less,axiom,
% 5.17/5.40 ! [A: int,N: nat] :
% 5.17/5.40 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.40 => ( ( ord_less_int @ A @ one_one_int )
% 5.17/5.40 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_less
% 5.17/5.41 thf(fact_2790_power__Suc__le__self,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.17/5.41 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_le_self
% 5.17/5.41 thf(fact_2791_power__Suc__le__self,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.17/5.41 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_le_self
% 5.17/5.41 thf(fact_2792_power__Suc__le__self,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.17/5.41 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_le_self
% 5.17/5.41 thf(fact_2793_power__Suc__le__self,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.17/5.41 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_le_self
% 5.17/5.41 thf(fact_2794_power__Suc__less__one,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_real @ A @ one_one_real )
% 5.17/5.41 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_less_one
% 5.17/5.41 thf(fact_2795_power__Suc__less__one,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.17/5.41 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_less_one
% 5.17/5.41 thf(fact_2796_power__Suc__less__one,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.17/5.41 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_less_one
% 5.17/5.41 thf(fact_2797_power__Suc__less__one,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_int @ A @ one_one_int )
% 5.17/5.41 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_Suc_less_one
% 5.17/5.41 thf(fact_2798_power__strict__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: real] :
% 5.17/5.41 ( ( ord_less_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_real @ A @ one_one_real )
% 5.17/5.41 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_decreasing
% 5.17/5.41 thf(fact_2799_power__strict__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: rat] :
% 5.17/5.41 ( ( ord_less_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.17/5.41 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_decreasing
% 5.17/5.41 thf(fact_2800_power__strict__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.17/5.41 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_decreasing
% 5.17/5.41 thf(fact_2801_power__strict__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: int] :
% 5.17/5.41 ( ( ord_less_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_int @ A @ one_one_int )
% 5.17/5.41 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_decreasing
% 5.17/5.41 thf(fact_2802_power__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: rat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.17/5.41 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_decreasing
% 5.17/5.41 thf(fact_2803_power__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.17/5.41 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_decreasing
% 5.17/5.41 thf(fact_2804_power__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: int] :
% 5.17/5.41 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.17/5.41 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_decreasing
% 5.17/5.41 thf(fact_2805_power__decreasing,axiom,
% 5.17/5.41 ! [N: nat,N5: nat,A: real] :
% 5.17/5.41 ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.17/5.41 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_decreasing
% 5.17/5.41 thf(fact_2806_power__le__imp__le__exp,axiom,
% 5.17/5.41 ! [A: rat,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_rat @ one_one_rat @ A )
% 5.17/5.41 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.17/5.41 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_le_imp_le_exp
% 5.17/5.41 thf(fact_2807_power__le__imp__le__exp,axiom,
% 5.17/5.41 ! [A: nat,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ one_one_nat @ A )
% 5.17/5.41 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.17/5.41 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_le_imp_le_exp
% 5.17/5.41 thf(fact_2808_power__le__imp__le__exp,axiom,
% 5.17/5.41 ! [A: int,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_int @ one_one_int @ A )
% 5.17/5.41 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.17/5.41 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_le_imp_le_exp
% 5.17/5.41 thf(fact_2809_power__le__imp__le__exp,axiom,
% 5.17/5.41 ! [A: real,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.41 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.17/5.41 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_le_imp_le_exp
% 5.17/5.41 thf(fact_2810_zero__power2,axiom,
% 5.17/5.41 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = zero_zero_rat ) ).
% 5.17/5.41
% 5.17/5.41 % zero_power2
% 5.17/5.41 thf(fact_2811_zero__power2,axiom,
% 5.17/5.41 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = zero_zero_int ) ).
% 5.17/5.41
% 5.17/5.41 % zero_power2
% 5.17/5.41 thf(fact_2812_zero__power2,axiom,
% 5.17/5.41 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = zero_zero_real ) ).
% 5.17/5.41
% 5.17/5.41 % zero_power2
% 5.17/5.41 thf(fact_2813_zero__power2,axiom,
% 5.17/5.41 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = zero_zero_nat ) ).
% 5.17/5.41
% 5.17/5.41 % zero_power2
% 5.17/5.41 thf(fact_2814_zero__power2,axiom,
% 5.17/5.41 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = zero_zero_complex ) ).
% 5.17/5.41
% 5.17/5.41 % zero_power2
% 5.17/5.41 thf(fact_2815_power__eq__iff__eq__base,axiom,
% 5.17/5.41 ! [N: nat,A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.41 => ( ( ( power_power_rat @ A @ N )
% 5.17/5.41 = ( power_power_rat @ B @ N ) )
% 5.17/5.41 = ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_iff_eq_base
% 5.17/5.41 thf(fact_2816_power__eq__iff__eq__base,axiom,
% 5.17/5.41 ! [N: nat,A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.41 => ( ( ( power_power_nat @ A @ N )
% 5.17/5.41 = ( power_power_nat @ B @ N ) )
% 5.17/5.41 = ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_iff_eq_base
% 5.17/5.41 thf(fact_2817_power__eq__iff__eq__base,axiom,
% 5.17/5.41 ! [N: nat,A: int,B: int] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.41 => ( ( ( power_power_int @ A @ N )
% 5.17/5.41 = ( power_power_int @ B @ N ) )
% 5.17/5.41 = ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_iff_eq_base
% 5.17/5.41 thf(fact_2818_power__eq__iff__eq__base,axiom,
% 5.17/5.41 ! [N: nat,A: real,B: real] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.41 => ( ( ( power_power_real @ A @ N )
% 5.17/5.41 = ( power_power_real @ B @ N ) )
% 5.17/5.41 = ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_iff_eq_base
% 5.17/5.41 thf(fact_2819_power__eq__imp__eq__base,axiom,
% 5.17/5.41 ! [A: rat,N: nat,B: rat] :
% 5.17/5.41 ( ( ( power_power_rat @ A @ N )
% 5.17/5.41 = ( power_power_rat @ B @ N ) )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_imp_eq_base
% 5.17/5.41 thf(fact_2820_power__eq__imp__eq__base,axiom,
% 5.17/5.41 ! [A: nat,N: nat,B: nat] :
% 5.17/5.41 ( ( ( power_power_nat @ A @ N )
% 5.17/5.41 = ( power_power_nat @ B @ N ) )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_imp_eq_base
% 5.17/5.41 thf(fact_2821_power__eq__imp__eq__base,axiom,
% 5.17/5.41 ! [A: int,N: nat,B: int] :
% 5.17/5.41 ( ( ( power_power_int @ A @ N )
% 5.17/5.41 = ( power_power_int @ B @ N ) )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_imp_eq_base
% 5.17/5.41 thf(fact_2822_power__eq__imp__eq__base,axiom,
% 5.17/5.41 ! [A: real,N: nat,B: real] :
% 5.17/5.41 ( ( ( power_power_real @ A @ N )
% 5.17/5.41 = ( power_power_real @ B @ N ) )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( A = B ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_imp_eq_base
% 5.17/5.41 thf(fact_2823_power2__eq__square,axiom,
% 5.17/5.41 ! [A: complex] :
% 5.17/5.41 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( times_times_complex @ A @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_square
% 5.17/5.41 thf(fact_2824_power2__eq__square,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( times_times_real @ A @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_square
% 5.17/5.41 thf(fact_2825_power2__eq__square,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( times_times_rat @ A @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_square
% 5.17/5.41 thf(fact_2826_power2__eq__square,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( times_times_nat @ A @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_square
% 5.17/5.41 thf(fact_2827_power2__eq__square,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( times_times_int @ A @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_square
% 5.17/5.41 thf(fact_2828_power4__eq__xxxx,axiom,
% 5.17/5.41 ! [X: complex] :
% 5.17/5.41 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.17/5.41
% 5.17/5.41 % power4_eq_xxxx
% 5.17/5.41 thf(fact_2829_power4__eq__xxxx,axiom,
% 5.17/5.41 ! [X: real] :
% 5.17/5.41 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.17/5.41
% 5.17/5.41 % power4_eq_xxxx
% 5.17/5.41 thf(fact_2830_power4__eq__xxxx,axiom,
% 5.17/5.41 ! [X: rat] :
% 5.17/5.41 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.17/5.41
% 5.17/5.41 % power4_eq_xxxx
% 5.17/5.41 thf(fact_2831_power4__eq__xxxx,axiom,
% 5.17/5.41 ! [X: nat] :
% 5.17/5.41 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.17/5.41
% 5.17/5.41 % power4_eq_xxxx
% 5.17/5.41 thf(fact_2832_power4__eq__xxxx,axiom,
% 5.17/5.41 ! [X: int] :
% 5.17/5.41 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.17/5.41
% 5.17/5.41 % power4_eq_xxxx
% 5.17/5.41 thf(fact_2833_one__power2,axiom,
% 5.17/5.41 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = one_one_rat ) ).
% 5.17/5.41
% 5.17/5.41 % one_power2
% 5.17/5.41 thf(fact_2834_one__power2,axiom,
% 5.17/5.41 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = one_one_int ) ).
% 5.17/5.41
% 5.17/5.41 % one_power2
% 5.17/5.41 thf(fact_2835_one__power2,axiom,
% 5.17/5.41 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = one_one_real ) ).
% 5.17/5.41
% 5.17/5.41 % one_power2
% 5.17/5.41 thf(fact_2836_one__power2,axiom,
% 5.17/5.41 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = one_one_nat ) ).
% 5.17/5.41
% 5.17/5.41 % one_power2
% 5.17/5.41 thf(fact_2837_one__power2,axiom,
% 5.17/5.41 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = one_one_complex ) ).
% 5.17/5.41
% 5.17/5.41 % one_power2
% 5.17/5.41 thf(fact_2838_self__le__power,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % self_le_power
% 5.17/5.41 thf(fact_2839_self__le__power,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % self_le_power
% 5.17/5.41 thf(fact_2840_self__le__power,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % self_le_power
% 5.17/5.41 thf(fact_2841_self__le__power,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % self_le_power
% 5.17/5.41 thf(fact_2842_power2__commute,axiom,
% 5.17/5.41 ! [X: complex,Y4: complex] :
% 5.17/5.41 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_complex @ ( minus_minus_complex @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_commute
% 5.17/5.41 thf(fact_2843_power2__commute,axiom,
% 5.17/5.41 ! [X: real,Y4: real] :
% 5.17/5.41 ( ( power_power_real @ ( minus_minus_real @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_real @ ( minus_minus_real @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_commute
% 5.17/5.41 thf(fact_2844_power2__commute,axiom,
% 5.17/5.41 ! [X: rat,Y4: rat] :
% 5.17/5.41 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_rat @ ( minus_minus_rat @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_commute
% 5.17/5.41 thf(fact_2845_power2__commute,axiom,
% 5.17/5.41 ! [X: int,Y4: int] :
% 5.17/5.41 ( ( power_power_int @ ( minus_minus_int @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_int @ ( minus_minus_int @ Y4 @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_commute
% 5.17/5.41 thf(fact_2846_one__less__power,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_less_power
% 5.17/5.41 thf(fact_2847_one__less__power,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_rat @ one_one_rat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_less_power
% 5.17/5.41 thf(fact_2848_one__less__power,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ one_one_nat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_less_power
% 5.17/5.41 thf(fact_2849_one__less__power,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( ord_less_int @ one_one_int @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_less_power
% 5.17/5.41 thf(fact_2850_dvd__power__iff,axiom,
% 5.17/5.41 ! [X: code_integer,M: nat,N: nat] :
% 5.17/5.41 ( ( X != zero_z3403309356797280102nteger )
% 5.17/5.41 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.17/5.41 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.17/5.41 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power_iff
% 5.17/5.41 thf(fact_2851_dvd__power__iff,axiom,
% 5.17/5.41 ! [X: int,M: nat,N: nat] :
% 5.17/5.41 ( ( X != zero_zero_int )
% 5.17/5.41 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 5.17/5.41 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.17/5.41 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power_iff
% 5.17/5.41 thf(fact_2852_dvd__power__iff,axiom,
% 5.17/5.41 ! [X: nat,M: nat,N: nat] :
% 5.17/5.41 ( ( X != zero_zero_nat )
% 5.17/5.41 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 5.17/5.41 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.17/5.41 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power_iff
% 5.17/5.41 thf(fact_2853_power3__eq__cube,axiom,
% 5.17/5.41 ! [A: complex] :
% 5.17/5.41 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.41 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power3_eq_cube
% 5.17/5.41 thf(fact_2854_power3__eq__cube,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.41 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power3_eq_cube
% 5.17/5.41 thf(fact_2855_power3__eq__cube,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.41 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power3_eq_cube
% 5.17/5.41 thf(fact_2856_power3__eq__cube,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.41 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power3_eq_cube
% 5.17/5.41 thf(fact_2857_power3__eq__cube,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.41 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % power3_eq_cube
% 5.17/5.41 thf(fact_2858_dvd__power,axiom,
% 5.17/5.41 ! [N: nat,X: code_integer] :
% 5.17/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 | ( X = one_one_Code_integer ) )
% 5.17/5.41 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power
% 5.17/5.41 thf(fact_2859_dvd__power,axiom,
% 5.17/5.41 ! [N: nat,X: rat] :
% 5.17/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 | ( X = one_one_rat ) )
% 5.17/5.41 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power
% 5.17/5.41 thf(fact_2860_dvd__power,axiom,
% 5.17/5.41 ! [N: nat,X: int] :
% 5.17/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 | ( X = one_one_int ) )
% 5.17/5.41 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power
% 5.17/5.41 thf(fact_2861_dvd__power,axiom,
% 5.17/5.41 ! [N: nat,X: real] :
% 5.17/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 | ( X = one_one_real ) )
% 5.17/5.41 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power
% 5.17/5.41 thf(fact_2862_dvd__power,axiom,
% 5.17/5.41 ! [N: nat,X: nat] :
% 5.17/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 | ( X = one_one_nat ) )
% 5.17/5.41 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power
% 5.17/5.41 thf(fact_2863_dvd__power,axiom,
% 5.17/5.41 ! [N: nat,X: complex] :
% 5.17/5.41 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 | ( X = one_one_complex ) )
% 5.17/5.41 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power
% 5.17/5.41 thf(fact_2864_power__diff,axiom,
% 5.17/5.41 ! [A: complex,N: nat,M: nat] :
% 5.17/5.41 ( ( A != zero_zero_complex )
% 5.17/5.41 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.41 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.41 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_diff
% 5.17/5.41 thf(fact_2865_power__diff,axiom,
% 5.17/5.41 ! [A: real,N: nat,M: nat] :
% 5.17/5.41 ( ( A != zero_zero_real )
% 5.17/5.41 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.41 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.41 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_diff
% 5.17/5.41 thf(fact_2866_power__diff,axiom,
% 5.17/5.41 ! [A: rat,N: nat,M: nat] :
% 5.17/5.41 ( ( A != zero_zero_rat )
% 5.17/5.41 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.41 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.41 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_diff
% 5.17/5.41 thf(fact_2867_power__diff,axiom,
% 5.17/5.41 ! [A: nat,N: nat,M: nat] :
% 5.17/5.41 ( ( A != zero_zero_nat )
% 5.17/5.41 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.41 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.41 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_diff
% 5.17/5.41 thf(fact_2868_power__diff,axiom,
% 5.17/5.41 ! [A: int,N: nat,M: nat] :
% 5.17/5.41 ( ( A != zero_zero_int )
% 5.17/5.41 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.41 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.41 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_diff
% 5.17/5.41 thf(fact_2869_power__even__eq,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_even_eq
% 5.17/5.41 thf(fact_2870_power__even__eq,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_even_eq
% 5.17/5.41 thf(fact_2871_power__even__eq,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_even_eq
% 5.17/5.41 thf(fact_2872_power__even__eq,axiom,
% 5.17/5.41 ! [A: complex,N: nat] :
% 5.17/5.41 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_even_eq
% 5.17/5.41 thf(fact_2873_diff__le__diff__pow,axiom,
% 5.17/5.41 ! [K: nat,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.17/5.41 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % diff_le_diff_pow
% 5.17/5.41 thf(fact_2874_dvd__power__iff__le,axiom,
% 5.17/5.41 ! [K: nat,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.17/5.41 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.17/5.41 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_power_iff_le
% 5.17/5.41 thf(fact_2875_power2__le__imp__le,axiom,
% 5.17/5.41 ! [X: rat,Y4: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.41 => ( ord_less_eq_rat @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_le_imp_le
% 5.17/5.41 thf(fact_2876_power2__le__imp__le,axiom,
% 5.17/5.41 ! [X: nat,Y4: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.17/5.41 => ( ord_less_eq_nat @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_le_imp_le
% 5.17/5.41 thf(fact_2877_power2__le__imp__le,axiom,
% 5.17/5.41 ! [X: int,Y4: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.41 => ( ord_less_eq_int @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_le_imp_le
% 5.17/5.41 thf(fact_2878_power2__le__imp__le,axiom,
% 5.17/5.41 ! [X: real,Y4: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.41 => ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_le_imp_le
% 5.17/5.41 thf(fact_2879_power2__eq__imp__eq,axiom,
% 5.17/5.41 ! [X: rat,Y4: rat] :
% 5.17/5.41 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.41 => ( X = Y4 ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_imp_eq
% 5.17/5.41 thf(fact_2880_power2__eq__imp__eq,axiom,
% 5.17/5.41 ! [X: nat,Y4: nat] :
% 5.17/5.41 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.17/5.41 => ( X = Y4 ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_imp_eq
% 5.17/5.41 thf(fact_2881_power2__eq__imp__eq,axiom,
% 5.17/5.41 ! [X: int,Y4: int] :
% 5.17/5.41 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.41 => ( X = Y4 ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_imp_eq
% 5.17/5.41 thf(fact_2882_power2__eq__imp__eq,axiom,
% 5.17/5.41 ! [X: real,Y4: real] :
% 5.17/5.41 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.41 => ( X = Y4 ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_eq_imp_eq
% 5.17/5.41 thf(fact_2883_zero__le__power2,axiom,
% 5.17/5.41 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_power2
% 5.17/5.41 thf(fact_2884_zero__le__power2,axiom,
% 5.17/5.41 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_power2
% 5.17/5.41 thf(fact_2885_zero__le__power2,axiom,
% 5.17/5.41 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_power2
% 5.17/5.41 thf(fact_2886_power2__less__0,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_0
% 5.17/5.41 thf(fact_2887_power2__less__0,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_0
% 5.17/5.41 thf(fact_2888_power2__less__0,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_0
% 5.17/5.41 thf(fact_2889_power__strict__mono,axiom,
% 5.17/5.41 ! [A: rat,B: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_rat @ A @ B )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_mono
% 5.17/5.41 thf(fact_2890_power__strict__mono,axiom,
% 5.17/5.41 ! [A: nat,B: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ A @ B )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_mono
% 5.17/5.41 thf(fact_2891_power__strict__mono,axiom,
% 5.17/5.41 ! [A: int,B: int,N: nat] :
% 5.17/5.41 ( ( ord_less_int @ A @ B )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_mono
% 5.17/5.41 thf(fact_2892_power__strict__mono,axiom,
% 5.17/5.41 ! [A: real,B: real,N: nat] :
% 5.17/5.41 ( ( ord_less_real @ A @ B )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_strict_mono
% 5.17/5.41 thf(fact_2893_power__eq__if,axiom,
% 5.17/5.41 ( power_power_complex
% 5.17/5.41 = ( ^ [P6: complex,M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P6 @ ( power_power_complex @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_if
% 5.17/5.41 thf(fact_2894_power__eq__if,axiom,
% 5.17/5.41 ( power_power_real
% 5.17/5.41 = ( ^ [P6: real,M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P6 @ ( power_power_real @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_if
% 5.17/5.41 thf(fact_2895_power__eq__if,axiom,
% 5.17/5.41 ( power_power_rat
% 5.17/5.41 = ( ^ [P6: rat,M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_if
% 5.17/5.41 thf(fact_2896_power__eq__if,axiom,
% 5.17/5.41 ( power_power_nat
% 5.17/5.41 = ( ^ [P6: nat,M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_if
% 5.17/5.41 thf(fact_2897_power__eq__if,axiom,
% 5.17/5.41 ( power_power_int
% 5.17/5.41 = ( ^ [P6: int,M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_eq_if
% 5.17/5.41 thf(fact_2898_power__minus__mult,axiom,
% 5.17/5.41 ! [N: nat,A: complex] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.17/5.41 = ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_minus_mult
% 5.17/5.41 thf(fact_2899_power__minus__mult,axiom,
% 5.17/5.41 ! [N: nat,A: real] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.17/5.41 = ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_minus_mult
% 5.17/5.41 thf(fact_2900_power__minus__mult,axiom,
% 5.17/5.41 ! [N: nat,A: rat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.17/5.41 = ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_minus_mult
% 5.17/5.41 thf(fact_2901_power__minus__mult,axiom,
% 5.17/5.41 ! [N: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.17/5.41 = ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_minus_mult
% 5.17/5.41 thf(fact_2902_power__minus__mult,axiom,
% 5.17/5.41 ! [N: nat,A: int] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.17/5.41 = ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_minus_mult
% 5.17/5.41 thf(fact_2903_power2__less__imp__less,axiom,
% 5.17/5.41 ! [X: rat,Y4: rat] :
% 5.17/5.41 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.41 => ( ord_less_rat @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_imp_less
% 5.17/5.41 thf(fact_2904_power2__less__imp__less,axiom,
% 5.17/5.41 ! [X: nat,Y4: nat] :
% 5.17/5.41 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.17/5.41 => ( ord_less_nat @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_imp_less
% 5.17/5.41 thf(fact_2905_power2__less__imp__less,axiom,
% 5.17/5.41 ! [X: int,Y4: int] :
% 5.17/5.41 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.41 => ( ord_less_int @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_imp_less
% 5.17/5.41 thf(fact_2906_power2__less__imp__less,axiom,
% 5.17/5.41 ! [X: real,Y4: real] :
% 5.17/5.41 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.41 => ( ord_less_real @ X @ Y4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power2_less_imp_less
% 5.17/5.41 thf(fact_2907_zero__le__even__power_H,axiom,
% 5.17/5.41 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_even_power'
% 5.17/5.41 thf(fact_2908_zero__le__even__power_H,axiom,
% 5.17/5.41 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_even_power'
% 5.17/5.41 thf(fact_2909_zero__le__even__power_H,axiom,
% 5.17/5.41 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_even_power'
% 5.17/5.41 thf(fact_2910_power__odd__eq,axiom,
% 5.17/5.41 ! [A: complex,N: nat] :
% 5.17/5.41 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.41 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_odd_eq
% 5.17/5.41 thf(fact_2911_power__odd__eq,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.41 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_odd_eq
% 5.17/5.41 thf(fact_2912_power__odd__eq,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.41 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_odd_eq
% 5.17/5.41 thf(fact_2913_power__odd__eq,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.41 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_odd_eq
% 5.17/5.41 thf(fact_2914_power__odd__eq,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.41 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % power_odd_eq
% 5.17/5.41 thf(fact_2915_odd__0__le__power__imp__0__le,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.17/5.41 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_0_le_power_imp_0_le
% 5.17/5.41 thf(fact_2916_odd__0__le__power__imp__0__le,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.17/5.41 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_0_le_power_imp_0_le
% 5.17/5.41 thf(fact_2917_odd__0__le__power__imp__0__le,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.17/5.41 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_0_le_power_imp_0_le
% 5.17/5.41 thf(fact_2918_odd__power__less__zero,axiom,
% 5.17/5.41 ! [A: real,N: nat] :
% 5.17/5.41 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.41 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_power_less_zero
% 5.17/5.41 thf(fact_2919_odd__power__less__zero,axiom,
% 5.17/5.41 ! [A: rat,N: nat] :
% 5.17/5.41 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.41 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_power_less_zero
% 5.17/5.41 thf(fact_2920_odd__power__less__zero,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.41 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_power_less_zero
% 5.17/5.41 thf(fact_2921_space__2__pow__bound,axiom,
% 5.17/5.41 ! [T: vEBT_VEBT,N: nat] :
% 5.17/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.17/5.41 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % space_2_pow_bound
% 5.17/5.41 thf(fact_2922_cnt__bound,axiom,
% 5.17/5.41 ! [T: vEBT_VEBT,N: nat] :
% 5.17/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.17/5.41 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % cnt_bound
% 5.17/5.41 thf(fact_2923_space__bound,axiom,
% 5.17/5.41 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 5.17/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.17/5.41 => ( ( U
% 5.17/5.41 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % space_bound
% 5.17/5.41 thf(fact_2924_cnt__bound_H,axiom,
% 5.17/5.41 ! [T: vEBT_VEBT,N: nat] :
% 5.17/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.17/5.41 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % cnt_bound'
% 5.17/5.41 thf(fact_2925_space_H__bound,axiom,
% 5.17/5.41 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 5.17/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.17/5.41 => ( ( U
% 5.17/5.41 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 => ( ord_less_eq_nat @ ( vEBT_VEBT_space2 @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % space'_bound
% 5.17/5.41 thf(fact_2926_nat__approx__posE,axiom,
% 5.17/5.41 ! [E2: real] :
% 5.17/5.41 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.17/5.41 => ~ ! [N2: nat] :
% 5.17/5.41 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 5.17/5.41
% 5.17/5.41 % nat_approx_posE
% 5.17/5.41 thf(fact_2927_nat__approx__posE,axiom,
% 5.17/5.41 ! [E2: rat] :
% 5.17/5.41 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.17/5.41 => ~ ! [N2: nat] :
% 5.17/5.41 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ E2 ) ) ).
% 5.17/5.41
% 5.17/5.41 % nat_approx_posE
% 5.17/5.41 thf(fact_2928_high__def,axiom,
% 5.17/5.41 ( vEBT_VEBT_high
% 5.17/5.41 = ( ^ [X3: nat,N4: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % high_def
% 5.17/5.41 thf(fact_2929_pow__sum,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( 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 ) )
% 5.17/5.41 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % pow_sum
% 5.17/5.41 thf(fact_2930_even__odd__cases,axiom,
% 5.17/5.41 ! [X: nat] :
% 5.17/5.41 ( ! [N2: nat] :
% 5.17/5.41 ( X
% 5.17/5.41 != ( plus_plus_nat @ N2 @ N2 ) )
% 5.17/5.41 => ~ ! [N2: nat] :
% 5.17/5.41 ( X
% 5.17/5.41 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_odd_cases
% 5.17/5.41 thf(fact_2931_deg__not__0,axiom,
% 5.17/5.41 ! [T: vEBT_VEBT,N: nat] :
% 5.17/5.41 ( ( vEBT_invar_vebt @ T @ N )
% 5.17/5.41 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.41
% 5.17/5.41 % deg_not_0
% 5.17/5.41 thf(fact_2932_buildup__gives__valid,axiom,
% 5.17/5.41 ! [N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.17/5.41
% 5.17/5.41 % buildup_gives_valid
% 5.17/5.41 thf(fact_2933_add__left__cancel,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ A @ B )
% 5.17/5.41 = ( plus_plus_real @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_cancel
% 5.17/5.41 thf(fact_2934_add__left__cancel,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ A @ B )
% 5.17/5.41 = ( plus_plus_rat @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_cancel
% 5.17/5.41 thf(fact_2935_add__left__cancel,axiom,
% 5.17/5.41 ! [A: nat,B: nat,C: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ A @ B )
% 5.17/5.41 = ( plus_plus_nat @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_cancel
% 5.17/5.41 thf(fact_2936_add__left__cancel,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ A @ B )
% 5.17/5.41 = ( plus_plus_int @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_cancel
% 5.17/5.41 thf(fact_2937_add__right__cancel,axiom,
% 5.17/5.41 ! [B: real,A: real,C: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ B @ A )
% 5.17/5.41 = ( plus_plus_real @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_cancel
% 5.17/5.41 thf(fact_2938_add__right__cancel,axiom,
% 5.17/5.41 ! [B: rat,A: rat,C: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ B @ A )
% 5.17/5.41 = ( plus_plus_rat @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_cancel
% 5.17/5.41 thf(fact_2939_add__right__cancel,axiom,
% 5.17/5.41 ! [B: nat,A: nat,C: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ B @ A )
% 5.17/5.41 = ( plus_plus_nat @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_cancel
% 5.17/5.41 thf(fact_2940_add__right__cancel,axiom,
% 5.17/5.41 ! [B: int,A: int,C: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ B @ A )
% 5.17/5.41 = ( plus_plus_int @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_cancel
% 5.17/5.41 thf(fact_2941_high__bound__aux,axiom,
% 5.17/5.41 ! [Ma: nat,N: nat,M: nat] :
% 5.17/5.41 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.17/5.41 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % high_bound_aux
% 5.17/5.41 thf(fact_2942_add__le__cancel__left,axiom,
% 5.17/5.41 ! [C: rat,A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.17/5.41 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_left
% 5.17/5.41 thf(fact_2943_add__le__cancel__left,axiom,
% 5.17/5.41 ! [C: nat,A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.17/5.41 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_left
% 5.17/5.41 thf(fact_2944_add__le__cancel__left,axiom,
% 5.17/5.41 ! [C: int,A: int,B: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.17/5.41 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_left
% 5.17/5.41 thf(fact_2945_add__le__cancel__left,axiom,
% 5.17/5.41 ! [C: real,A: real,B: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.17/5.41 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_left
% 5.17/5.41 thf(fact_2946_add__le__cancel__right,axiom,
% 5.17/5.41 ! [A: rat,C: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.41 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_right
% 5.17/5.41 thf(fact_2947_add__le__cancel__right,axiom,
% 5.17/5.41 ! [A: nat,C: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.41 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_right
% 5.17/5.41 thf(fact_2948_add__le__cancel__right,axiom,
% 5.17/5.41 ! [A: int,C: int,B: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.17/5.41 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_right
% 5.17/5.41 thf(fact_2949_add__le__cancel__right,axiom,
% 5.17/5.41 ! [A: real,C: real,B: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.17/5.41 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_cancel_right
% 5.17/5.41 thf(fact_2950_double__eq__0__iff,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ A @ A )
% 5.17/5.41 = zero_zero_real )
% 5.17/5.41 = ( A = zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_eq_0_iff
% 5.17/5.41 thf(fact_2951_double__eq__0__iff,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ A @ A )
% 5.17/5.41 = zero_zero_rat )
% 5.17/5.41 = ( A = zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_eq_0_iff
% 5.17/5.41 thf(fact_2952_double__eq__0__iff,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ A @ A )
% 5.17/5.41 = zero_zero_int )
% 5.17/5.41 = ( A = zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_eq_0_iff
% 5.17/5.41 thf(fact_2953_add__0,axiom,
% 5.17/5.41 ! [A: complex] :
% 5.17/5.41 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_0
% 5.17/5.41 thf(fact_2954_add__0,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_0
% 5.17/5.41 thf(fact_2955_add__0,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_0
% 5.17/5.41 thf(fact_2956_add__0,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_0
% 5.17/5.41 thf(fact_2957_add__0,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_0
% 5.17/5.41 thf(fact_2958_zero__eq__add__iff__both__eq__0,axiom,
% 5.17/5.41 ! [X: nat,Y4: nat] :
% 5.17/5.41 ( ( zero_zero_nat
% 5.17/5.41 = ( plus_plus_nat @ X @ Y4 ) )
% 5.17/5.41 = ( ( X = zero_zero_nat )
% 5.17/5.41 & ( Y4 = zero_zero_nat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_eq_add_iff_both_eq_0
% 5.17/5.41 thf(fact_2959_add__eq__0__iff__both__eq__0,axiom,
% 5.17/5.41 ! [X: nat,Y4: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ X @ Y4 )
% 5.17/5.41 = zero_zero_nat )
% 5.17/5.41 = ( ( X = zero_zero_nat )
% 5.17/5.41 & ( Y4 = zero_zero_nat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_eq_0_iff_both_eq_0
% 5.17/5.41 thf(fact_2960_add__cancel__right__right,axiom,
% 5.17/5.41 ! [A: complex,B: complex] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_complex @ A @ B ) )
% 5.17/5.41 = ( B = zero_zero_complex ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_right
% 5.17/5.41 thf(fact_2961_add__cancel__right__right,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_real @ A @ B ) )
% 5.17/5.41 = ( B = zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_right
% 5.17/5.41 thf(fact_2962_add__cancel__right__right,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_rat @ A @ B ) )
% 5.17/5.41 = ( B = zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_right
% 5.17/5.41 thf(fact_2963_add__cancel__right__right,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_nat @ A @ B ) )
% 5.17/5.41 = ( B = zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_right
% 5.17/5.41 thf(fact_2964_add__cancel__right__right,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_int @ A @ B ) )
% 5.17/5.41 = ( B = zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_right
% 5.17/5.41 thf(fact_2965_add__cancel__right__left,axiom,
% 5.17/5.41 ! [A: complex,B: complex] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_complex @ B @ A ) )
% 5.17/5.41 = ( B = zero_zero_complex ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_left
% 5.17/5.41 thf(fact_2966_add__cancel__right__left,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_real @ B @ A ) )
% 5.17/5.41 = ( B = zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_left
% 5.17/5.41 thf(fact_2967_add__cancel__right__left,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_rat @ B @ A ) )
% 5.17/5.41 = ( B = zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_left
% 5.17/5.41 thf(fact_2968_add__cancel__right__left,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_nat @ B @ A ) )
% 5.17/5.41 = ( B = zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_left
% 5.17/5.41 thf(fact_2969_add__cancel__right__left,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( A
% 5.17/5.41 = ( plus_plus_int @ B @ A ) )
% 5.17/5.41 = ( B = zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_right_left
% 5.17/5.41 thf(fact_2970_add__cancel__left__right,axiom,
% 5.17/5.41 ! [A: complex,B: complex] :
% 5.17/5.41 ( ( ( plus_plus_complex @ A @ B )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_complex ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_right
% 5.17/5.41 thf(fact_2971_add__cancel__left__right,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ A @ B )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_right
% 5.17/5.41 thf(fact_2972_add__cancel__left__right,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ A @ B )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_right
% 5.17/5.41 thf(fact_2973_add__cancel__left__right,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ A @ B )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_right
% 5.17/5.41 thf(fact_2974_add__cancel__left__right,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ A @ B )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_right
% 5.17/5.41 thf(fact_2975_add__cancel__left__left,axiom,
% 5.17/5.41 ! [B: complex,A: complex] :
% 5.17/5.41 ( ( ( plus_plus_complex @ B @ A )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_complex ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_left
% 5.17/5.41 thf(fact_2976_add__cancel__left__left,axiom,
% 5.17/5.41 ! [B: real,A: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ B @ A )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_left
% 5.17/5.41 thf(fact_2977_add__cancel__left__left,axiom,
% 5.17/5.41 ! [B: rat,A: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ B @ A )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_left
% 5.17/5.41 thf(fact_2978_add__cancel__left__left,axiom,
% 5.17/5.41 ! [B: nat,A: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ B @ A )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_left
% 5.17/5.41 thf(fact_2979_add__cancel__left__left,axiom,
% 5.17/5.41 ! [B: int,A: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ B @ A )
% 5.17/5.41 = A )
% 5.17/5.41 = ( B = zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_cancel_left_left
% 5.17/5.41 thf(fact_2980_double__zero__sym,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( zero_zero_real
% 5.17/5.41 = ( plus_plus_real @ A @ A ) )
% 5.17/5.41 = ( A = zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_zero_sym
% 5.17/5.41 thf(fact_2981_double__zero__sym,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( zero_zero_rat
% 5.17/5.41 = ( plus_plus_rat @ A @ A ) )
% 5.17/5.41 = ( A = zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_zero_sym
% 5.17/5.41 thf(fact_2982_double__zero__sym,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( zero_zero_int
% 5.17/5.41 = ( plus_plus_int @ A @ A ) )
% 5.17/5.41 = ( A = zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_zero_sym
% 5.17/5.41 thf(fact_2983_add_Oright__neutral,axiom,
% 5.17/5.41 ! [A: complex] :
% 5.17/5.41 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_neutral
% 5.17/5.41 thf(fact_2984_add_Oright__neutral,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_neutral
% 5.17/5.41 thf(fact_2985_add_Oright__neutral,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_neutral
% 5.17/5.41 thf(fact_2986_add_Oright__neutral,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_neutral
% 5.17/5.41 thf(fact_2987_add_Oright__neutral,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_neutral
% 5.17/5.41 thf(fact_2988_add__less__cancel__left,axiom,
% 5.17/5.41 ! [C: real,A: real,B: real] :
% 5.17/5.41 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.17/5.41 = ( ord_less_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_left
% 5.17/5.41 thf(fact_2989_add__less__cancel__left,axiom,
% 5.17/5.41 ! [C: rat,A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.17/5.41 = ( ord_less_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_left
% 5.17/5.41 thf(fact_2990_add__less__cancel__left,axiom,
% 5.17/5.41 ! [C: nat,A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.17/5.41 = ( ord_less_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_left
% 5.17/5.41 thf(fact_2991_add__less__cancel__left,axiom,
% 5.17/5.41 ! [C: int,A: int,B: int] :
% 5.17/5.41 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.17/5.41 = ( ord_less_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_left
% 5.17/5.41 thf(fact_2992_add__less__cancel__right,axiom,
% 5.17/5.41 ! [A: real,C: real,B: real] :
% 5.17/5.41 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.17/5.41 = ( ord_less_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_right
% 5.17/5.41 thf(fact_2993_add__less__cancel__right,axiom,
% 5.17/5.41 ! [A: rat,C: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.41 = ( ord_less_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_right
% 5.17/5.41 thf(fact_2994_add__less__cancel__right,axiom,
% 5.17/5.41 ! [A: nat,C: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.41 = ( ord_less_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_right
% 5.17/5.41 thf(fact_2995_add__less__cancel__right,axiom,
% 5.17/5.41 ! [A: int,C: int,B: int] :
% 5.17/5.41 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.17/5.41 = ( ord_less_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_cancel_right
% 5.17/5.41 thf(fact_2996_numeral__plus__numeral,axiom,
% 5.17/5.41 ! [M: num,N: num] :
% 5.17/5.41 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.41 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_numeral
% 5.17/5.41 thf(fact_2997_numeral__plus__numeral,axiom,
% 5.17/5.41 ! [M: num,N: num] :
% 5.17/5.41 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.41 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_numeral
% 5.17/5.41 thf(fact_2998_numeral__plus__numeral,axiom,
% 5.17/5.41 ! [M: num,N: num] :
% 5.17/5.41 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.41 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_numeral
% 5.17/5.41 thf(fact_2999_numeral__plus__numeral,axiom,
% 5.17/5.41 ! [M: num,N: num] :
% 5.17/5.41 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.41 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_numeral
% 5.17/5.41 thf(fact_3000_numeral__plus__numeral,axiom,
% 5.17/5.41 ! [M: num,N: num] :
% 5.17/5.41 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.41 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_numeral
% 5.17/5.41 thf(fact_3001_add__numeral__left,axiom,
% 5.17/5.41 ! [V: num,W: num,Z: complex] :
% 5.17/5.41 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.17/5.41 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_numeral_left
% 5.17/5.41 thf(fact_3002_add__numeral__left,axiom,
% 5.17/5.41 ! [V: num,W: num,Z: real] :
% 5.17/5.41 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.17/5.41 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_numeral_left
% 5.17/5.41 thf(fact_3003_add__numeral__left,axiom,
% 5.17/5.41 ! [V: num,W: num,Z: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.17/5.41 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_numeral_left
% 5.17/5.41 thf(fact_3004_add__numeral__left,axiom,
% 5.17/5.41 ! [V: num,W: num,Z: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.17/5.41 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_numeral_left
% 5.17/5.41 thf(fact_3005_add__numeral__left,axiom,
% 5.17/5.41 ! [V: num,W: num,Z: int] :
% 5.17/5.41 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.17/5.41 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_numeral_left
% 5.17/5.41 thf(fact_3006_add__diff__cancel__right_H,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right'
% 5.17/5.41 thf(fact_3007_add__diff__cancel__right_H,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right'
% 5.17/5.41 thf(fact_3008_add__diff__cancel__right_H,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right'
% 5.17/5.41 thf(fact_3009_add__diff__cancel__right_H,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right'
% 5.17/5.41 thf(fact_3010_add__diff__cancel__right,axiom,
% 5.17/5.41 ! [A: real,C: real,B: real] :
% 5.17/5.41 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.17/5.41 = ( minus_minus_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right
% 5.17/5.41 thf(fact_3011_add__diff__cancel__right,axiom,
% 5.17/5.41 ! [A: rat,C: rat,B: rat] :
% 5.17/5.41 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.41 = ( minus_minus_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right
% 5.17/5.41 thf(fact_3012_add__diff__cancel__right,axiom,
% 5.17/5.41 ! [A: nat,C: nat,B: nat] :
% 5.17/5.41 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.41 = ( minus_minus_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right
% 5.17/5.41 thf(fact_3013_add__diff__cancel__right,axiom,
% 5.17/5.41 ! [A: int,C: int,B: int] :
% 5.17/5.41 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.17/5.41 = ( minus_minus_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_right
% 5.17/5.41 thf(fact_3014_add__diff__cancel__left_H,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.17/5.41 = B ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left'
% 5.17/5.41 thf(fact_3015_add__diff__cancel__left_H,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.17/5.41 = B ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left'
% 5.17/5.41 thf(fact_3016_add__diff__cancel__left_H,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.17/5.41 = B ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left'
% 5.17/5.41 thf(fact_3017_add__diff__cancel__left_H,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.17/5.41 = B ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left'
% 5.17/5.41 thf(fact_3018_add__diff__cancel__left,axiom,
% 5.17/5.41 ! [C: real,A: real,B: real] :
% 5.17/5.41 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.17/5.41 = ( minus_minus_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left
% 5.17/5.41 thf(fact_3019_add__diff__cancel__left,axiom,
% 5.17/5.41 ! [C: rat,A: rat,B: rat] :
% 5.17/5.41 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.17/5.41 = ( minus_minus_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left
% 5.17/5.41 thf(fact_3020_add__diff__cancel__left,axiom,
% 5.17/5.41 ! [C: nat,A: nat,B: nat] :
% 5.17/5.41 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.17/5.41 = ( minus_minus_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left
% 5.17/5.41 thf(fact_3021_add__diff__cancel__left,axiom,
% 5.17/5.41 ! [C: int,A: int,B: int] :
% 5.17/5.41 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.17/5.41 = ( minus_minus_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel_left
% 5.17/5.41 thf(fact_3022_diff__add__cancel,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % diff_add_cancel
% 5.17/5.41 thf(fact_3023_diff__add__cancel,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % diff_add_cancel
% 5.17/5.41 thf(fact_3024_diff__add__cancel,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % diff_add_cancel
% 5.17/5.41 thf(fact_3025_add__diff__cancel,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel
% 5.17/5.41 thf(fact_3026_add__diff__cancel,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel
% 5.17/5.41 thf(fact_3027_add__diff__cancel,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.17/5.41 = A ) ).
% 5.17/5.41
% 5.17/5.41 % add_diff_cancel
% 5.17/5.41 thf(fact_3028_high__inv,axiom,
% 5.17/5.41 ! [X: nat,N: nat,Y4: nat] :
% 5.17/5.41 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.17/5.41 = Y4 ) ) ).
% 5.17/5.41
% 5.17/5.41 % high_inv
% 5.17/5.41 thf(fact_3029_dvd__add__triv__right__iff,axiom,
% 5.17/5.41 ! [A: code_integer,B: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.17/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_right_iff
% 5.17/5.41 thf(fact_3030_dvd__add__triv__right__iff,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.17/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_right_iff
% 5.17/5.41 thf(fact_3031_dvd__add__triv__right__iff,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.17/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_right_iff
% 5.17/5.41 thf(fact_3032_dvd__add__triv__right__iff,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.17/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_right_iff
% 5.17/5.41 thf(fact_3033_dvd__add__triv__right__iff,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.17/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_right_iff
% 5.17/5.41 thf(fact_3034_dvd__add__triv__left__iff,axiom,
% 5.17/5.41 ! [A: code_integer,B: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_left_iff
% 5.17/5.41 thf(fact_3035_dvd__add__triv__left__iff,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_left_iff
% 5.17/5.41 thf(fact_3036_dvd__add__triv__left__iff,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_left_iff
% 5.17/5.41 thf(fact_3037_dvd__add__triv__left__iff,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_left_iff
% 5.17/5.41 thf(fact_3038_dvd__add__triv__left__iff,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_triv_left_iff
% 5.17/5.41 thf(fact_3039_add__Suc__right,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.17/5.41 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_Suc_right
% 5.17/5.41 thf(fact_3040_add__is__0,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ M @ N )
% 5.17/5.41 = zero_zero_nat )
% 5.17/5.41 = ( ( M = zero_zero_nat )
% 5.17/5.41 & ( N = zero_zero_nat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_is_0
% 5.17/5.41 thf(fact_3041_Nat_Oadd__0__right,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.17/5.41 = M ) ).
% 5.17/5.41
% 5.17/5.41 % Nat.add_0_right
% 5.17/5.41 thf(fact_3042_nat__add__left__cancel__less,axiom,
% 5.17/5.41 ! [K: nat,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.17/5.41 = ( ord_less_nat @ M @ N ) ) ).
% 5.17/5.41
% 5.17/5.41 % nat_add_left_cancel_less
% 5.17/5.41 thf(fact_3043_nat__add__left__cancel__le,axiom,
% 5.17/5.41 ! [K: nat,M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.17/5.41 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.41
% 5.17/5.41 % nat_add_left_cancel_le
% 5.17/5.41 thf(fact_3044_diff__diff__left,axiom,
% 5.17/5.41 ! [I: nat,J: nat,K: nat] :
% 5.17/5.41 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.17/5.41 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % diff_diff_left
% 5.17/5.41 thf(fact_3045_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.17/5.41 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_double_add_iff_zero_le_single_add
% 5.17/5.41 thf(fact_3046_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.17/5.41 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_double_add_iff_zero_le_single_add
% 5.17/5.41 thf(fact_3047_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.17/5.41 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_le_double_add_iff_zero_le_single_add
% 5.17/5.41 thf(fact_3048_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.17/5.41 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_add_le_zero_iff_single_add_le_zero
% 5.17/5.41 thf(fact_3049_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.17/5.41 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_add_le_zero_iff_single_add_le_zero
% 5.17/5.41 thf(fact_3050_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.17/5.41 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_add_le_zero_iff_single_add_le_zero
% 5.17/5.41 thf(fact_3051_le__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.17/5.41 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel2
% 5.17/5.41 thf(fact_3052_le__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.17/5.41 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel2
% 5.17/5.41 thf(fact_3053_le__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.17/5.41 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel2
% 5.17/5.41 thf(fact_3054_le__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.17/5.41 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel2
% 5.17/5.41 thf(fact_3055_le__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.41 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel1
% 5.17/5.41 thf(fact_3056_le__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.41 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel1
% 5.17/5.41 thf(fact_3057_le__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.17/5.41 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel1
% 5.17/5.41 thf(fact_3058_le__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.17/5.41 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_same_cancel1
% 5.17/5.41 thf(fact_3059_add__le__same__cancel2,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel2
% 5.17/5.41 thf(fact_3060_add__le__same__cancel2,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel2
% 5.17/5.41 thf(fact_3061_add__le__same__cancel2,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel2
% 5.17/5.41 thf(fact_3062_add__le__same__cancel2,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel2
% 5.17/5.41 thf(fact_3063_add__le__same__cancel1,axiom,
% 5.17/5.41 ! [B: rat,A: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel1
% 5.17/5.41 thf(fact_3064_add__le__same__cancel1,axiom,
% 5.17/5.41 ! [B: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel1
% 5.17/5.41 thf(fact_3065_add__le__same__cancel1,axiom,
% 5.17/5.41 ! [B: int,A: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel1
% 5.17/5.41 thf(fact_3066_add__le__same__cancel1,axiom,
% 5.17/5.41 ! [B: real,A: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_le_same_cancel1
% 5.17/5.41 thf(fact_3067_add__less__same__cancel1,axiom,
% 5.17/5.41 ! [B: real,A: real] :
% 5.17/5.41 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel1
% 5.17/5.41 thf(fact_3068_add__less__same__cancel1,axiom,
% 5.17/5.41 ! [B: rat,A: rat] :
% 5.17/5.41 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel1
% 5.17/5.41 thf(fact_3069_add__less__same__cancel1,axiom,
% 5.17/5.41 ! [B: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel1
% 5.17/5.41 thf(fact_3070_add__less__same__cancel1,axiom,
% 5.17/5.41 ! [B: int,A: int] :
% 5.17/5.41 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.17/5.41 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel1
% 5.17/5.41 thf(fact_3071_add__less__same__cancel2,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel2
% 5.17/5.41 thf(fact_3072_add__less__same__cancel2,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel2
% 5.17/5.41 thf(fact_3073_add__less__same__cancel2,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel2
% 5.17/5.41 thf(fact_3074_add__less__same__cancel2,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.17/5.41 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_less_same_cancel2
% 5.17/5.41 thf(fact_3075_less__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.17/5.41 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel1
% 5.17/5.41 thf(fact_3076_less__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.41 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel1
% 5.17/5.41 thf(fact_3077_less__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.41 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel1
% 5.17/5.41 thf(fact_3078_less__add__same__cancel1,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.17/5.41 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel1
% 5.17/5.41 thf(fact_3079_less__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: real,B: real] :
% 5.17/5.41 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.17/5.41 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel2
% 5.17/5.41 thf(fact_3080_less__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: rat,B: rat] :
% 5.17/5.41 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.17/5.41 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel2
% 5.17/5.41 thf(fact_3081_less__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.17/5.41 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel2
% 5.17/5.41 thf(fact_3082_less__add__same__cancel2,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.17/5.41 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % less_add_same_cancel2
% 5.17/5.41 thf(fact_3083_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.17/5.41 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_add_less_zero_iff_single_add_less_zero
% 5.17/5.41 thf(fact_3084_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.17/5.41 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_add_less_zero_iff_single_add_less_zero
% 5.17/5.41 thf(fact_3085_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.17/5.41 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.41
% 5.17/5.41 % double_add_less_zero_iff_single_add_less_zero
% 5.17/5.41 thf(fact_3086_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.17/5.41 ! [A: real] :
% 5.17/5.41 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.17/5.41 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_less_double_add_iff_zero_less_single_add
% 5.17/5.41 thf(fact_3087_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.17/5.41 ! [A: rat] :
% 5.17/5.41 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.17/5.41 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_less_double_add_iff_zero_less_single_add
% 5.17/5.41 thf(fact_3088_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.17/5.41 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.17/5.41
% 5.17/5.41 % zero_less_double_add_iff_zero_less_single_add
% 5.17/5.41 thf(fact_3089_sum__squares__eq__zero__iff,axiom,
% 5.17/5.41 ! [X: real,Y4: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) )
% 5.17/5.41 = zero_zero_real )
% 5.17/5.41 = ( ( X = zero_zero_real )
% 5.17/5.41 & ( Y4 = zero_zero_real ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % sum_squares_eq_zero_iff
% 5.17/5.41 thf(fact_3090_sum__squares__eq__zero__iff,axiom,
% 5.17/5.41 ! [X: rat,Y4: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) )
% 5.17/5.41 = zero_zero_rat )
% 5.17/5.41 = ( ( X = zero_zero_rat )
% 5.17/5.41 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % sum_squares_eq_zero_iff
% 5.17/5.41 thf(fact_3091_sum__squares__eq__zero__iff,axiom,
% 5.17/5.41 ! [X: int,Y4: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) )
% 5.17/5.41 = zero_zero_int )
% 5.17/5.41 = ( ( X = zero_zero_int )
% 5.17/5.41 & ( Y4 = zero_zero_int ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % sum_squares_eq_zero_iff
% 5.17/5.41 thf(fact_3092_le__add__diff__inverse,axiom,
% 5.17/5.41 ! [B: rat,A: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.41 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse
% 5.17/5.41 thf(fact_3093_le__add__diff__inverse,axiom,
% 5.17/5.41 ! [B: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.41 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse
% 5.17/5.41 thf(fact_3094_le__add__diff__inverse,axiom,
% 5.17/5.41 ! [B: int,A: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.41 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse
% 5.17/5.41 thf(fact_3095_le__add__diff__inverse,axiom,
% 5.17/5.41 ! [B: real,A: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.41 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse
% 5.17/5.41 thf(fact_3096_le__add__diff__inverse2,axiom,
% 5.17/5.41 ! [B: rat,A: rat] :
% 5.17/5.41 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.41 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse2
% 5.17/5.41 thf(fact_3097_le__add__diff__inverse2,axiom,
% 5.17/5.41 ! [B: nat,A: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.41 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse2
% 5.17/5.41 thf(fact_3098_le__add__diff__inverse2,axiom,
% 5.17/5.41 ! [B: int,A: int] :
% 5.17/5.41 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.41 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse2
% 5.17/5.41 thf(fact_3099_le__add__diff__inverse2,axiom,
% 5.17/5.41 ! [B: real,A: real] :
% 5.17/5.41 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.41 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % le_add_diff_inverse2
% 5.17/5.41 thf(fact_3100_diff__add__zero,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.41 = zero_zero_nat ) ).
% 5.17/5.41
% 5.17/5.41 % diff_add_zero
% 5.17/5.41 thf(fact_3101_distrib__left__numeral,axiom,
% 5.17/5.41 ! [V: num,B: complex,C: complex] :
% 5.17/5.41 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.17/5.41 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_left_numeral
% 5.17/5.41 thf(fact_3102_distrib__left__numeral,axiom,
% 5.17/5.41 ! [V: num,B: real,C: real] :
% 5.17/5.41 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.17/5.41 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_left_numeral
% 5.17/5.41 thf(fact_3103_distrib__left__numeral,axiom,
% 5.17/5.41 ! [V: num,B: rat,C: rat] :
% 5.17/5.41 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.41 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_left_numeral
% 5.17/5.41 thf(fact_3104_distrib__left__numeral,axiom,
% 5.17/5.41 ! [V: num,B: nat,C: nat] :
% 5.17/5.41 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.41 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_left_numeral
% 5.17/5.41 thf(fact_3105_distrib__left__numeral,axiom,
% 5.17/5.41 ! [V: num,B: int,C: int] :
% 5.17/5.41 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.17/5.41 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_left_numeral
% 5.17/5.41 thf(fact_3106_distrib__right__numeral,axiom,
% 5.17/5.41 ! [A: complex,B: complex,V: num] :
% 5.17/5.41 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.17/5.41 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_right_numeral
% 5.17/5.41 thf(fact_3107_distrib__right__numeral,axiom,
% 5.17/5.41 ! [A: real,B: real,V: num] :
% 5.17/5.41 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.41 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_right_numeral
% 5.17/5.41 thf(fact_3108_distrib__right__numeral,axiom,
% 5.17/5.41 ! [A: rat,B: rat,V: num] :
% 5.17/5.41 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.41 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_right_numeral
% 5.17/5.41 thf(fact_3109_distrib__right__numeral,axiom,
% 5.17/5.41 ! [A: nat,B: nat,V: num] :
% 5.17/5.41 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.41 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_right_numeral
% 5.17/5.41 thf(fact_3110_distrib__right__numeral,axiom,
% 5.17/5.41 ! [A: int,B: int,V: num] :
% 5.17/5.41 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.41 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % distrib_right_numeral
% 5.17/5.41 thf(fact_3111_dvd__add__times__triv__left__iff,axiom,
% 5.17/5.41 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.17/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_left_iff
% 5.17/5.41 thf(fact_3112_dvd__add__times__triv__left__iff,axiom,
% 5.17/5.41 ! [A: real,C: real,B: real] :
% 5.17/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.17/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_left_iff
% 5.17/5.41 thf(fact_3113_dvd__add__times__triv__left__iff,axiom,
% 5.17/5.41 ! [A: rat,C: rat,B: rat] :
% 5.17/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.17/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_left_iff
% 5.17/5.41 thf(fact_3114_dvd__add__times__triv__left__iff,axiom,
% 5.17/5.41 ! [A: nat,C: nat,B: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.17/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_left_iff
% 5.17/5.41 thf(fact_3115_dvd__add__times__triv__left__iff,axiom,
% 5.17/5.41 ! [A: int,C: int,B: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.17/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_left_iff
% 5.17/5.41 thf(fact_3116_dvd__add__times__triv__right__iff,axiom,
% 5.17/5.41 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.17/5.41 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_right_iff
% 5.17/5.41 thf(fact_3117_dvd__add__times__triv__right__iff,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.17/5.41 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_right_iff
% 5.17/5.41 thf(fact_3118_dvd__add__times__triv__right__iff,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.17/5.41 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_right_iff
% 5.17/5.41 thf(fact_3119_dvd__add__times__triv__right__iff,axiom,
% 5.17/5.41 ! [A: nat,B: nat,C: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.17/5.41 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_right_iff
% 5.17/5.41 thf(fact_3120_dvd__add__times__triv__right__iff,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.17/5.41 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.17/5.41
% 5.17/5.41 % dvd_add_times_triv_right_iff
% 5.17/5.41 thf(fact_3121_div__add,axiom,
% 5.17/5.41 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.17/5.41 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.17/5.41 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_add
% 5.17/5.41 thf(fact_3122_div__add,axiom,
% 5.17/5.41 ! [C: nat,A: nat,B: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ C @ A )
% 5.17/5.41 => ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_add
% 5.17/5.41 thf(fact_3123_div__add,axiom,
% 5.17/5.41 ! [C: int,A: int,B: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ C @ A )
% 5.17/5.41 => ( ( dvd_dvd_int @ C @ B )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_add
% 5.17/5.41 thf(fact_3124_of__nat__add,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.41 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_add
% 5.17/5.41 thf(fact_3125_of__nat__add,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.41 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_add
% 5.17/5.41 thf(fact_3126_of__nat__add,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.41 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_add
% 5.17/5.41 thf(fact_3127_of__nat__add,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.41 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_add
% 5.17/5.41 thf(fact_3128_of__nat__add,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.41 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_add
% 5.17/5.41 thf(fact_3129_add__gr__0,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.41 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.41 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_gr_0
% 5.17/5.41 thf(fact_3130_mult__Suc__right,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.17/5.41 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % mult_Suc_right
% 5.17/5.41 thf(fact_3131_Nat_Odiff__diff__right,axiom,
% 5.17/5.41 ! [K: nat,J: nat,I: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.41 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.17/5.41 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % Nat.diff_diff_right
% 5.17/5.41 thf(fact_3132_Nat_Oadd__diff__assoc2,axiom,
% 5.17/5.41 ! [K: nat,J: nat,I: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.41 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.17/5.41 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % Nat.add_diff_assoc2
% 5.17/5.41 thf(fact_3133_Nat_Oadd__diff__assoc,axiom,
% 5.17/5.41 ! [K: nat,J: nat,I: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.41 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.17/5.41 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % Nat.add_diff_assoc
% 5.17/5.41 thf(fact_3134_triangle__Suc,axiom,
% 5.17/5.41 ! [N: nat] :
% 5.17/5.41 ( ( nat_triangle @ ( suc @ N ) )
% 5.17/5.41 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % triangle_Suc
% 5.17/5.41 thf(fact_3135_div__mult__self1,axiom,
% 5.17/5.41 ! [B: nat,A: nat,C: nat] :
% 5.17/5.41 ( ( B != zero_zero_nat )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.17/5.41 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self1
% 5.17/5.41 thf(fact_3136_div__mult__self1,axiom,
% 5.17/5.41 ! [B: int,A: int,C: int] :
% 5.17/5.41 ( ( B != zero_zero_int )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.17/5.41 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self1
% 5.17/5.41 thf(fact_3137_div__mult__self2,axiom,
% 5.17/5.41 ! [B: nat,A: nat,C: nat] :
% 5.17/5.41 ( ( B != zero_zero_nat )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.17/5.41 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self2
% 5.17/5.41 thf(fact_3138_div__mult__self2,axiom,
% 5.17/5.41 ! [B: int,A: int,C: int] :
% 5.17/5.41 ( ( B != zero_zero_int )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.17/5.41 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self2
% 5.17/5.41 thf(fact_3139_div__mult__self3,axiom,
% 5.17/5.41 ! [B: nat,C: nat,A: nat] :
% 5.17/5.41 ( ( B != zero_zero_nat )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.17/5.41 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self3
% 5.17/5.41 thf(fact_3140_div__mult__self3,axiom,
% 5.17/5.41 ! [B: int,C: int,A: int] :
% 5.17/5.41 ( ( B != zero_zero_int )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.17/5.41 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self3
% 5.17/5.41 thf(fact_3141_div__mult__self4,axiom,
% 5.17/5.41 ! [B: nat,C: nat,A: nat] :
% 5.17/5.41 ( ( B != zero_zero_nat )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.17/5.41 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self4
% 5.17/5.41 thf(fact_3142_div__mult__self4,axiom,
% 5.17/5.41 ! [B: int,C: int,A: int] :
% 5.17/5.41 ( ( B != zero_zero_int )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.17/5.41 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_mult_self4
% 5.17/5.41 thf(fact_3143_numeral__plus__one,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.17/5.41 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_one
% 5.17/5.41 thf(fact_3144_numeral__plus__one,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.17/5.41 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_one
% 5.17/5.41 thf(fact_3145_numeral__plus__one,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.17/5.41 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_one
% 5.17/5.41 thf(fact_3146_numeral__plus__one,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.17/5.41 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_one
% 5.17/5.41 thf(fact_3147_numeral__plus__one,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.17/5.41 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % numeral_plus_one
% 5.17/5.41 thf(fact_3148_one__plus__numeral,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.41 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_plus_numeral
% 5.17/5.41 thf(fact_3149_one__plus__numeral,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.17/5.41 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_plus_numeral
% 5.17/5.41 thf(fact_3150_one__plus__numeral,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.17/5.41 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_plus_numeral
% 5.17/5.41 thf(fact_3151_one__plus__numeral,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.17/5.41 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_plus_numeral
% 5.17/5.41 thf(fact_3152_one__plus__numeral,axiom,
% 5.17/5.41 ! [N: num] :
% 5.17/5.41 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.17/5.41 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_plus_numeral
% 5.17/5.41 thf(fact_3153_of__nat__Suc,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.17/5.41 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_Suc
% 5.17/5.41 thf(fact_3154_of__nat__Suc,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.17/5.41 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_Suc
% 5.17/5.41 thf(fact_3155_of__nat__Suc,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.17/5.41 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_Suc
% 5.17/5.41 thf(fact_3156_of__nat__Suc,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.17/5.41 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_Suc
% 5.17/5.41 thf(fact_3157_of__nat__Suc,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.17/5.41 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % of_nat_Suc
% 5.17/5.41 thf(fact_3158_diff__Suc__diff__eq2,axiom,
% 5.17/5.41 ! [K: nat,J: nat,I: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.41 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.17/5.41 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % diff_Suc_diff_eq2
% 5.17/5.41 thf(fact_3159_diff__Suc__diff__eq1,axiom,
% 5.17/5.41 ! [K: nat,J: nat,I: nat] :
% 5.17/5.41 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.41 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.17/5.41 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % diff_Suc_diff_eq1
% 5.17/5.41 thf(fact_3160_one__add__one,axiom,
% 5.17/5.41 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.17/5.41 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_add_one
% 5.17/5.41 thf(fact_3161_one__add__one,axiom,
% 5.17/5.41 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.17/5.41 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_add_one
% 5.17/5.41 thf(fact_3162_one__add__one,axiom,
% 5.17/5.41 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.17/5.41 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_add_one
% 5.17/5.41 thf(fact_3163_one__add__one,axiom,
% 5.17/5.41 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.17/5.41 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_add_one
% 5.17/5.41 thf(fact_3164_one__add__one,axiom,
% 5.17/5.41 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.17/5.41 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % one_add_one
% 5.17/5.41 thf(fact_3165_odd__add,axiom,
% 5.17/5.41 ! [A: code_integer,B: code_integer] :
% 5.17/5.41 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.17/5.41 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.41 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_add
% 5.17/5.41 thf(fact_3166_odd__add,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.17/5.41 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.41 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_add
% 5.17/5.41 thf(fact_3167_odd__add,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.17/5.41 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.41 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_add
% 5.17/5.41 thf(fact_3168_even__add,axiom,
% 5.17/5.41 ! [A: code_integer,B: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.41 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_add
% 5.17/5.41 thf(fact_3169_even__add,axiom,
% 5.17/5.41 ! [A: nat,B: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.41 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_add
% 5.17/5.41 thf(fact_3170_even__add,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.17/5.41 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_add
% 5.17/5.41 thf(fact_3171_add__2__eq__Suc,axiom,
% 5.17/5.41 ! [N: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.41 = ( suc @ ( suc @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_2_eq_Suc
% 5.17/5.41 thf(fact_3172_add__2__eq__Suc_H,axiom,
% 5.17/5.41 ! [N: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( suc @ ( suc @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_2_eq_Suc'
% 5.17/5.41 thf(fact_3173_add__self__div__2,axiom,
% 5.17/5.41 ! [M: nat] :
% 5.17/5.41 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = M ) ).
% 5.17/5.41
% 5.17/5.41 % add_self_div_2
% 5.17/5.41 thf(fact_3174_even__plus__one__iff,axiom,
% 5.17/5.41 ! [A: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.17/5.41 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_plus_one_iff
% 5.17/5.41 thf(fact_3175_even__plus__one__iff,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.17/5.41 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_plus_one_iff
% 5.17/5.41 thf(fact_3176_even__plus__one__iff,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.17/5.41 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_plus_one_iff
% 5.17/5.41 thf(fact_3177_sum__power2__eq__zero__iff,axiom,
% 5.17/5.41 ! [X: rat,Y4: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = zero_zero_rat )
% 5.17/5.41 = ( ( X = zero_zero_rat )
% 5.17/5.41 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % sum_power2_eq_zero_iff
% 5.17/5.41 thf(fact_3178_sum__power2__eq__zero__iff,axiom,
% 5.17/5.41 ! [X: int,Y4: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = zero_zero_int )
% 5.17/5.41 = ( ( X = zero_zero_int )
% 5.17/5.41 & ( Y4 = zero_zero_int ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % sum_power2_eq_zero_iff
% 5.17/5.41 thf(fact_3179_sum__power2__eq__zero__iff,axiom,
% 5.17/5.41 ! [X: real,Y4: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.41 = zero_zero_real )
% 5.17/5.41 = ( ( X = zero_zero_real )
% 5.17/5.41 & ( Y4 = zero_zero_real ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % sum_power2_eq_zero_iff
% 5.17/5.41 thf(fact_3180_even__diff,axiom,
% 5.17/5.41 ! [A: code_integer,B: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_diff
% 5.17/5.41 thf(fact_3181_even__diff,axiom,
% 5.17/5.41 ! [A: int,B: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.17/5.41 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_diff
% 5.17/5.41 thf(fact_3182_div__Suc__eq__div__add3,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.17/5.41 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % div_Suc_eq_div_add3
% 5.17/5.41 thf(fact_3183_Suc__div__eq__add3__div__numeral,axiom,
% 5.17/5.41 ! [M: nat,V: num] :
% 5.17/5.41 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.41 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % Suc_div_eq_add3_div_numeral
% 5.17/5.41 thf(fact_3184_odd__succ__div__two,axiom,
% 5.17/5.41 ! [A: code_integer] :
% 5.17/5.41 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_succ_div_two
% 5.17/5.41 thf(fact_3185_odd__succ__div__two,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_succ_div_two
% 5.17/5.41 thf(fact_3186_odd__succ__div__two,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_succ_div_two
% 5.17/5.41 thf(fact_3187_even__succ__div__two,axiom,
% 5.17/5.41 ! [A: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_two
% 5.17/5.41 thf(fact_3188_even__succ__div__two,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_two
% 5.17/5.41 thf(fact_3189_even__succ__div__two,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_two
% 5.17/5.41 thf(fact_3190_even__succ__div__2,axiom,
% 5.17/5.41 ! [A: code_integer] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_2
% 5.17/5.41 thf(fact_3191_even__succ__div__2,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_2
% 5.17/5.41 thf(fact_3192_even__succ__div__2,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.41 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_2
% 5.17/5.41 thf(fact_3193_even__diff__nat,axiom,
% 5.17/5.41 ! [M: nat,N: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.41 = ( ( ord_less_nat @ M @ N )
% 5.17/5.41 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_diff_nat
% 5.17/5.41 thf(fact_3194_odd__two__times__div__two__succ,axiom,
% 5.17/5.41 ! [A: code_integer] :
% 5.17/5.41 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_two_times_div_two_succ
% 5.17/5.41 thf(fact_3195_odd__two__times__div__two__succ,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_two_times_div_two_succ
% 5.17/5.41 thf(fact_3196_odd__two__times__div__two__succ,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.17/5.41 = A ) ) ).
% 5.17/5.41
% 5.17/5.41 % odd_two_times_div_two_succ
% 5.17/5.41 thf(fact_3197_set__bit__0,axiom,
% 5.17/5.41 ! [A: int] :
% 5.17/5.41 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.17/5.41 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % set_bit_0
% 5.17/5.41 thf(fact_3198_set__bit__0,axiom,
% 5.17/5.41 ! [A: nat] :
% 5.17/5.41 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.17/5.41 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % set_bit_0
% 5.17/5.41 thf(fact_3199_set__bit__0,axiom,
% 5.17/5.41 ! [A: code_integer] :
% 5.17/5.41 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 5.17/5.41 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % set_bit_0
% 5.17/5.41 thf(fact_3200_even__succ__div__exp,axiom,
% 5.17/5.41 ! [A: code_integer,N: nat] :
% 5.17/5.41 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_exp
% 5.17/5.41 thf(fact_3201_even__succ__div__exp,axiom,
% 5.17/5.41 ! [A: nat,N: nat] :
% 5.17/5.41 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_exp
% 5.17/5.41 thf(fact_3202_even__succ__div__exp,axiom,
% 5.17/5.41 ! [A: int,N: nat] :
% 5.17/5.41 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.41 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.41 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.41 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % even_succ_div_exp
% 5.17/5.41 thf(fact_3203_psubsetD,axiom,
% 5.17/5.41 ! [A2: set_complex,B4: set_complex,C: complex] :
% 5.17/5.41 ( ( ord_less_set_complex @ A2 @ B4 )
% 5.17/5.41 => ( ( member_complex @ C @ A2 )
% 5.17/5.41 => ( member_complex @ C @ B4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % psubsetD
% 5.17/5.41 thf(fact_3204_psubsetD,axiom,
% 5.17/5.41 ! [A2: set_real,B4: set_real,C: real] :
% 5.17/5.41 ( ( ord_less_set_real @ A2 @ B4 )
% 5.17/5.41 => ( ( member_real @ C @ A2 )
% 5.17/5.41 => ( member_real @ C @ B4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % psubsetD
% 5.17/5.41 thf(fact_3205_psubsetD,axiom,
% 5.17/5.41 ! [A2: set_set_nat,B4: set_set_nat,C: set_nat] :
% 5.17/5.41 ( ( ord_less_set_set_nat @ A2 @ B4 )
% 5.17/5.41 => ( ( member_set_nat @ C @ A2 )
% 5.17/5.41 => ( member_set_nat @ C @ B4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % psubsetD
% 5.17/5.41 thf(fact_3206_psubsetD,axiom,
% 5.17/5.41 ! [A2: set_nat,B4: set_nat,C: nat] :
% 5.17/5.41 ( ( ord_less_set_nat @ A2 @ B4 )
% 5.17/5.41 => ( ( member_nat @ C @ A2 )
% 5.17/5.41 => ( member_nat @ C @ B4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % psubsetD
% 5.17/5.41 thf(fact_3207_psubsetD,axiom,
% 5.17/5.41 ! [A2: set_int,B4: set_int,C: int] :
% 5.17/5.41 ( ( ord_less_set_int @ A2 @ B4 )
% 5.17/5.41 => ( ( member_int @ C @ A2 )
% 5.17/5.41 => ( member_int @ C @ B4 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % psubsetD
% 5.17/5.41 thf(fact_3208_enat__less__induct,axiom,
% 5.17/5.41 ! [P: extended_enat > $o,N: extended_enat] :
% 5.17/5.41 ( ! [N2: extended_enat] :
% 5.17/5.41 ( ! [M2: extended_enat] :
% 5.17/5.41 ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 5.17/5.41 => ( P @ M2 ) )
% 5.17/5.41 => ( P @ N2 ) )
% 5.17/5.41 => ( P @ N ) ) ).
% 5.17/5.41
% 5.17/5.41 % enat_less_induct
% 5.17/5.41 thf(fact_3209_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % ab_semigroup_add_class.add_ac(1)
% 5.17/5.41 thf(fact_3210_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % ab_semigroup_add_class.add_ac(1)
% 5.17/5.41 thf(fact_3211_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.17/5.41 ! [A: nat,B: nat,C: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % ab_semigroup_add_class.add_ac(1)
% 5.17/5.41 thf(fact_3212_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % ab_semigroup_add_class.add_ac(1)
% 5.17/5.41 thf(fact_3213_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.17/5.41 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.41 ( ( ( I = J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ( plus_plus_real @ I @ K )
% 5.17/5.41 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(4)
% 5.17/5.41 thf(fact_3214_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.17/5.41 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.41 ( ( ( I = J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ( plus_plus_rat @ I @ K )
% 5.17/5.41 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(4)
% 5.17/5.41 thf(fact_3215_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.17/5.41 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.41 ( ( ( I = J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ( plus_plus_nat @ I @ K )
% 5.17/5.41 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(4)
% 5.17/5.41 thf(fact_3216_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.17/5.41 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.41 ( ( ( I = J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ( plus_plus_int @ I @ K )
% 5.17/5.41 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(4)
% 5.17/5.41 thf(fact_3217_group__cancel_Oadd1,axiom,
% 5.17/5.41 ! [A2: real,K: real,A: real,B: real] :
% 5.17/5.41 ( ( A2
% 5.17/5.41 = ( plus_plus_real @ K @ A ) )
% 5.17/5.41 => ( ( plus_plus_real @ A2 @ B )
% 5.17/5.41 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add1
% 5.17/5.41 thf(fact_3218_group__cancel_Oadd1,axiom,
% 5.17/5.41 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.17/5.41 ( ( A2
% 5.17/5.41 = ( plus_plus_rat @ K @ A ) )
% 5.17/5.41 => ( ( plus_plus_rat @ A2 @ B )
% 5.17/5.41 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add1
% 5.17/5.41 thf(fact_3219_group__cancel_Oadd1,axiom,
% 5.17/5.41 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.17/5.41 ( ( A2
% 5.17/5.41 = ( plus_plus_nat @ K @ A ) )
% 5.17/5.41 => ( ( plus_plus_nat @ A2 @ B )
% 5.17/5.41 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add1
% 5.17/5.41 thf(fact_3220_group__cancel_Oadd1,axiom,
% 5.17/5.41 ! [A2: int,K: int,A: int,B: int] :
% 5.17/5.41 ( ( A2
% 5.17/5.41 = ( plus_plus_int @ K @ A ) )
% 5.17/5.41 => ( ( plus_plus_int @ A2 @ B )
% 5.17/5.41 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add1
% 5.17/5.41 thf(fact_3221_group__cancel_Oadd2,axiom,
% 5.17/5.41 ! [B4: real,K: real,B: real,A: real] :
% 5.17/5.41 ( ( B4
% 5.17/5.41 = ( plus_plus_real @ K @ B ) )
% 5.17/5.41 => ( ( plus_plus_real @ A @ B4 )
% 5.17/5.41 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add2
% 5.17/5.41 thf(fact_3222_group__cancel_Oadd2,axiom,
% 5.17/5.41 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.17/5.41 ( ( B4
% 5.17/5.41 = ( plus_plus_rat @ K @ B ) )
% 5.17/5.41 => ( ( plus_plus_rat @ A @ B4 )
% 5.17/5.41 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add2
% 5.17/5.41 thf(fact_3223_group__cancel_Oadd2,axiom,
% 5.17/5.41 ! [B4: nat,K: nat,B: nat,A: nat] :
% 5.17/5.41 ( ( B4
% 5.17/5.41 = ( plus_plus_nat @ K @ B ) )
% 5.17/5.41 => ( ( plus_plus_nat @ A @ B4 )
% 5.17/5.41 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add2
% 5.17/5.41 thf(fact_3224_group__cancel_Oadd2,axiom,
% 5.17/5.41 ! [B4: int,K: int,B: int,A: int] :
% 5.17/5.41 ( ( B4
% 5.17/5.41 = ( plus_plus_int @ K @ B ) )
% 5.17/5.41 => ( ( plus_plus_int @ A @ B4 )
% 5.17/5.41 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % group_cancel.add2
% 5.17/5.41 thf(fact_3225_add_Oassoc,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.assoc
% 5.17/5.41 thf(fact_3226_add_Oassoc,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.assoc
% 5.17/5.41 thf(fact_3227_add_Oassoc,axiom,
% 5.17/5.41 ! [A: nat,B: nat,C: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.assoc
% 5.17/5.41 thf(fact_3228_add_Oassoc,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.assoc
% 5.17/5.41 thf(fact_3229_add_Oleft__cancel,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ A @ B )
% 5.17/5.41 = ( plus_plus_real @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_cancel
% 5.17/5.41 thf(fact_3230_add_Oleft__cancel,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ A @ B )
% 5.17/5.41 = ( plus_plus_rat @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_cancel
% 5.17/5.41 thf(fact_3231_add_Oleft__cancel,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ A @ B )
% 5.17/5.41 = ( plus_plus_int @ A @ C ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_cancel
% 5.17/5.41 thf(fact_3232_add_Oright__cancel,axiom,
% 5.17/5.41 ! [B: real,A: real,C: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ B @ A )
% 5.17/5.41 = ( plus_plus_real @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_cancel
% 5.17/5.41 thf(fact_3233_add_Oright__cancel,axiom,
% 5.17/5.41 ! [B: rat,A: rat,C: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ B @ A )
% 5.17/5.41 = ( plus_plus_rat @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_cancel
% 5.17/5.41 thf(fact_3234_add_Oright__cancel,axiom,
% 5.17/5.41 ! [B: int,A: int,C: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ B @ A )
% 5.17/5.41 = ( plus_plus_int @ C @ A ) )
% 5.17/5.41 = ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.right_cancel
% 5.17/5.41 thf(fact_3235_add_Ocommute,axiom,
% 5.17/5.41 ( plus_plus_real
% 5.17/5.41 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.commute
% 5.17/5.41 thf(fact_3236_add_Ocommute,axiom,
% 5.17/5.41 ( plus_plus_rat
% 5.17/5.41 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.commute
% 5.17/5.41 thf(fact_3237_add_Ocommute,axiom,
% 5.17/5.41 ( plus_plus_nat
% 5.17/5.41 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.commute
% 5.17/5.41 thf(fact_3238_add_Ocommute,axiom,
% 5.17/5.41 ( plus_plus_int
% 5.17/5.41 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.commute
% 5.17/5.41 thf(fact_3239_add_Oleft__commute,axiom,
% 5.17/5.41 ! [B: real,A: real,C: real] :
% 5.17/5.41 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.17/5.41 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_commute
% 5.17/5.41 thf(fact_3240_add_Oleft__commute,axiom,
% 5.17/5.41 ! [B: rat,A: rat,C: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.17/5.41 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_commute
% 5.17/5.41 thf(fact_3241_add_Oleft__commute,axiom,
% 5.17/5.41 ! [B: nat,A: nat,C: nat] :
% 5.17/5.41 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.17/5.41 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_commute
% 5.17/5.41 thf(fact_3242_add_Oleft__commute,axiom,
% 5.17/5.41 ! [B: int,A: int,C: int] :
% 5.17/5.41 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.17/5.41 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add.left_commute
% 5.17/5.41 thf(fact_3243_add__left__imp__eq,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ A @ B )
% 5.17/5.41 = ( plus_plus_real @ A @ C ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_imp_eq
% 5.17/5.41 thf(fact_3244_add__left__imp__eq,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ A @ B )
% 5.17/5.41 = ( plus_plus_rat @ A @ C ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_imp_eq
% 5.17/5.41 thf(fact_3245_add__left__imp__eq,axiom,
% 5.17/5.41 ! [A: nat,B: nat,C: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ A @ B )
% 5.17/5.41 = ( plus_plus_nat @ A @ C ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_imp_eq
% 5.17/5.41 thf(fact_3246_add__left__imp__eq,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ A @ B )
% 5.17/5.41 = ( plus_plus_int @ A @ C ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_left_imp_eq
% 5.17/5.41 thf(fact_3247_add__right__imp__eq,axiom,
% 5.17/5.41 ! [B: real,A: real,C: real] :
% 5.17/5.41 ( ( ( plus_plus_real @ B @ A )
% 5.17/5.41 = ( plus_plus_real @ C @ A ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_imp_eq
% 5.17/5.41 thf(fact_3248_add__right__imp__eq,axiom,
% 5.17/5.41 ! [B: rat,A: rat,C: rat] :
% 5.17/5.41 ( ( ( plus_plus_rat @ B @ A )
% 5.17/5.41 = ( plus_plus_rat @ C @ A ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_imp_eq
% 5.17/5.41 thf(fact_3249_add__right__imp__eq,axiom,
% 5.17/5.41 ! [B: nat,A: nat,C: nat] :
% 5.17/5.41 ( ( ( plus_plus_nat @ B @ A )
% 5.17/5.41 = ( plus_plus_nat @ C @ A ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_imp_eq
% 5.17/5.41 thf(fact_3250_add__right__imp__eq,axiom,
% 5.17/5.41 ! [B: int,A: int,C: int] :
% 5.17/5.41 ( ( ( plus_plus_int @ B @ A )
% 5.17/5.41 = ( plus_plus_int @ C @ A ) )
% 5.17/5.41 => ( B = C ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_right_imp_eq
% 5.17/5.41 thf(fact_3251_is__num__normalize_I1_J,axiom,
% 5.17/5.41 ! [A: real,B: real,C: real] :
% 5.17/5.41 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % is_num_normalize(1)
% 5.17/5.41 thf(fact_3252_is__num__normalize_I1_J,axiom,
% 5.17/5.41 ! [A: rat,B: rat,C: rat] :
% 5.17/5.41 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % is_num_normalize(1)
% 5.17/5.41 thf(fact_3253_is__num__normalize_I1_J,axiom,
% 5.17/5.41 ! [A: int,B: int,C: int] :
% 5.17/5.41 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.41 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % is_num_normalize(1)
% 5.17/5.41 thf(fact_3254_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.17/5.41 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.41 ( ( ( ord_less_eq_rat @ I @ J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(3)
% 5.17/5.41 thf(fact_3255_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.17/5.41 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.41 ( ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(3)
% 5.17/5.41 thf(fact_3256_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.17/5.41 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.41 ( ( ( ord_less_eq_int @ I @ J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(3)
% 5.17/5.41 thf(fact_3257_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.17/5.41 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.41 ( ( ( ord_less_eq_real @ I @ J )
% 5.17/5.41 & ( K = L ) )
% 5.17/5.41 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(3)
% 5.17/5.41 thf(fact_3258_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.17/5.41 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.41 ( ( ( I = J )
% 5.17/5.41 & ( ord_less_eq_rat @ K @ L ) )
% 5.17/5.41 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(2)
% 5.17/5.41 thf(fact_3259_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.17/5.41 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.41 ( ( ( I = J )
% 5.17/5.41 & ( ord_less_eq_nat @ K @ L ) )
% 5.17/5.41 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.41
% 5.17/5.41 % add_mono_thms_linordered_semiring(2)
% 5.17/5.41 thf(fact_3260_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.17/5.41 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( I = J )
% 5.17/5.42 & ( ord_less_eq_int @ K @ L ) )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_semiring(2)
% 5.17/5.42 thf(fact_3261_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( I = J )
% 5.17/5.42 & ( ord_less_eq_real @ K @ L ) )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_semiring(2)
% 5.17/5.42 thf(fact_3262_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.17/5.42 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.42 ( ( ( ord_less_eq_rat @ I @ J )
% 5.17/5.42 & ( ord_less_eq_rat @ K @ L ) )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_semiring(1)
% 5.17/5.42 thf(fact_3263_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 & ( ord_less_eq_nat @ K @ L ) )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_semiring(1)
% 5.17/5.42 thf(fact_3264_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.17/5.42 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( ord_less_eq_int @ I @ J )
% 5.17/5.42 & ( ord_less_eq_int @ K @ L ) )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_semiring(1)
% 5.17/5.42 thf(fact_3265_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( ord_less_eq_real @ I @ J )
% 5.17/5.42 & ( ord_less_eq_real @ K @ L ) )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_semiring(1)
% 5.17/5.42 thf(fact_3266_add__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_rat @ C @ D )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono
% 5.17/5.42 thf(fact_3267_add__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_nat @ C @ D )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono
% 5.17/5.42 thf(fact_3268_add__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_int @ C @ D )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono
% 5.17/5.42 thf(fact_3269_add__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_real @ C @ D )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono
% 5.17/5.42 thf(fact_3270_add__left__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_left_mono
% 5.17/5.42 thf(fact_3271_add__left__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_left_mono
% 5.17/5.42 thf(fact_3272_add__left__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_left_mono
% 5.17/5.42 thf(fact_3273_add__left__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_left_mono
% 5.17/5.42 thf(fact_3274_less__eqE,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ~ ! [C3: nat] :
% 5.17/5.42 ( B
% 5.17/5.42 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_eqE
% 5.17/5.42 thf(fact_3275_add__right__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_right_mono
% 5.17/5.42 thf(fact_3276_add__right__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_right_mono
% 5.17/5.42 thf(fact_3277_add__right__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_right_mono
% 5.17/5.42 thf(fact_3278_add__right__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_right_mono
% 5.17/5.42 thf(fact_3279_le__iff__add,axiom,
% 5.17/5.42 ( ord_less_eq_nat
% 5.17/5.42 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.42 ? [C5: nat] :
% 5.17/5.42 ( B2
% 5.17/5.42 = ( plus_plus_nat @ A3 @ C5 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_iff_add
% 5.17/5.42 thf(fact_3280_add__le__imp__le__left,axiom,
% 5.17/5.42 ! [C: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.17/5.42 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_left
% 5.17/5.42 thf(fact_3281_add__le__imp__le__left,axiom,
% 5.17/5.42 ! [C: nat,A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.17/5.42 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_left
% 5.17/5.42 thf(fact_3282_add__le__imp__le__left,axiom,
% 5.17/5.42 ! [C: int,A: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.17/5.42 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_left
% 5.17/5.42 thf(fact_3283_add__le__imp__le__left,axiom,
% 5.17/5.42 ! [C: real,A: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.17/5.42 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_left
% 5.17/5.42 thf(fact_3284_add__le__imp__le__right,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_right
% 5.17/5.42 thf(fact_3285_add__le__imp__le__right,axiom,
% 5.17/5.42 ! [A: nat,C: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.42 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_right
% 5.17/5.42 thf(fact_3286_add__le__imp__le__right,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_right
% 5.17/5.42 thf(fact_3287_add__le__imp__le__right,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_right
% 5.17/5.42 thf(fact_3288_verit__sum__simplify,axiom,
% 5.17/5.42 ! [A: complex] :
% 5.17/5.42 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % verit_sum_simplify
% 5.17/5.42 thf(fact_3289_verit__sum__simplify,axiom,
% 5.17/5.42 ! [A: real] :
% 5.17/5.42 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % verit_sum_simplify
% 5.17/5.42 thf(fact_3290_verit__sum__simplify,axiom,
% 5.17/5.42 ! [A: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % verit_sum_simplify
% 5.17/5.42 thf(fact_3291_verit__sum__simplify,axiom,
% 5.17/5.42 ! [A: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % verit_sum_simplify
% 5.17/5.42 thf(fact_3292_verit__sum__simplify,axiom,
% 5.17/5.42 ! [A: int] :
% 5.17/5.42 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % verit_sum_simplify
% 5.17/5.42 thf(fact_3293_add_Ogroup__left__neutral,axiom,
% 5.17/5.42 ! [A: complex] :
% 5.17/5.42 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.group_left_neutral
% 5.17/5.42 thf(fact_3294_add_Ogroup__left__neutral,axiom,
% 5.17/5.42 ! [A: real] :
% 5.17/5.42 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.group_left_neutral
% 5.17/5.42 thf(fact_3295_add_Ogroup__left__neutral,axiom,
% 5.17/5.42 ! [A: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.group_left_neutral
% 5.17/5.42 thf(fact_3296_add_Ogroup__left__neutral,axiom,
% 5.17/5.42 ! [A: int] :
% 5.17/5.42 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.group_left_neutral
% 5.17/5.42 thf(fact_3297_add_Ocomm__neutral,axiom,
% 5.17/5.42 ! [A: complex] :
% 5.17/5.42 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.comm_neutral
% 5.17/5.42 thf(fact_3298_add_Ocomm__neutral,axiom,
% 5.17/5.42 ! [A: real] :
% 5.17/5.42 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.comm_neutral
% 5.17/5.42 thf(fact_3299_add_Ocomm__neutral,axiom,
% 5.17/5.42 ! [A: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.comm_neutral
% 5.17/5.42 thf(fact_3300_add_Ocomm__neutral,axiom,
% 5.17/5.42 ! [A: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.comm_neutral
% 5.17/5.42 thf(fact_3301_add_Ocomm__neutral,axiom,
% 5.17/5.42 ! [A: int] :
% 5.17/5.42 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % add.comm_neutral
% 5.17/5.42 thf(fact_3302_comm__monoid__add__class_Oadd__0,axiom,
% 5.17/5.42 ! [A: complex] :
% 5.17/5.42 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % comm_monoid_add_class.add_0
% 5.17/5.42 thf(fact_3303_comm__monoid__add__class_Oadd__0,axiom,
% 5.17/5.42 ! [A: real] :
% 5.17/5.42 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % comm_monoid_add_class.add_0
% 5.17/5.42 thf(fact_3304_comm__monoid__add__class_Oadd__0,axiom,
% 5.17/5.42 ! [A: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % comm_monoid_add_class.add_0
% 5.17/5.42 thf(fact_3305_comm__monoid__add__class_Oadd__0,axiom,
% 5.17/5.42 ! [A: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % comm_monoid_add_class.add_0
% 5.17/5.42 thf(fact_3306_comm__monoid__add__class_Oadd__0,axiom,
% 5.17/5.42 ! [A: int] :
% 5.17/5.42 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.17/5.42 = A ) ).
% 5.17/5.42
% 5.17/5.42 % comm_monoid_add_class.add_0
% 5.17/5.42 thf(fact_3307_add__mono__thms__linordered__field_I5_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( ord_less_real @ I @ J )
% 5.17/5.42 & ( ord_less_real @ K @ L ) )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(5)
% 5.17/5.42 thf(fact_3308_add__mono__thms__linordered__field_I5_J,axiom,
% 5.17/5.42 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.42 ( ( ( ord_less_rat @ I @ J )
% 5.17/5.42 & ( ord_less_rat @ K @ L ) )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(5)
% 5.17/5.42 thf(fact_3309_add__mono__thms__linordered__field_I5_J,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ( ord_less_nat @ I @ J )
% 5.17/5.42 & ( ord_less_nat @ K @ L ) )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(5)
% 5.17/5.42 thf(fact_3310_add__mono__thms__linordered__field_I5_J,axiom,
% 5.17/5.42 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( ord_less_int @ I @ J )
% 5.17/5.42 & ( ord_less_int @ K @ L ) )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(5)
% 5.17/5.42 thf(fact_3311_add__mono__thms__linordered__field_I2_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( I = J )
% 5.17/5.42 & ( ord_less_real @ K @ L ) )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(2)
% 5.17/5.42 thf(fact_3312_add__mono__thms__linordered__field_I2_J,axiom,
% 5.17/5.42 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.42 ( ( ( I = J )
% 5.17/5.42 & ( ord_less_rat @ K @ L ) )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(2)
% 5.17/5.42 thf(fact_3313_add__mono__thms__linordered__field_I2_J,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ( I = J )
% 5.17/5.42 & ( ord_less_nat @ K @ L ) )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(2)
% 5.17/5.42 thf(fact_3314_add__mono__thms__linordered__field_I2_J,axiom,
% 5.17/5.42 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( I = J )
% 5.17/5.42 & ( ord_less_int @ K @ L ) )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(2)
% 5.17/5.42 thf(fact_3315_add__mono__thms__linordered__field_I1_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( ord_less_real @ I @ J )
% 5.17/5.42 & ( K = L ) )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(1)
% 5.17/5.42 thf(fact_3316_add__mono__thms__linordered__field_I1_J,axiom,
% 5.17/5.42 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.42 ( ( ( ord_less_rat @ I @ J )
% 5.17/5.42 & ( K = L ) )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(1)
% 5.17/5.42 thf(fact_3317_add__mono__thms__linordered__field_I1_J,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ( ord_less_nat @ I @ J )
% 5.17/5.42 & ( K = L ) )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(1)
% 5.17/5.42 thf(fact_3318_add__mono__thms__linordered__field_I1_J,axiom,
% 5.17/5.42 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( ord_less_int @ I @ J )
% 5.17/5.42 & ( K = L ) )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(1)
% 5.17/5.42 thf(fact_3319_add__strict__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ B )
% 5.17/5.42 => ( ( ord_less_real @ C @ D )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_mono
% 5.17/5.42 thf(fact_3320_add__strict__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ B )
% 5.17/5.42 => ( ( ord_less_rat @ C @ D )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_mono
% 5.17/5.42 thf(fact_3321_add__strict__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ B )
% 5.17/5.42 => ( ( ord_less_nat @ C @ D )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_mono
% 5.17/5.42 thf(fact_3322_add__strict__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ B )
% 5.17/5.42 => ( ( ord_less_int @ C @ D )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_mono
% 5.17/5.42 thf(fact_3323_add__strict__left__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ B )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_left_mono
% 5.17/5.42 thf(fact_3324_add__strict__left__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ B )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_left_mono
% 5.17/5.42 thf(fact_3325_add__strict__left__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ B )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_left_mono
% 5.17/5.42 thf(fact_3326_add__strict__left__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ B )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_left_mono
% 5.17/5.42 thf(fact_3327_add__strict__right__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ B )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_right_mono
% 5.17/5.42 thf(fact_3328_add__strict__right__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ B )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_right_mono
% 5.17/5.42 thf(fact_3329_add__strict__right__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ B )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_right_mono
% 5.17/5.42 thf(fact_3330_add__strict__right__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ B )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_right_mono
% 5.17/5.42 thf(fact_3331_add__less__imp__less__left,axiom,
% 5.17/5.42 ! [C: real,A: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.17/5.42 => ( ord_less_real @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_left
% 5.17/5.42 thf(fact_3332_add__less__imp__less__left,axiom,
% 5.17/5.42 ! [C: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.17/5.42 => ( ord_less_rat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_left
% 5.17/5.42 thf(fact_3333_add__less__imp__less__left,axiom,
% 5.17/5.42 ! [C: nat,A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.17/5.42 => ( ord_less_nat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_left
% 5.17/5.42 thf(fact_3334_add__less__imp__less__left,axiom,
% 5.17/5.42 ! [C: int,A: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.17/5.42 => ( ord_less_int @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_left
% 5.17/5.42 thf(fact_3335_add__less__imp__less__right,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 => ( ord_less_real @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_right
% 5.17/5.42 thf(fact_3336_add__less__imp__less__right,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 => ( ord_less_rat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_right
% 5.17/5.42 thf(fact_3337_add__less__imp__less__right,axiom,
% 5.17/5.42 ! [A: nat,C: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.42 => ( ord_less_nat @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_right
% 5.17/5.42 thf(fact_3338_add__less__imp__less__right,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 => ( ord_less_int @ A @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_imp_less_right
% 5.17/5.42 thf(fact_3339_ring__class_Oring__distribs_I2_J,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ring_class.ring_distribs(2)
% 5.17/5.42 thf(fact_3340_ring__class_Oring__distribs_I2_J,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ring_class.ring_distribs(2)
% 5.17/5.42 thf(fact_3341_ring__class_Oring__distribs_I2_J,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ring_class.ring_distribs(2)
% 5.17/5.42 thf(fact_3342_ring__class_Oring__distribs_I1_J,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ring_class.ring_distribs(1)
% 5.17/5.42 thf(fact_3343_ring__class_Oring__distribs_I1_J,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ring_class.ring_distribs(1)
% 5.17/5.42 thf(fact_3344_ring__class_Oring__distribs_I1_J,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ring_class.ring_distribs(1)
% 5.17/5.42 thf(fact_3345_comm__semiring__class_Odistrib,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % comm_semiring_class.distrib
% 5.17/5.42 thf(fact_3346_comm__semiring__class_Odistrib,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % comm_semiring_class.distrib
% 5.17/5.42 thf(fact_3347_comm__semiring__class_Odistrib,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % comm_semiring_class.distrib
% 5.17/5.42 thf(fact_3348_comm__semiring__class_Odistrib,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % comm_semiring_class.distrib
% 5.17/5.42 thf(fact_3349_distrib__left,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_left
% 5.17/5.42 thf(fact_3350_distrib__left,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_left
% 5.17/5.42 thf(fact_3351_distrib__left,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_left
% 5.17/5.42 thf(fact_3352_distrib__left,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_left
% 5.17/5.42 thf(fact_3353_distrib__right,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_right
% 5.17/5.42 thf(fact_3354_distrib__right,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_right
% 5.17/5.42 thf(fact_3355_distrib__right,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_right
% 5.17/5.42 thf(fact_3356_distrib__right,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % distrib_right
% 5.17/5.42 thf(fact_3357_combine__common__factor,axiom,
% 5.17/5.42 ! [A: real,E2: real,B: real,C: real] :
% 5.17/5.42 ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % combine_common_factor
% 5.17/5.42 thf(fact_3358_combine__common__factor,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % combine_common_factor
% 5.17/5.42 thf(fact_3359_combine__common__factor,axiom,
% 5.17/5.42 ! [A: nat,E2: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % combine_common_factor
% 5.17/5.42 thf(fact_3360_combine__common__factor,axiom,
% 5.17/5.42 ! [A: int,E2: int,B: int,C: int] :
% 5.17/5.42 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % combine_common_factor
% 5.17/5.42 thf(fact_3361_diff__diff__eq,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq
% 5.17/5.42 thf(fact_3362_diff__diff__eq,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq
% 5.17/5.42 thf(fact_3363_diff__diff__eq,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq
% 5.17/5.42 thf(fact_3364_diff__diff__eq,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq
% 5.17/5.42 thf(fact_3365_add__implies__diff,axiom,
% 5.17/5.42 ! [C: real,B: real,A: real] :
% 5.17/5.42 ( ( ( plus_plus_real @ C @ B )
% 5.17/5.42 = A )
% 5.17/5.42 => ( C
% 5.17/5.42 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_implies_diff
% 5.17/5.42 thf(fact_3366_add__implies__diff,axiom,
% 5.17/5.42 ! [C: rat,B: rat,A: rat] :
% 5.17/5.42 ( ( ( plus_plus_rat @ C @ B )
% 5.17/5.42 = A )
% 5.17/5.42 => ( C
% 5.17/5.42 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_implies_diff
% 5.17/5.42 thf(fact_3367_add__implies__diff,axiom,
% 5.17/5.42 ! [C: nat,B: nat,A: nat] :
% 5.17/5.42 ( ( ( plus_plus_nat @ C @ B )
% 5.17/5.42 = A )
% 5.17/5.42 => ( C
% 5.17/5.42 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_implies_diff
% 5.17/5.42 thf(fact_3368_add__implies__diff,axiom,
% 5.17/5.42 ! [C: int,B: int,A: int] :
% 5.17/5.42 ( ( ( plus_plus_int @ C @ B )
% 5.17/5.42 = A )
% 5.17/5.42 => ( C
% 5.17/5.42 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_implies_diff
% 5.17/5.42 thf(fact_3369_diff__add__eq__diff__diff__swap,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_eq_diff_diff_swap
% 5.17/5.42 thf(fact_3370_diff__add__eq__diff__diff__swap,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_eq_diff_diff_swap
% 5.17/5.42 thf(fact_3371_diff__add__eq__diff__diff__swap,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_eq_diff_diff_swap
% 5.17/5.42 thf(fact_3372_diff__add__eq,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_eq
% 5.17/5.42 thf(fact_3373_diff__add__eq,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_eq
% 5.17/5.42 thf(fact_3374_diff__add__eq,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.42 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_eq
% 5.17/5.42 thf(fact_3375_diff__diff__eq2,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.17/5.42 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq2
% 5.17/5.42 thf(fact_3376_diff__diff__eq2,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.17/5.42 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq2
% 5.17/5.42 thf(fact_3377_diff__diff__eq2,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.17/5.42 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_diff_eq2
% 5.17/5.42 thf(fact_3378_add__diff__eq,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.17/5.42 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_eq
% 5.17/5.42 thf(fact_3379_add__diff__eq,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.17/5.42 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_eq
% 5.17/5.42 thf(fact_3380_add__diff__eq,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.17/5.42 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_eq
% 5.17/5.42 thf(fact_3381_eq__diff__eq,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( A
% 5.17/5.42 = ( minus_minus_real @ C @ B ) )
% 5.17/5.42 = ( ( plus_plus_real @ A @ B )
% 5.17/5.42 = C ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_diff_eq
% 5.17/5.42 thf(fact_3382_eq__diff__eq,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( A
% 5.17/5.42 = ( minus_minus_rat @ C @ B ) )
% 5.17/5.42 = ( ( plus_plus_rat @ A @ B )
% 5.17/5.42 = C ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_diff_eq
% 5.17/5.42 thf(fact_3383_eq__diff__eq,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( A
% 5.17/5.42 = ( minus_minus_int @ C @ B ) )
% 5.17/5.42 = ( ( plus_plus_int @ A @ B )
% 5.17/5.42 = C ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_diff_eq
% 5.17/5.42 thf(fact_3384_diff__eq__eq,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ( minus_minus_real @ A @ B )
% 5.17/5.42 = C )
% 5.17/5.42 = ( A
% 5.17/5.42 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_eq_eq
% 5.17/5.42 thf(fact_3385_diff__eq__eq,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ( minus_minus_rat @ A @ B )
% 5.17/5.42 = C )
% 5.17/5.42 = ( A
% 5.17/5.42 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_eq_eq
% 5.17/5.42 thf(fact_3386_diff__eq__eq,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ( minus_minus_int @ A @ B )
% 5.17/5.42 = C )
% 5.17/5.42 = ( A
% 5.17/5.42 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_eq_eq
% 5.17/5.42 thf(fact_3387_group__cancel_Osub1,axiom,
% 5.17/5.42 ! [A2: real,K: real,A: real,B: real] :
% 5.17/5.42 ( ( A2
% 5.17/5.42 = ( plus_plus_real @ K @ A ) )
% 5.17/5.42 => ( ( minus_minus_real @ A2 @ B )
% 5.17/5.42 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % group_cancel.sub1
% 5.17/5.42 thf(fact_3388_group__cancel_Osub1,axiom,
% 5.17/5.42 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( A2
% 5.17/5.42 = ( plus_plus_rat @ K @ A ) )
% 5.17/5.42 => ( ( minus_minus_rat @ A2 @ B )
% 5.17/5.42 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % group_cancel.sub1
% 5.17/5.42 thf(fact_3389_group__cancel_Osub1,axiom,
% 5.17/5.42 ! [A2: int,K: int,A: int,B: int] :
% 5.17/5.42 ( ( A2
% 5.17/5.42 = ( plus_plus_int @ K @ A ) )
% 5.17/5.42 => ( ( minus_minus_int @ A2 @ B )
% 5.17/5.42 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % group_cancel.sub1
% 5.17/5.42 thf(fact_3390_add__diff__add,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.17/5.42 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_add
% 5.17/5.42 thf(fact_3391_add__diff__add,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.17/5.42 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_add
% 5.17/5.42 thf(fact_3392_add__diff__add,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.17/5.42 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_add
% 5.17/5.42 thf(fact_3393_add__divide__distrib,axiom,
% 5.17/5.42 ! [A: complex,B: complex,C: complex] :
% 5.17/5.42 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_distrib
% 5.17/5.42 thf(fact_3394_add__divide__distrib,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_distrib
% 5.17/5.42 thf(fact_3395_add__divide__distrib,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_distrib
% 5.17/5.42 thf(fact_3396_dvd__add__right__iff,axiom,
% 5.17/5.42 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.42 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_right_iff
% 5.17/5.42 thf(fact_3397_dvd__add__right__iff,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( dvd_dvd_real @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_right_iff
% 5.17/5.42 thf(fact_3398_dvd__add__right__iff,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( dvd_dvd_rat @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_right_iff
% 5.17/5.42 thf(fact_3399_dvd__add__right__iff,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_right_iff
% 5.17/5.42 thf(fact_3400_dvd__add__right__iff,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_right_iff
% 5.17/5.42 thf(fact_3401_dvd__add__left__iff,axiom,
% 5.17/5.42 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.42 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.17/5.42 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_left_iff
% 5.17/5.42 thf(fact_3402_dvd__add__left__iff,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( dvd_dvd_real @ A @ C )
% 5.17/5.42 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_left_iff
% 5.17/5.42 thf(fact_3403_dvd__add__left__iff,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( dvd_dvd_rat @ A @ C )
% 5.17/5.42 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_left_iff
% 5.17/5.42 thf(fact_3404_dvd__add__left__iff,axiom,
% 5.17/5.42 ! [A: nat,C: nat,B: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.42 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_left_iff
% 5.17/5.42 thf(fact_3405_dvd__add__left__iff,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( dvd_dvd_int @ A @ C )
% 5.17/5.42 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.17/5.42 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add_left_iff
% 5.17/5.42 thf(fact_3406_dvd__add,axiom,
% 5.17/5.42 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.42 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.17/5.42 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add
% 5.17/5.42 thf(fact_3407_dvd__add,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( dvd_dvd_real @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_real @ A @ C )
% 5.17/5.42 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add
% 5.17/5.42 thf(fact_3408_dvd__add,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( dvd_dvd_rat @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_rat @ A @ C )
% 5.17/5.42 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add
% 5.17/5.42 thf(fact_3409_dvd__add,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.42 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add
% 5.17/5.42 thf(fact_3410_dvd__add,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.42 => ( ( dvd_dvd_int @ A @ C )
% 5.17/5.42 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % dvd_add
% 5.17/5.42 thf(fact_3411_nat__arith_Osuc1,axiom,
% 5.17/5.42 ! [A2: nat,K: nat,A: nat] :
% 5.17/5.42 ( ( A2
% 5.17/5.42 = ( plus_plus_nat @ K @ A ) )
% 5.17/5.42 => ( ( suc @ A2 )
% 5.17/5.42 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % nat_arith.suc1
% 5.17/5.42 thf(fact_3412_add__Suc,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.17/5.42 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_Suc
% 5.17/5.42 thf(fact_3413_add__Suc__shift,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.17/5.42 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_Suc_shift
% 5.17/5.42 thf(fact_3414_Euclid__induct,axiom,
% 5.17/5.42 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.17/5.42 ( ! [A4: nat,B3: nat] :
% 5.17/5.42 ( ( P @ A4 @ B3 )
% 5.17/5.42 = ( P @ B3 @ A4 ) )
% 5.17/5.42 => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 5.17/5.42 => ( ! [A4: nat,B3: nat] :
% 5.17/5.42 ( ( P @ A4 @ B3 )
% 5.17/5.42 => ( P @ A4 @ ( plus_plus_nat @ A4 @ B3 ) ) )
% 5.17/5.42 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % Euclid_induct
% 5.17/5.42 thf(fact_3415_plus__nat_Oadd__0,axiom,
% 5.17/5.42 ! [N: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.17/5.42 = N ) ).
% 5.17/5.42
% 5.17/5.42 % plus_nat.add_0
% 5.17/5.42 thf(fact_3416_add__eq__self__zero,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( ( plus_plus_nat @ M @ N )
% 5.17/5.42 = M )
% 5.17/5.42 => ( N = zero_zero_nat ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_eq_self_zero
% 5.17/5.42 thf(fact_3417_add__lessD1,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat] :
% 5.17/5.42 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.17/5.42 => ( ord_less_nat @ I @ K ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_lessD1
% 5.17/5.42 thf(fact_3418_add__less__mono,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ord_less_nat @ I @ J )
% 5.17/5.42 => ( ( ord_less_nat @ K @ L )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_mono
% 5.17/5.42 thf(fact_3419_not__add__less1,axiom,
% 5.17/5.42 ! [I: nat,J: nat] :
% 5.17/5.42 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.17/5.42
% 5.17/5.42 % not_add_less1
% 5.17/5.42 thf(fact_3420_not__add__less2,axiom,
% 5.17/5.42 ! [J: nat,I: nat] :
% 5.17/5.42 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.17/5.42
% 5.17/5.42 % not_add_less2
% 5.17/5.42 thf(fact_3421_add__less__mono1,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat] :
% 5.17/5.42 ( ( ord_less_nat @ I @ J )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_mono1
% 5.17/5.42 thf(fact_3422_trans__less__add1,axiom,
% 5.17/5.42 ! [I: nat,J: nat,M: nat] :
% 5.17/5.42 ( ( ord_less_nat @ I @ J )
% 5.17/5.42 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % trans_less_add1
% 5.17/5.42 thf(fact_3423_trans__less__add2,axiom,
% 5.17/5.42 ! [I: nat,J: nat,M: nat] :
% 5.17/5.42 ( ( ord_less_nat @ I @ J )
% 5.17/5.42 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % trans_less_add2
% 5.17/5.42 thf(fact_3424_less__add__eq__less,axiom,
% 5.17/5.42 ! [K: nat,L: nat,M: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_nat @ K @ L )
% 5.17/5.42 => ( ( ( plus_plus_nat @ M @ L )
% 5.17/5.42 = ( plus_plus_nat @ K @ N ) )
% 5.17/5.42 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_eq_less
% 5.17/5.42 thf(fact_3425_nat__le__iff__add,axiom,
% 5.17/5.42 ( ord_less_eq_nat
% 5.17/5.42 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.42 ? [K3: nat] :
% 5.17/5.42 ( N4
% 5.17/5.42 = ( plus_plus_nat @ M5 @ K3 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % nat_le_iff_add
% 5.17/5.42 thf(fact_3426_trans__le__add2,axiom,
% 5.17/5.42 ! [I: nat,J: nat,M: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % trans_le_add2
% 5.17/5.42 thf(fact_3427_trans__le__add1,axiom,
% 5.17/5.42 ! [I: nat,J: nat,M: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % trans_le_add1
% 5.17/5.42 thf(fact_3428_add__le__mono1,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_mono1
% 5.17/5.42 thf(fact_3429_add__le__mono,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 => ( ( ord_less_eq_nat @ K @ L )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_mono
% 5.17/5.42 thf(fact_3430_le__Suc__ex,axiom,
% 5.17/5.42 ! [K: nat,L: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ K @ L )
% 5.17/5.42 => ? [N2: nat] :
% 5.17/5.42 ( L
% 5.17/5.42 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_Suc_ex
% 5.17/5.42 thf(fact_3431_add__leD2,axiom,
% 5.17/5.42 ! [M: nat,K: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.17/5.42 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_leD2
% 5.17/5.42 thf(fact_3432_add__leD1,axiom,
% 5.17/5.42 ! [M: nat,K: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.17/5.42 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_leD1
% 5.17/5.42 thf(fact_3433_le__add2,axiom,
% 5.17/5.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_add2
% 5.17/5.42 thf(fact_3434_le__add1,axiom,
% 5.17/5.42 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_add1
% 5.17/5.42 thf(fact_3435_add__leE,axiom,
% 5.17/5.42 ! [M: nat,K: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.17/5.42 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.42 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_leE
% 5.17/5.42 thf(fact_3436_Nat_Odiff__cancel,axiom,
% 5.17/5.42 ! [K: nat,M: nat,N: nat] :
% 5.17/5.42 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.17/5.42 = ( minus_minus_nat @ M @ N ) ) ).
% 5.17/5.42
% 5.17/5.42 % Nat.diff_cancel
% 5.17/5.42 thf(fact_3437_diff__cancel2,axiom,
% 5.17/5.42 ! [M: nat,K: nat,N: nat] :
% 5.17/5.42 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.17/5.42 = ( minus_minus_nat @ M @ N ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_cancel2
% 5.17/5.42 thf(fact_3438_diff__add__inverse,axiom,
% 5.17/5.42 ! [N: nat,M: nat] :
% 5.17/5.42 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.17/5.42 = M ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_inverse
% 5.17/5.42 thf(fact_3439_diff__add__inverse2,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.17/5.42 = M ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_inverse2
% 5.17/5.42 thf(fact_3440_left__add__mult__distrib,axiom,
% 5.17/5.42 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.17/5.42 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.17/5.42
% 5.17/5.42 % left_add_mult_distrib
% 5.17/5.42 thf(fact_3441_add__mult__distrib2,axiom,
% 5.17/5.42 ! [K: nat,M: nat,N: nat] :
% 5.17/5.42 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mult_distrib2
% 5.17/5.42 thf(fact_3442_add__mult__distrib,axiom,
% 5.17/5.42 ! [M: nat,N: nat,K: nat] :
% 5.17/5.42 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mult_distrib
% 5.17/5.42 thf(fact_3443_add__nonpos__eq__0__iff,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.17/5.42 => ( ( ( plus_plus_rat @ X @ Y4 )
% 5.17/5.42 = zero_zero_rat )
% 5.17/5.42 = ( ( X = zero_zero_rat )
% 5.17/5.42 & ( Y4 = zero_zero_rat ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_eq_0_iff
% 5.17/5.42 thf(fact_3444_add__nonpos__eq__0__iff,axiom,
% 5.17/5.42 ! [X: nat,Y4: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_eq_nat @ Y4 @ zero_zero_nat )
% 5.17/5.42 => ( ( ( plus_plus_nat @ X @ Y4 )
% 5.17/5.42 = zero_zero_nat )
% 5.17/5.42 = ( ( X = zero_zero_nat )
% 5.17/5.42 & ( Y4 = zero_zero_nat ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_eq_0_iff
% 5.17/5.42 thf(fact_3445_add__nonpos__eq__0__iff,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_eq_int @ Y4 @ zero_zero_int )
% 5.17/5.42 => ( ( ( plus_plus_int @ X @ Y4 )
% 5.17/5.42 = zero_zero_int )
% 5.17/5.42 = ( ( X = zero_zero_int )
% 5.17/5.42 & ( Y4 = zero_zero_int ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_eq_0_iff
% 5.17/5.42 thf(fact_3446_add__nonpos__eq__0__iff,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.17/5.42 => ( ( ( plus_plus_real @ X @ Y4 )
% 5.17/5.42 = zero_zero_real )
% 5.17/5.42 = ( ( X = zero_zero_real )
% 5.17/5.42 & ( Y4 = zero_zero_real ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_eq_0_iff
% 5.17/5.42 thf(fact_3447_add__nonneg__eq__0__iff,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.42 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.42 => ( ( ( plus_plus_rat @ X @ Y4 )
% 5.17/5.42 = zero_zero_rat )
% 5.17/5.42 = ( ( X = zero_zero_rat )
% 5.17/5.42 & ( Y4 = zero_zero_rat ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_eq_0_iff
% 5.17/5.42 thf(fact_3448_add__nonneg__eq__0__iff,axiom,
% 5.17/5.42 ! [X: nat,Y4: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.17/5.42 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.17/5.42 => ( ( ( plus_plus_nat @ X @ Y4 )
% 5.17/5.42 = zero_zero_nat )
% 5.17/5.42 = ( ( X = zero_zero_nat )
% 5.17/5.42 & ( Y4 = zero_zero_nat ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_eq_0_iff
% 5.17/5.42 thf(fact_3449_add__nonneg__eq__0__iff,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.42 => ( ( ( plus_plus_int @ X @ Y4 )
% 5.17/5.42 = zero_zero_int )
% 5.17/5.42 = ( ( X = zero_zero_int )
% 5.17/5.42 & ( Y4 = zero_zero_int ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_eq_0_iff
% 5.17/5.42 thf(fact_3450_add__nonneg__eq__0__iff,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.42 => ( ( ( plus_plus_real @ X @ Y4 )
% 5.17/5.42 = zero_zero_real )
% 5.17/5.42 = ( ( X = zero_zero_real )
% 5.17/5.42 & ( Y4 = zero_zero_real ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_eq_0_iff
% 5.17/5.42 thf(fact_3451_add__nonpos__nonpos,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_nonpos
% 5.17/5.42 thf(fact_3452_add__nonpos__nonpos,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_nonpos
% 5.17/5.42 thf(fact_3453_add__nonpos__nonpos,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_nonpos
% 5.17/5.42 thf(fact_3454_add__nonpos__nonpos,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_nonpos
% 5.17/5.42 thf(fact_3455_add__nonneg__nonneg,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.42 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_nonneg
% 5.17/5.42 thf(fact_3456_add__nonneg__nonneg,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.42 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_nonneg
% 5.17/5.42 thf(fact_3457_add__nonneg__nonneg,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.42 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_nonneg
% 5.17/5.42 thf(fact_3458_add__nonneg__nonneg,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.42 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_nonneg
% 5.17/5.42 thf(fact_3459_add__increasing2,axiom,
% 5.17/5.42 ! [C: rat,B: rat,A: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.17/5.42 => ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.42 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing2
% 5.17/5.42 thf(fact_3460_add__increasing2,axiom,
% 5.17/5.42 ! [C: nat,B: nat,A: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.42 => ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.42 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing2
% 5.17/5.42 thf(fact_3461_add__increasing2,axiom,
% 5.17/5.42 ! [C: int,B: int,A: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.42 => ( ( ord_less_eq_int @ B @ A )
% 5.17/5.42 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing2
% 5.17/5.42 thf(fact_3462_add__increasing2,axiom,
% 5.17/5.42 ! [C: real,B: real,A: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.42 => ( ( ord_less_eq_real @ B @ A )
% 5.17/5.42 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing2
% 5.17/5.42 thf(fact_3463_add__decreasing2,axiom,
% 5.17/5.42 ! [C: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing2
% 5.17/5.42 thf(fact_3464_add__decreasing2,axiom,
% 5.17/5.42 ! [C: nat,A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing2
% 5.17/5.42 thf(fact_3465_add__decreasing2,axiom,
% 5.17/5.42 ! [C: int,A: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_eq_int @ A @ B )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing2
% 5.17/5.42 thf(fact_3466_add__decreasing2,axiom,
% 5.17/5.42 ! [C: real,A: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing2
% 5.17/5.42 thf(fact_3467_add__increasing,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.42 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing
% 5.17/5.42 thf(fact_3468_add__increasing,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.42 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing
% 5.17/5.42 thf(fact_3469_add__increasing,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.42 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing
% 5.17/5.42 thf(fact_3470_add__increasing,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.42 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_increasing
% 5.17/5.42 thf(fact_3471_add__decreasing,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_eq_rat @ C @ B )
% 5.17/5.42 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing
% 5.17/5.42 thf(fact_3472_add__decreasing,axiom,
% 5.17/5.42 ! [A: nat,C: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_eq_nat @ C @ B )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing
% 5.17/5.42 thf(fact_3473_add__decreasing,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_eq_int @ C @ B )
% 5.17/5.42 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing
% 5.17/5.42 thf(fact_3474_add__decreasing,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_eq_real @ C @ B )
% 5.17/5.42 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_decreasing
% 5.17/5.42 thf(fact_3475_add__mono__thms__linordered__field_I4_J,axiom,
% 5.17/5.42 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.42 ( ( ( ord_less_eq_rat @ I @ J )
% 5.17/5.42 & ( ord_less_rat @ K @ L ) )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(4)
% 5.17/5.42 thf(fact_3476_add__mono__thms__linordered__field_I4_J,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 & ( ord_less_nat @ K @ L ) )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(4)
% 5.17/5.42 thf(fact_3477_add__mono__thms__linordered__field_I4_J,axiom,
% 5.17/5.42 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( ord_less_eq_int @ I @ J )
% 5.17/5.42 & ( ord_less_int @ K @ L ) )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(4)
% 5.17/5.42 thf(fact_3478_add__mono__thms__linordered__field_I4_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( ord_less_eq_real @ I @ J )
% 5.17/5.42 & ( ord_less_real @ K @ L ) )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(4)
% 5.17/5.42 thf(fact_3479_add__mono__thms__linordered__field_I3_J,axiom,
% 5.17/5.42 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.17/5.42 ( ( ( ord_less_rat @ I @ J )
% 5.17/5.42 & ( ord_less_eq_rat @ K @ L ) )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(3)
% 5.17/5.42 thf(fact_3480_add__mono__thms__linordered__field_I3_J,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.17/5.42 ( ( ( ord_less_nat @ I @ J )
% 5.17/5.42 & ( ord_less_eq_nat @ K @ L ) )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(3)
% 5.17/5.42 thf(fact_3481_add__mono__thms__linordered__field_I3_J,axiom,
% 5.17/5.42 ! [I: int,J: int,K: int,L: int] :
% 5.17/5.42 ( ( ( ord_less_int @ I @ J )
% 5.17/5.42 & ( ord_less_eq_int @ K @ L ) )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(3)
% 5.17/5.42 thf(fact_3482_add__mono__thms__linordered__field_I3_J,axiom,
% 5.17/5.42 ! [I: real,J: real,K: real,L: real] :
% 5.17/5.42 ( ( ( ord_less_real @ I @ J )
% 5.17/5.42 & ( ord_less_eq_real @ K @ L ) )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono_thms_linordered_field(3)
% 5.17/5.42 thf(fact_3483_add__le__less__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.42 => ( ( ord_less_rat @ C @ D )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_less_mono
% 5.17/5.42 thf(fact_3484_add__le__less__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( ord_less_nat @ C @ D )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_less_mono
% 5.17/5.42 thf(fact_3485_add__le__less__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.42 => ( ( ord_less_int @ C @ D )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_less_mono
% 5.17/5.42 thf(fact_3486_add__le__less__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.42 => ( ( ord_less_real @ C @ D )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_less_mono
% 5.17/5.42 thf(fact_3487_add__less__le__mono,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_rat @ C @ D )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_le_mono
% 5.17/5.42 thf(fact_3488_add__less__le__mono,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_nat @ C @ D )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_le_mono
% 5.17/5.42 thf(fact_3489_add__less__le__mono,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_int @ C @ D )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_le_mono
% 5.17/5.42 thf(fact_3490_add__less__le__mono,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_real @ C @ D )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_le_mono
% 5.17/5.42 thf(fact_3491_add__less__zeroD,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ( ord_less_real @ ( plus_plus_real @ X @ Y4 ) @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.42 | ( ord_less_real @ Y4 @ zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_zeroD
% 5.17/5.42 thf(fact_3492_add__less__zeroD,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y4 ) @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.17/5.42 | ( ord_less_rat @ Y4 @ zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_zeroD
% 5.17/5.42 thf(fact_3493_add__less__zeroD,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ( ( ord_less_int @ ( plus_plus_int @ X @ Y4 ) @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.17/5.42 | ( ord_less_int @ Y4 @ zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_less_zeroD
% 5.17/5.42 thf(fact_3494_add__neg__neg,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_neg
% 5.17/5.42 thf(fact_3495_add__neg__neg,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_neg
% 5.17/5.42 thf(fact_3496_add__neg__neg,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_neg
% 5.17/5.42 thf(fact_3497_add__neg__neg,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_neg
% 5.17/5.42 thf(fact_3498_add__pos__pos,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.42 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_pos
% 5.17/5.42 thf(fact_3499_add__pos__pos,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.42 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_pos
% 5.17/5.42 thf(fact_3500_add__pos__pos,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.42 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_pos
% 5.17/5.42 thf(fact_3501_add__pos__pos,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.42 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_pos
% 5.17/5.42 thf(fact_3502_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ B )
% 5.17/5.42 => ~ ! [C3: nat] :
% 5.17/5.42 ( ( B
% 5.17/5.42 = ( plus_plus_nat @ A @ C3 ) )
% 5.17/5.42 => ( C3 = zero_zero_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % canonically_ordered_monoid_add_class.lessE
% 5.17/5.42 thf(fact_3503_pos__add__strict,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_real @ B @ C )
% 5.17/5.42 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pos_add_strict
% 5.17/5.42 thf(fact_3504_pos__add__strict,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_rat @ B @ C )
% 5.17/5.42 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pos_add_strict
% 5.17/5.42 thf(fact_3505_pos__add__strict,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_nat @ B @ C )
% 5.17/5.42 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pos_add_strict
% 5.17/5.42 thf(fact_3506_pos__add__strict,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_int @ B @ C )
% 5.17/5.42 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pos_add_strict
% 5.17/5.42 thf(fact_3507_add__le__imp__le__diff,axiom,
% 5.17/5.42 ! [I: rat,K: rat,N: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.17/5.42 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_diff
% 5.17/5.42 thf(fact_3508_add__le__imp__le__diff,axiom,
% 5.17/5.42 ! [I: nat,K: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.17/5.42 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_diff
% 5.17/5.42 thf(fact_3509_add__le__imp__le__diff,axiom,
% 5.17/5.42 ! [I: int,K: int,N: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.17/5.42 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_diff
% 5.17/5.42 thf(fact_3510_add__le__imp__le__diff,axiom,
% 5.17/5.42 ! [I: real,K: real,N: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.17/5.42 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_imp_le_diff
% 5.17/5.42 thf(fact_3511_add__le__add__imp__diff__le,axiom,
% 5.17/5.42 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.17/5.42 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.17/5.42 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_add_imp_diff_le
% 5.17/5.42 thf(fact_3512_add__le__add__imp__diff__le,axiom,
% 5.17/5.42 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.17/5.42 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.17/5.42 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_add_imp_diff_le
% 5.17/5.42 thf(fact_3513_add__le__add__imp__diff__le,axiom,
% 5.17/5.42 ! [I: int,K: int,N: int,J: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.17/5.42 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.17/5.42 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_add_imp_diff_le
% 5.17/5.42 thf(fact_3514_add__le__add__imp__diff__le,axiom,
% 5.17/5.42 ! [I: real,K: real,N: real,J: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.17/5.42 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.17/5.42 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.17/5.42 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_le_add_imp_diff_le
% 5.17/5.42 thf(fact_3515_diff__le__eq,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_le_eq
% 5.17/5.42 thf(fact_3516_diff__le__eq,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.42 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_le_eq
% 5.17/5.42 thf(fact_3517_diff__le__eq,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.17/5.42 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_le_eq
% 5.17/5.42 thf(fact_3518_le__diff__eq,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.17/5.42 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_diff_eq
% 5.17/5.42 thf(fact_3519_le__diff__eq,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.17/5.42 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_diff_eq
% 5.17/5.42 thf(fact_3520_le__diff__eq,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.17/5.42 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_diff_eq
% 5.17/5.42 thf(fact_3521_diff__add,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.17/5.42 = B ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add
% 5.17/5.42 thf(fact_3522_le__add__diff,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_add_diff
% 5.17/5.42 thf(fact_3523_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.17/5.42 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.17/5.42 thf(fact_3524_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.17/5.42 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.17/5.42 thf(fact_3525_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.17/5.42 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.17/5.42 thf(fact_3526_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.17/5.42 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.17/5.42 thf(fact_3527_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.17/5.42 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.17/5.42 thf(fact_3528_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.17/5.42 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.17/5.42 thf(fact_3529_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.17/5.42 = B ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.17/5.42 thf(fact_3530_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.42 => ( ( ( minus_minus_nat @ B @ A )
% 5.17/5.42 = C )
% 5.17/5.42 = ( B
% 5.17/5.42 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.17/5.42 thf(fact_3531_less__add__one,axiom,
% 5.17/5.42 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_one
% 5.17/5.42 thf(fact_3532_less__add__one,axiom,
% 5.17/5.42 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_one
% 5.17/5.42 thf(fact_3533_less__add__one,axiom,
% 5.17/5.42 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_one
% 5.17/5.42 thf(fact_3534_less__add__one,axiom,
% 5.17/5.42 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_one
% 5.17/5.42 thf(fact_3535_add__mono1,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ B )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono1
% 5.17/5.42 thf(fact_3536_add__mono1,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ B )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono1
% 5.17/5.42 thf(fact_3537_add__mono1,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ B )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono1
% 5.17/5.42 thf(fact_3538_add__mono1,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ B )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_mono1
% 5.17/5.42 thf(fact_3539_numeral__Bit0,axiom,
% 5.17/5.42 ! [N: num] :
% 5.17/5.42 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.17/5.42 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % numeral_Bit0
% 5.17/5.42 thf(fact_3540_numeral__Bit0,axiom,
% 5.17/5.42 ! [N: num] :
% 5.17/5.42 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.17/5.42 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % numeral_Bit0
% 5.17/5.42 thf(fact_3541_numeral__Bit0,axiom,
% 5.17/5.42 ! [N: num] :
% 5.17/5.42 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.17/5.42 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % numeral_Bit0
% 5.17/5.42 thf(fact_3542_numeral__Bit0,axiom,
% 5.17/5.42 ! [N: num] :
% 5.17/5.42 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.17/5.42 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % numeral_Bit0
% 5.17/5.42 thf(fact_3543_numeral__Bit0,axiom,
% 5.17/5.42 ! [N: num] :
% 5.17/5.42 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.17/5.42 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % numeral_Bit0
% 5.17/5.42 thf(fact_3544_less__diff__eq,axiom,
% 5.17/5.42 ! [A: real,C: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.17/5.42 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_diff_eq
% 5.17/5.42 thf(fact_3545_less__diff__eq,axiom,
% 5.17/5.42 ! [A: rat,C: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.17/5.42 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_diff_eq
% 5.17/5.42 thf(fact_3546_less__diff__eq,axiom,
% 5.17/5.42 ! [A: int,C: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.17/5.42 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_diff_eq
% 5.17/5.42 thf(fact_3547_diff__less__eq,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.17/5.42 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_less_eq
% 5.17/5.42 thf(fact_3548_diff__less__eq,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.17/5.42 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_less_eq
% 5.17/5.42 thf(fact_3549_diff__less__eq,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.42 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % diff_less_eq
% 5.17/5.42 thf(fact_3550_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ~ ( ord_less_real @ A @ B )
% 5.17/5.42 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.17/5.42 = A ) ) ).
% 5.17/5.42
% 5.17/5.42 % linordered_semidom_class.add_diff_inverse
% 5.17/5.42 thf(fact_3551_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ~ ( ord_less_rat @ A @ B )
% 5.17/5.42 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.17/5.42 = A ) ) ).
% 5.17/5.42
% 5.17/5.42 % linordered_semidom_class.add_diff_inverse
% 5.17/5.42 thf(fact_3552_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ~ ( ord_less_nat @ A @ B )
% 5.17/5.42 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.17/5.42 = A ) ) ).
% 5.17/5.42
% 5.17/5.42 % linordered_semidom_class.add_diff_inverse
% 5.17/5.42 thf(fact_3553_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ~ ( ord_less_int @ A @ B )
% 5.17/5.42 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.17/5.42 = A ) ) ).
% 5.17/5.42
% 5.17/5.42 % linordered_semidom_class.add_diff_inverse
% 5.17/5.42 thf(fact_3554_one__plus__numeral__commute,axiom,
% 5.17/5.42 ! [X: num] :
% 5.17/5.42 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.17/5.42 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.17/5.42
% 5.17/5.42 % one_plus_numeral_commute
% 5.17/5.42 thf(fact_3555_one__plus__numeral__commute,axiom,
% 5.17/5.42 ! [X: num] :
% 5.17/5.42 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.17/5.42 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.17/5.42
% 5.17/5.42 % one_plus_numeral_commute
% 5.17/5.42 thf(fact_3556_one__plus__numeral__commute,axiom,
% 5.17/5.42 ! [X: num] :
% 5.17/5.42 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.17/5.42 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.17/5.42
% 5.17/5.42 % one_plus_numeral_commute
% 5.17/5.42 thf(fact_3557_one__plus__numeral__commute,axiom,
% 5.17/5.42 ! [X: num] :
% 5.17/5.42 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.17/5.42 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.17/5.42
% 5.17/5.42 % one_plus_numeral_commute
% 5.17/5.42 thf(fact_3558_one__plus__numeral__commute,axiom,
% 5.17/5.42 ! [X: num] :
% 5.17/5.42 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.17/5.42 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.17/5.42
% 5.17/5.42 % one_plus_numeral_commute
% 5.17/5.42 thf(fact_3559_eq__add__iff1,axiom,
% 5.17/5.42 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 5.17/5.42 = D ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_add_iff1
% 5.17/5.42 thf(fact_3560_eq__add__iff1,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 5.17/5.42 = D ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_add_iff1
% 5.17/5.42 thf(fact_3561_eq__add__iff1,axiom,
% 5.17/5.42 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 5.17/5.42 = D ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_add_iff1
% 5.17/5.42 thf(fact_3562_eq__add__iff2,axiom,
% 5.17/5.42 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( C
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_add_iff2
% 5.17/5.42 thf(fact_3563_eq__add__iff2,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( C
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_add_iff2
% 5.17/5.42 thf(fact_3564_eq__add__iff2,axiom,
% 5.17/5.42 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( C
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % eq_add_iff2
% 5.17/5.42 thf(fact_3565_square__diff__square__factored,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) )
% 5.17/5.42 = ( times_times_real @ ( plus_plus_real @ X @ Y4 ) @ ( minus_minus_real @ X @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % square_diff_square_factored
% 5.17/5.42 thf(fact_3566_square__diff__square__factored,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) )
% 5.17/5.42 = ( times_times_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( minus_minus_rat @ X @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % square_diff_square_factored
% 5.17/5.42 thf(fact_3567_square__diff__square__factored,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) )
% 5.17/5.42 = ( times_times_int @ ( plus_plus_int @ X @ Y4 ) @ ( minus_minus_int @ X @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % square_diff_square_factored
% 5.17/5.42 thf(fact_3568_mult__diff__mult,axiom,
% 5.17/5.42 ! [X: real,Y4: real,A: real,B: real] :
% 5.17/5.42 ( ( minus_minus_real @ ( times_times_real @ X @ Y4 ) @ ( times_times_real @ A @ B ) )
% 5.17/5.42 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y4 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % mult_diff_mult
% 5.17/5.42 thf(fact_3569_mult__diff__mult,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y4 ) @ ( times_times_rat @ A @ B ) )
% 5.17/5.42 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y4 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % mult_diff_mult
% 5.17/5.42 thf(fact_3570_mult__diff__mult,axiom,
% 5.17/5.42 ! [X: int,Y4: int,A: int,B: int] :
% 5.17/5.42 ( ( minus_minus_int @ ( times_times_int @ X @ Y4 ) @ ( times_times_int @ A @ B ) )
% 5.17/5.42 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y4 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % mult_diff_mult
% 5.17/5.42 thf(fact_3571_minf_I10_J,axiom,
% 5.17/5.42 ! [D: code_integer,S2: code_integer] :
% 5.17/5.42 ? [Z2: code_integer] :
% 5.17/5.42 ! [X5: code_integer] :
% 5.17/5.42 ( ( ord_le6747313008572928689nteger @ X5 @ Z2 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(10)
% 5.17/5.42 thf(fact_3572_minf_I10_J,axiom,
% 5.17/5.42 ! [D: real,S2: real] :
% 5.17/5.42 ? [Z2: real] :
% 5.17/5.42 ! [X5: real] :
% 5.17/5.42 ( ( ord_less_real @ X5 @ Z2 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(10)
% 5.17/5.42 thf(fact_3573_minf_I10_J,axiom,
% 5.17/5.42 ! [D: rat,S2: rat] :
% 5.17/5.42 ? [Z2: rat] :
% 5.17/5.42 ! [X5: rat] :
% 5.17/5.42 ( ( ord_less_rat @ X5 @ Z2 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(10)
% 5.17/5.42 thf(fact_3574_minf_I10_J,axiom,
% 5.17/5.42 ! [D: nat,S2: nat] :
% 5.17/5.42 ? [Z2: nat] :
% 5.17/5.42 ! [X5: nat] :
% 5.17/5.42 ( ( ord_less_nat @ X5 @ Z2 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(10)
% 5.17/5.42 thf(fact_3575_minf_I10_J,axiom,
% 5.17/5.42 ! [D: int,S2: int] :
% 5.17/5.42 ? [Z2: int] :
% 5.17/5.42 ! [X5: int] :
% 5.17/5.42 ( ( ord_less_int @ X5 @ Z2 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(10)
% 5.17/5.42 thf(fact_3576_minf_I9_J,axiom,
% 5.17/5.42 ! [D: code_integer,S2: code_integer] :
% 5.17/5.42 ? [Z2: code_integer] :
% 5.17/5.42 ! [X5: code_integer] :
% 5.17/5.42 ( ( ord_le6747313008572928689nteger @ X5 @ Z2 )
% 5.17/5.42 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(9)
% 5.17/5.42 thf(fact_3577_minf_I9_J,axiom,
% 5.17/5.42 ! [D: real,S2: real] :
% 5.17/5.42 ? [Z2: real] :
% 5.17/5.42 ! [X5: real] :
% 5.17/5.42 ( ( ord_less_real @ X5 @ Z2 )
% 5.17/5.42 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(9)
% 5.17/5.42 thf(fact_3578_minf_I9_J,axiom,
% 5.17/5.42 ! [D: rat,S2: rat] :
% 5.17/5.42 ? [Z2: rat] :
% 5.17/5.42 ! [X5: rat] :
% 5.17/5.42 ( ( ord_less_rat @ X5 @ Z2 )
% 5.17/5.42 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(9)
% 5.17/5.42 thf(fact_3579_minf_I9_J,axiom,
% 5.17/5.42 ! [D: nat,S2: nat] :
% 5.17/5.42 ? [Z2: nat] :
% 5.17/5.42 ! [X5: nat] :
% 5.17/5.42 ( ( ord_less_nat @ X5 @ Z2 )
% 5.17/5.42 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(9)
% 5.17/5.42 thf(fact_3580_minf_I9_J,axiom,
% 5.17/5.42 ! [D: int,S2: int] :
% 5.17/5.42 ? [Z2: int] :
% 5.17/5.42 ! [X5: int] :
% 5.17/5.42 ( ( ord_less_int @ X5 @ Z2 )
% 5.17/5.42 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % minf(9)
% 5.17/5.42 thf(fact_3581_pinf_I10_J,axiom,
% 5.17/5.42 ! [D: code_integer,S2: code_integer] :
% 5.17/5.42 ? [Z2: code_integer] :
% 5.17/5.42 ! [X5: code_integer] :
% 5.17/5.42 ( ( ord_le6747313008572928689nteger @ Z2 @ X5 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(10)
% 5.17/5.42 thf(fact_3582_pinf_I10_J,axiom,
% 5.17/5.42 ! [D: real,S2: real] :
% 5.17/5.42 ? [Z2: real] :
% 5.17/5.42 ! [X5: real] :
% 5.17/5.42 ( ( ord_less_real @ Z2 @ X5 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(10)
% 5.17/5.42 thf(fact_3583_pinf_I10_J,axiom,
% 5.17/5.42 ! [D: rat,S2: rat] :
% 5.17/5.42 ? [Z2: rat] :
% 5.17/5.42 ! [X5: rat] :
% 5.17/5.42 ( ( ord_less_rat @ Z2 @ X5 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(10)
% 5.17/5.42 thf(fact_3584_pinf_I10_J,axiom,
% 5.17/5.42 ! [D: nat,S2: nat] :
% 5.17/5.42 ? [Z2: nat] :
% 5.17/5.42 ! [X5: nat] :
% 5.17/5.42 ( ( ord_less_nat @ Z2 @ X5 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(10)
% 5.17/5.42 thf(fact_3585_pinf_I10_J,axiom,
% 5.17/5.42 ! [D: int,S2: int] :
% 5.17/5.42 ? [Z2: int] :
% 5.17/5.42 ! [X5: int] :
% 5.17/5.42 ( ( ord_less_int @ Z2 @ X5 )
% 5.17/5.42 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) )
% 5.17/5.42 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(10)
% 5.17/5.42 thf(fact_3586_pinf_I9_J,axiom,
% 5.17/5.42 ! [D: code_integer,S2: code_integer] :
% 5.17/5.42 ? [Z2: code_integer] :
% 5.17/5.42 ! [X5: code_integer] :
% 5.17/5.42 ( ( ord_le6747313008572928689nteger @ Z2 @ X5 )
% 5.17/5.42 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(9)
% 5.17/5.42 thf(fact_3587_pinf_I9_J,axiom,
% 5.17/5.42 ! [D: real,S2: real] :
% 5.17/5.42 ? [Z2: real] :
% 5.17/5.42 ! [X5: real] :
% 5.17/5.42 ( ( ord_less_real @ Z2 @ X5 )
% 5.17/5.42 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(9)
% 5.17/5.42 thf(fact_3588_pinf_I9_J,axiom,
% 5.17/5.42 ! [D: rat,S2: rat] :
% 5.17/5.42 ? [Z2: rat] :
% 5.17/5.42 ! [X5: rat] :
% 5.17/5.42 ( ( ord_less_rat @ Z2 @ X5 )
% 5.17/5.42 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(9)
% 5.17/5.42 thf(fact_3589_pinf_I9_J,axiom,
% 5.17/5.42 ! [D: nat,S2: nat] :
% 5.17/5.42 ? [Z2: nat] :
% 5.17/5.42 ! [X5: nat] :
% 5.17/5.42 ( ( ord_less_nat @ Z2 @ X5 )
% 5.17/5.42 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(9)
% 5.17/5.42 thf(fact_3590_pinf_I9_J,axiom,
% 5.17/5.42 ! [D: int,S2: int] :
% 5.17/5.42 ? [Z2: int] :
% 5.17/5.42 ! [X5: int] :
% 5.17/5.42 ( ( ord_less_int @ Z2 @ X5 )
% 5.17/5.42 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) )
% 5.17/5.42 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ S2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % pinf(9)
% 5.17/5.42 thf(fact_3591_div__plus__div__distrib__dvd__left,axiom,
% 5.17/5.42 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.42 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.17/5.42 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.17/5.42 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_plus_div_distrib_dvd_left
% 5.17/5.42 thf(fact_3592_div__plus__div__distrib__dvd__left,axiom,
% 5.17/5.42 ! [C: nat,A: nat,B: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ C @ A )
% 5.17/5.42 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_plus_div_distrib_dvd_left
% 5.17/5.42 thf(fact_3593_div__plus__div__distrib__dvd__left,axiom,
% 5.17/5.42 ! [C: int,A: int,B: int] :
% 5.17/5.42 ( ( dvd_dvd_int @ C @ A )
% 5.17/5.42 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_plus_div_distrib_dvd_left
% 5.17/5.42 thf(fact_3594_div__plus__div__distrib__dvd__right,axiom,
% 5.17/5.42 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.42 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.42 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.17/5.42 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_plus_div_distrib_dvd_right
% 5.17/5.42 thf(fact_3595_div__plus__div__distrib__dvd__right,axiom,
% 5.17/5.42 ! [C: nat,B: nat,A: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.42 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_plus_div_distrib_dvd_right
% 5.17/5.42 thf(fact_3596_div__plus__div__distrib__dvd__right,axiom,
% 5.17/5.42 ! [C: int,B: int,A: int] :
% 5.17/5.42 ( ( dvd_dvd_int @ C @ B )
% 5.17/5.42 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.42 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_plus_div_distrib_dvd_right
% 5.17/5.42 thf(fact_3597_power__add,axiom,
% 5.17/5.42 ! [A: complex,M: nat,N: nat] :
% 5.17/5.42 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % power_add
% 5.17/5.42 thf(fact_3598_power__add,axiom,
% 5.17/5.42 ! [A: real,M: nat,N: nat] :
% 5.17/5.42 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % power_add
% 5.17/5.42 thf(fact_3599_power__add,axiom,
% 5.17/5.42 ! [A: rat,M: nat,N: nat] :
% 5.17/5.42 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % power_add
% 5.17/5.42 thf(fact_3600_power__add,axiom,
% 5.17/5.42 ! [A: nat,M: nat,N: nat] :
% 5.17/5.42 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % power_add
% 5.17/5.42 thf(fact_3601_power__add,axiom,
% 5.17/5.42 ! [A: int,M: nat,N: nat] :
% 5.17/5.42 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % power_add
% 5.17/5.42 thf(fact_3602_one__is__add,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( ( suc @ zero_zero_nat )
% 5.17/5.42 = ( plus_plus_nat @ M @ N ) )
% 5.17/5.42 = ( ( ( M
% 5.17/5.42 = ( suc @ zero_zero_nat ) )
% 5.17/5.42 & ( N = zero_zero_nat ) )
% 5.17/5.42 | ( ( M = zero_zero_nat )
% 5.17/5.42 & ( N
% 5.17/5.42 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % one_is_add
% 5.17/5.42 thf(fact_3603_add__is__1,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( ( plus_plus_nat @ M @ N )
% 5.17/5.42 = ( suc @ zero_zero_nat ) )
% 5.17/5.42 = ( ( ( M
% 5.17/5.42 = ( suc @ zero_zero_nat ) )
% 5.17/5.42 & ( N = zero_zero_nat ) )
% 5.17/5.42 | ( ( M = zero_zero_nat )
% 5.17/5.42 & ( N
% 5.17/5.42 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_is_1
% 5.17/5.42 thf(fact_3604_less__imp__Suc__add,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_nat @ M @ N )
% 5.17/5.42 => ? [K2: nat] :
% 5.17/5.42 ( N
% 5.17/5.42 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_imp_Suc_add
% 5.17/5.42 thf(fact_3605_less__iff__Suc__add,axiom,
% 5.17/5.42 ( ord_less_nat
% 5.17/5.42 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.42 ? [K3: nat] :
% 5.17/5.42 ( N4
% 5.17/5.42 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_iff_Suc_add
% 5.17/5.42 thf(fact_3606_less__add__Suc2,axiom,
% 5.17/5.42 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_Suc2
% 5.17/5.42 thf(fact_3607_less__add__Suc1,axiom,
% 5.17/5.42 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_Suc1
% 5.17/5.42 thf(fact_3608_less__natE,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( ord_less_nat @ M @ N )
% 5.17/5.42 => ~ ! [Q4: nat] :
% 5.17/5.42 ( N
% 5.17/5.42 != ( suc @ ( plus_plus_nat @ M @ Q4 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_natE
% 5.17/5.42 thf(fact_3609_less__imp__add__positive,axiom,
% 5.17/5.42 ! [I: nat,J: nat] :
% 5.17/5.42 ( ( ord_less_nat @ I @ J )
% 5.17/5.42 => ? [K2: nat] :
% 5.17/5.42 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.17/5.42 & ( ( plus_plus_nat @ I @ K2 )
% 5.17/5.42 = J ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_imp_add_positive
% 5.17/5.42 thf(fact_3610_mono__nat__linear__lb,axiom,
% 5.17/5.42 ! [F: nat > nat,M: nat,K: nat] :
% 5.17/5.42 ( ! [M4: nat,N2: nat] :
% 5.17/5.42 ( ( ord_less_nat @ M4 @ N2 )
% 5.17/5.42 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N2 ) ) )
% 5.17/5.42 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % mono_nat_linear_lb
% 5.17/5.42 thf(fact_3611_mult__Suc,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.17/5.42 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % mult_Suc
% 5.17/5.42 thf(fact_3612_diff__add__0,axiom,
% 5.17/5.42 ! [N: nat,M: nat] :
% 5.17/5.42 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.42 = zero_zero_nat ) ).
% 5.17/5.42
% 5.17/5.42 % diff_add_0
% 5.17/5.42 thf(fact_3613_less__diff__conv,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat] :
% 5.17/5.42 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.17/5.42 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_diff_conv
% 5.17/5.42 thf(fact_3614_add__diff__inverse__nat,axiom,
% 5.17/5.42 ! [M: nat,N: nat] :
% 5.17/5.42 ( ~ ( ord_less_nat @ M @ N )
% 5.17/5.42 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.17/5.42 = M ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_diff_inverse_nat
% 5.17/5.42 thf(fact_3615_Suc__eq__plus1__left,axiom,
% 5.17/5.42 ( suc
% 5.17/5.42 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.17/5.42
% 5.17/5.42 % Suc_eq_plus1_left
% 5.17/5.42 thf(fact_3616_plus__1__eq__Suc,axiom,
% 5.17/5.42 ( ( plus_plus_nat @ one_one_nat )
% 5.17/5.42 = suc ) ).
% 5.17/5.42
% 5.17/5.42 % plus_1_eq_Suc
% 5.17/5.42 thf(fact_3617_Suc__eq__plus1,axiom,
% 5.17/5.42 ( suc
% 5.17/5.42 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % Suc_eq_plus1
% 5.17/5.42 thf(fact_3618_Nat_Ole__imp__diff__is__add,axiom,
% 5.17/5.42 ! [I: nat,J: nat,K: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.42 => ( ( ( minus_minus_nat @ J @ I )
% 5.17/5.42 = K )
% 5.17/5.42 = ( J
% 5.17/5.42 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % Nat.le_imp_diff_is_add
% 5.17/5.42 thf(fact_3619_Nat_Odiff__add__assoc2,axiom,
% 5.17/5.42 ! [K: nat,J: nat,I: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.42 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.17/5.42 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % Nat.diff_add_assoc2
% 5.17/5.42 thf(fact_3620_Nat_Odiff__add__assoc,axiom,
% 5.17/5.42 ! [K: nat,J: nat,I: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.42 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.17/5.42 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % Nat.diff_add_assoc
% 5.17/5.42 thf(fact_3621_Nat_Ole__diff__conv2,axiom,
% 5.17/5.42 ! [K: nat,J: nat,I: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.42 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.17/5.42 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % Nat.le_diff_conv2
% 5.17/5.42 thf(fact_3622_le__diff__conv,axiom,
% 5.17/5.42 ! [J: nat,K: nat,I: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.17/5.42 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % le_diff_conv
% 5.17/5.42 thf(fact_3623_bezout__lemma__nat,axiom,
% 5.17/5.42 ! [D: nat,A: nat,B: nat,X: nat,Y4: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ D @ A )
% 5.17/5.42 => ( ( dvd_dvd_nat @ D @ B )
% 5.17/5.42 => ( ( ( ( times_times_nat @ A @ X )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D ) )
% 5.17/5.42 | ( ( times_times_nat @ B @ X )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) )
% 5.17/5.42 => ? [X4: nat,Y: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ D @ A )
% 5.17/5.42 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.42 & ( ( ( times_times_nat @ A @ X4 )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y ) @ D ) )
% 5.17/5.42 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % bezout_lemma_nat
% 5.17/5.42 thf(fact_3624_bezout__add__nat,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ? [D2: nat,X4: nat,Y: nat] :
% 5.17/5.42 ( ( dvd_dvd_nat @ D2 @ A )
% 5.17/5.42 & ( dvd_dvd_nat @ D2 @ B )
% 5.17/5.42 & ( ( ( times_times_nat @ A @ X4 )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) )
% 5.17/5.42 | ( ( times_times_nat @ B @ X4 )
% 5.17/5.42 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D2 ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % bezout_add_nat
% 5.17/5.42 thf(fact_3625_field__le__epsilon,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ! [E: rat] :
% 5.17/5.42 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.17/5.42 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y4 @ E ) ) )
% 5.17/5.42 => ( ord_less_eq_rat @ X @ Y4 ) ) ).
% 5.17/5.42
% 5.17/5.42 % field_le_epsilon
% 5.17/5.42 thf(fact_3626_field__le__epsilon,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ! [E: real] :
% 5.17/5.42 ( ( ord_less_real @ zero_zero_real @ E )
% 5.17/5.42 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y4 @ E ) ) )
% 5.17/5.42 => ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.42
% 5.17/5.42 % field_le_epsilon
% 5.17/5.42 thf(fact_3627_add__strict__increasing2,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_rat @ B @ C )
% 5.17/5.42 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing2
% 5.17/5.42 thf(fact_3628_add__strict__increasing2,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_nat @ B @ C )
% 5.17/5.42 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing2
% 5.17/5.42 thf(fact_3629_add__strict__increasing2,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_int @ B @ C )
% 5.17/5.42 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing2
% 5.17/5.42 thf(fact_3630_add__strict__increasing2,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_real @ B @ C )
% 5.17/5.42 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing2
% 5.17/5.42 thf(fact_3631_add__strict__increasing,axiom,
% 5.17/5.42 ! [A: rat,B: rat,C: rat] :
% 5.17/5.42 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_eq_rat @ B @ C )
% 5.17/5.42 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing
% 5.17/5.42 thf(fact_3632_add__strict__increasing,axiom,
% 5.17/5.42 ! [A: nat,B: nat,C: nat] :
% 5.17/5.42 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_eq_nat @ B @ C )
% 5.17/5.42 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing
% 5.17/5.42 thf(fact_3633_add__strict__increasing,axiom,
% 5.17/5.42 ! [A: int,B: int,C: int] :
% 5.17/5.42 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_eq_int @ B @ C )
% 5.17/5.42 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing
% 5.17/5.42 thf(fact_3634_add__strict__increasing,axiom,
% 5.17/5.42 ! [A: real,B: real,C: real] :
% 5.17/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_eq_real @ B @ C )
% 5.17/5.42 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_strict_increasing
% 5.17/5.42 thf(fact_3635_add__pos__nonneg,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.42 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_nonneg
% 5.17/5.42 thf(fact_3636_add__pos__nonneg,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.17/5.42 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_nonneg
% 5.17/5.42 thf(fact_3637_add__pos__nonneg,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.42 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_nonneg
% 5.17/5.42 thf(fact_3638_add__pos__nonneg,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.42 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_pos_nonneg
% 5.17/5.42 thf(fact_3639_add__nonpos__neg,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_neg
% 5.17/5.42 thf(fact_3640_add__nonpos__neg,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_neg
% 5.17/5.42 thf(fact_3641_add__nonpos__neg,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_neg
% 5.17/5.42 thf(fact_3642_add__nonpos__neg,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonpos_neg
% 5.17/5.42 thf(fact_3643_add__nonneg__pos,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.42 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.42 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_pos
% 5.17/5.42 thf(fact_3644_add__nonneg__pos,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.42 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.42 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_pos
% 5.17/5.42 thf(fact_3645_add__nonneg__pos,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.42 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.42 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_pos
% 5.17/5.42 thf(fact_3646_add__nonneg__pos,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.42 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.42 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_nonneg_pos
% 5.17/5.42 thf(fact_3647_add__neg__nonpos,axiom,
% 5.17/5.42 ! [A: rat,B: rat] :
% 5.17/5.42 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.42 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.17/5.42 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_nonpos
% 5.17/5.42 thf(fact_3648_add__neg__nonpos,axiom,
% 5.17/5.42 ! [A: nat,B: nat] :
% 5.17/5.42 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.17/5.42 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.17/5.42 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_nonpos
% 5.17/5.42 thf(fact_3649_add__neg__nonpos,axiom,
% 5.17/5.42 ! [A: int,B: int] :
% 5.17/5.42 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.42 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.17/5.42 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_nonpos
% 5.17/5.42 thf(fact_3650_add__neg__nonpos,axiom,
% 5.17/5.42 ! [A: real,B: real] :
% 5.17/5.42 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.42 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.17/5.42 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_neg_nonpos
% 5.17/5.42 thf(fact_3651_sum__squares__ge__zero,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_ge_zero
% 5.17/5.42 thf(fact_3652_sum__squares__ge__zero,axiom,
% 5.17/5.42 ! [X: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_ge_zero
% 5.17/5.42 thf(fact_3653_sum__squares__ge__zero,axiom,
% 5.17/5.42 ! [X: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_ge_zero
% 5.17/5.42 thf(fact_3654_sum__squares__le__zero__iff,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) @ zero_zero_rat )
% 5.17/5.42 = ( ( X = zero_zero_rat )
% 5.17/5.42 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_le_zero_iff
% 5.17/5.42 thf(fact_3655_sum__squares__le__zero__iff,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) @ zero_zero_int )
% 5.17/5.42 = ( ( X = zero_zero_int )
% 5.17/5.42 & ( Y4 = zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_le_zero_iff
% 5.17/5.42 thf(fact_3656_sum__squares__le__zero__iff,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) @ zero_zero_real )
% 5.17/5.42 = ( ( X = zero_zero_real )
% 5.17/5.42 & ( Y4 = zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_le_zero_iff
% 5.17/5.42 thf(fact_3657_not__sum__squares__lt__zero,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) @ zero_zero_real ) ).
% 5.17/5.42
% 5.17/5.42 % not_sum_squares_lt_zero
% 5.17/5.42 thf(fact_3658_not__sum__squares__lt__zero,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) @ zero_zero_rat ) ).
% 5.17/5.42
% 5.17/5.42 % not_sum_squares_lt_zero
% 5.17/5.42 thf(fact_3659_not__sum__squares__lt__zero,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) @ zero_zero_int ) ).
% 5.17/5.42
% 5.17/5.42 % not_sum_squares_lt_zero
% 5.17/5.42 thf(fact_3660_sum__squares__gt__zero__iff,axiom,
% 5.17/5.42 ! [X: real,Y4: real] :
% 5.17/5.42 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) )
% 5.17/5.42 = ( ( X != zero_zero_real )
% 5.17/5.42 | ( Y4 != zero_zero_real ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_gt_zero_iff
% 5.17/5.42 thf(fact_3661_sum__squares__gt__zero__iff,axiom,
% 5.17/5.42 ! [X: rat,Y4: rat] :
% 5.17/5.42 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y4 @ Y4 ) ) )
% 5.17/5.42 = ( ( X != zero_zero_rat )
% 5.17/5.42 | ( Y4 != zero_zero_rat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_gt_zero_iff
% 5.17/5.42 thf(fact_3662_sum__squares__gt__zero__iff,axiom,
% 5.17/5.42 ! [X: int,Y4: int] :
% 5.17/5.42 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y4 @ Y4 ) ) )
% 5.17/5.42 = ( ( X != zero_zero_int )
% 5.17/5.42 | ( Y4 != zero_zero_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % sum_squares_gt_zero_iff
% 5.17/5.42 thf(fact_3663_discrete,axiom,
% 5.17/5.42 ( ord_less_nat
% 5.17/5.42 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % discrete
% 5.17/5.42 thf(fact_3664_discrete,axiom,
% 5.17/5.42 ( ord_less_int
% 5.17/5.42 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % discrete
% 5.17/5.42 thf(fact_3665_zero__less__two,axiom,
% 5.17/5.42 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.17/5.42
% 5.17/5.42 % zero_less_two
% 5.17/5.42 thf(fact_3666_zero__less__two,axiom,
% 5.17/5.42 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.17/5.42
% 5.17/5.42 % zero_less_two
% 5.17/5.42 thf(fact_3667_zero__less__two,axiom,
% 5.17/5.42 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.17/5.42
% 5.17/5.42 % zero_less_two
% 5.17/5.42 thf(fact_3668_zero__less__two,axiom,
% 5.17/5.42 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.17/5.42
% 5.17/5.42 % zero_less_two
% 5.17/5.42 thf(fact_3669_ordered__ring__class_Ole__add__iff1,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_ring_class.le_add_iff1
% 5.17/5.42 thf(fact_3670_ordered__ring__class_Ole__add__iff1,axiom,
% 5.17/5.42 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_ring_class.le_add_iff1
% 5.17/5.42 thf(fact_3671_ordered__ring__class_Ole__add__iff1,axiom,
% 5.17/5.42 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_ring_class.le_add_iff1
% 5.17/5.42 thf(fact_3672_ordered__ring__class_Ole__add__iff2,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_ring_class.le_add_iff2
% 5.17/5.42 thf(fact_3673_ordered__ring__class_Ole__add__iff2,axiom,
% 5.17/5.42 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_ring_class.le_add_iff2
% 5.17/5.42 thf(fact_3674_ordered__ring__class_Ole__add__iff2,axiom,
% 5.17/5.42 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % ordered_ring_class.le_add_iff2
% 5.17/5.42 thf(fact_3675_add__divide__eq__if__simps_I2_J,axiom,
% 5.17/5.42 ! [Z: complex,A: complex,B: complex] :
% 5.17/5.42 ( ( ( Z = zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.17/5.42 = B ) )
% 5.17/5.42 & ( ( Z != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_if_simps(2)
% 5.17/5.42 thf(fact_3676_add__divide__eq__if__simps_I2_J,axiom,
% 5.17/5.42 ! [Z: real,A: real,B: real] :
% 5.17/5.42 ( ( ( Z = zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.17/5.42 = B ) )
% 5.17/5.42 & ( ( Z != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_if_simps(2)
% 5.17/5.42 thf(fact_3677_add__divide__eq__if__simps_I2_J,axiom,
% 5.17/5.42 ! [Z: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( ( Z = zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.17/5.42 = B ) )
% 5.17/5.42 & ( ( Z != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_if_simps(2)
% 5.17/5.42 thf(fact_3678_add__divide__eq__if__simps_I1_J,axiom,
% 5.17/5.42 ! [Z: complex,A: complex,B: complex] :
% 5.17/5.42 ( ( ( Z = zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.17/5.42 = A ) )
% 5.17/5.42 & ( ( Z != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_if_simps(1)
% 5.17/5.42 thf(fact_3679_add__divide__eq__if__simps_I1_J,axiom,
% 5.17/5.42 ! [Z: real,A: real,B: real] :
% 5.17/5.42 ( ( ( Z = zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.17/5.42 = A ) )
% 5.17/5.42 & ( ( Z != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_if_simps(1)
% 5.17/5.42 thf(fact_3680_add__divide__eq__if__simps_I1_J,axiom,
% 5.17/5.42 ! [Z: rat,A: rat,B: rat] :
% 5.17/5.42 ( ( ( Z = zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.17/5.42 = A ) )
% 5.17/5.42 & ( ( Z != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_if_simps(1)
% 5.17/5.42 thf(fact_3681_add__frac__eq,axiom,
% 5.17/5.42 ! [Y4: complex,Z: complex,X: complex,W: complex] :
% 5.17/5.42 ( ( Y4 != zero_zero_complex )
% 5.17/5.42 => ( ( Z != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y4 ) ) @ ( times_times_complex @ Y4 @ Z ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_frac_eq
% 5.17/5.42 thf(fact_3682_add__frac__eq,axiom,
% 5.17/5.42 ! [Y4: real,Z: real,X: real,W: real] :
% 5.17/5.42 ( ( Y4 != zero_zero_real )
% 5.17/5.42 => ( ( Z != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_frac_eq
% 5.17/5.42 thf(fact_3683_add__frac__eq,axiom,
% 5.17/5.42 ! [Y4: rat,Z: rat,X: rat,W: rat] :
% 5.17/5.42 ( ( Y4 != zero_zero_rat )
% 5.17/5.42 => ( ( Z != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_frac_eq
% 5.17/5.42 thf(fact_3684_add__frac__num,axiom,
% 5.17/5.42 ! [Y4: complex,X: complex,Z: complex] :
% 5.17/5.42 ( ( Y4 != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y4 ) @ Z )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_frac_num
% 5.17/5.42 thf(fact_3685_add__frac__num,axiom,
% 5.17/5.42 ! [Y4: real,X: real,Z: real] :
% 5.17/5.42 ( ( Y4 != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y4 ) @ Z )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_frac_num
% 5.17/5.42 thf(fact_3686_add__frac__num,axiom,
% 5.17/5.42 ! [Y4: rat,X: rat,Z: rat] :
% 5.17/5.42 ( ( Y4 != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y4 ) @ Z )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_frac_num
% 5.17/5.42 thf(fact_3687_add__num__frac,axiom,
% 5.17/5.42 ! [Y4: complex,Z: complex,X: complex] :
% 5.17/5.42 ( ( Y4 != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y4 ) )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_num_frac
% 5.17/5.42 thf(fact_3688_add__num__frac,axiom,
% 5.17/5.42 ! [Y4: real,Z: real,X: real] :
% 5.17/5.42 ( ( Y4 != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_num_frac
% 5.17/5.42 thf(fact_3689_add__num__frac,axiom,
% 5.17/5.42 ! [Y4: rat,Z: rat,X: rat] :
% 5.17/5.42 ( ( Y4 != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y4 ) )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_num_frac
% 5.17/5.42 thf(fact_3690_add__divide__eq__iff,axiom,
% 5.17/5.42 ! [Z: complex,X: complex,Y4: complex] :
% 5.17/5.42 ( ( Z != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y4 @ Z ) )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_iff
% 5.17/5.42 thf(fact_3691_add__divide__eq__iff,axiom,
% 5.17/5.42 ! [Z: real,X: real,Y4: real] :
% 5.17/5.42 ( ( Z != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y4 @ Z ) )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_iff
% 5.17/5.42 thf(fact_3692_add__divide__eq__iff,axiom,
% 5.17/5.42 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.42 ( ( Z != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y4 @ Z ) )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % add_divide_eq_iff
% 5.17/5.42 thf(fact_3693_divide__add__eq__iff,axiom,
% 5.17/5.42 ! [Z: complex,X: complex,Y4: complex] :
% 5.17/5.42 ( ( Z != zero_zero_complex )
% 5.17/5.42 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y4 )
% 5.17/5.42 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % divide_add_eq_iff
% 5.17/5.42 thf(fact_3694_divide__add__eq__iff,axiom,
% 5.17/5.42 ! [Z: real,X: real,Y4: real] :
% 5.17/5.42 ( ( Z != zero_zero_real )
% 5.17/5.42 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y4 )
% 5.17/5.42 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % divide_add_eq_iff
% 5.17/5.42 thf(fact_3695_divide__add__eq__iff,axiom,
% 5.17/5.42 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.42 ( ( Z != zero_zero_rat )
% 5.17/5.42 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y4 )
% 5.17/5.42 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % divide_add_eq_iff
% 5.17/5.42 thf(fact_3696_less__add__iff1,axiom,
% 5.17/5.42 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_iff1
% 5.17/5.42 thf(fact_3697_less__add__iff1,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_iff1
% 5.17/5.42 thf(fact_3698_less__add__iff1,axiom,
% 5.17/5.42 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_iff1
% 5.17/5.42 thf(fact_3699_less__add__iff2,axiom,
% 5.17/5.42 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.42 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_iff2
% 5.17/5.42 thf(fact_3700_less__add__iff2,axiom,
% 5.17/5.42 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.17/5.42 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_iff2
% 5.17/5.42 thf(fact_3701_less__add__iff2,axiom,
% 5.17/5.42 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.17/5.42 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.17/5.42 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % less_add_iff2
% 5.17/5.42 thf(fact_3702_div__add__self2,axiom,
% 5.17/5.42 ! [B: nat,A: nat] :
% 5.17/5.42 ( ( B != zero_zero_nat )
% 5.17/5.42 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.17/5.42 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_add_self2
% 5.17/5.42 thf(fact_3703_div__add__self2,axiom,
% 5.17/5.42 ! [B: int,A: int] :
% 5.17/5.42 ( ( B != zero_zero_int )
% 5.17/5.42 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.17/5.42 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.17/5.42
% 5.17/5.42 % div_add_self2
% 5.17/5.42 thf(fact_3704_div__add__self1,axiom,
% 5.17/5.42 ! [B: nat,A: nat] :
% 5.17/5.42 ( ( B != zero_zero_nat )
% 5.17/5.42 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.17/5.43 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % div_add_self1
% 5.17/5.43 thf(fact_3705_div__add__self1,axiom,
% 5.17/5.43 ! [B: int,A: int] :
% 5.17/5.43 ( ( B != zero_zero_int )
% 5.17/5.43 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.17/5.43 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % div_add_self1
% 5.17/5.43 thf(fact_3706_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.17/5.43 ! [X: nat,N: nat,M: nat] :
% 5.17/5.43 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.17/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.43 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % VEBT_internal.exp_split_high_low(1)
% 5.17/5.43 thf(fact_3707_less__half__sum,axiom,
% 5.17/5.43 ! [A: real,B: real] :
% 5.17/5.43 ( ( ord_less_real @ A @ B )
% 5.17/5.43 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % less_half_sum
% 5.17/5.43 thf(fact_3708_less__half__sum,axiom,
% 5.17/5.43 ! [A: rat,B: rat] :
% 5.17/5.43 ( ( ord_less_rat @ A @ B )
% 5.17/5.43 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % less_half_sum
% 5.17/5.43 thf(fact_3709_gt__half__sum,axiom,
% 5.17/5.43 ! [A: real,B: real] :
% 5.17/5.43 ( ( ord_less_real @ A @ B )
% 5.17/5.43 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % gt_half_sum
% 5.17/5.43 thf(fact_3710_gt__half__sum,axiom,
% 5.17/5.43 ! [A: rat,B: rat] :
% 5.17/5.43 ( ( ord_less_rat @ A @ B )
% 5.17/5.43 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % gt_half_sum
% 5.17/5.43 thf(fact_3711_square__diff__one__factored,axiom,
% 5.17/5.43 ! [X: complex] :
% 5.17/5.43 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.17/5.43 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % square_diff_one_factored
% 5.17/5.43 thf(fact_3712_square__diff__one__factored,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.17/5.43 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % square_diff_one_factored
% 5.17/5.43 thf(fact_3713_square__diff__one__factored,axiom,
% 5.17/5.43 ! [X: rat] :
% 5.17/5.43 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.17/5.43 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % square_diff_one_factored
% 5.17/5.43 thf(fact_3714_square__diff__one__factored,axiom,
% 5.17/5.43 ! [X: int] :
% 5.17/5.43 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.17/5.43 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % square_diff_one_factored
% 5.17/5.43 thf(fact_3715_unity__coeff__ex,axiom,
% 5.17/5.43 ! [P: code_integer > $o,L: code_integer] :
% 5.17/5.43 ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X3 ) ) )
% 5.17/5.43 = ( ? [X3: code_integer] :
% 5.17/5.43 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 5.17/5.43 & ( P @ X3 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unity_coeff_ex
% 5.17/5.43 thf(fact_3716_unity__coeff__ex,axiom,
% 5.17/5.43 ! [P: complex > $o,L: complex] :
% 5.17/5.43 ( ( ? [X3: complex] : ( P @ ( times_times_complex @ L @ X3 ) ) )
% 5.17/5.43 = ( ? [X3: complex] :
% 5.17/5.43 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X3 @ zero_zero_complex ) )
% 5.17/5.43 & ( P @ X3 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unity_coeff_ex
% 5.17/5.43 thf(fact_3717_unity__coeff__ex,axiom,
% 5.17/5.43 ! [P: real > $o,L: real] :
% 5.17/5.43 ( ( ? [X3: real] : ( P @ ( times_times_real @ L @ X3 ) ) )
% 5.17/5.43 = ( ? [X3: real] :
% 5.17/5.43 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X3 @ zero_zero_real ) )
% 5.17/5.43 & ( P @ X3 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unity_coeff_ex
% 5.17/5.43 thf(fact_3718_unity__coeff__ex,axiom,
% 5.17/5.43 ! [P: rat > $o,L: rat] :
% 5.17/5.43 ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 5.17/5.43 = ( ? [X3: rat] :
% 5.17/5.43 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 5.17/5.43 & ( P @ X3 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unity_coeff_ex
% 5.17/5.43 thf(fact_3719_unity__coeff__ex,axiom,
% 5.17/5.43 ! [P: nat > $o,L: nat] :
% 5.17/5.43 ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 5.17/5.43 = ( ? [X3: nat] :
% 5.17/5.43 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 5.17/5.43 & ( P @ X3 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unity_coeff_ex
% 5.17/5.43 thf(fact_3720_unity__coeff__ex,axiom,
% 5.17/5.43 ! [P: int > $o,L: int] :
% 5.17/5.43 ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 5.17/5.43 = ( ? [X3: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 5.17/5.43 & ( P @ X3 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unity_coeff_ex
% 5.17/5.43 thf(fact_3721_inf__period_I3_J,axiom,
% 5.17/5.43 ! [D: code_integer,D3: code_integer,T: code_integer] :
% 5.17/5.43 ( ( dvd_dvd_Code_integer @ D @ D3 )
% 5.17/5.43 => ! [X5: code_integer,K4: code_integer] :
% 5.17/5.43 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) )
% 5.17/5.43 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(3)
% 5.17/5.43 thf(fact_3722_inf__period_I3_J,axiom,
% 5.17/5.43 ! [D: real,D3: real,T: real] :
% 5.17/5.43 ( ( dvd_dvd_real @ D @ D3 )
% 5.17/5.43 => ! [X5: real,K4: real] :
% 5.17/5.43 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 5.17/5.43 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(3)
% 5.17/5.43 thf(fact_3723_inf__period_I3_J,axiom,
% 5.17/5.43 ! [D: rat,D3: rat,T: rat] :
% 5.17/5.43 ( ( dvd_dvd_rat @ D @ D3 )
% 5.17/5.43 => ! [X5: rat,K4: rat] :
% 5.17/5.43 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 5.17/5.43 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(3)
% 5.17/5.43 thf(fact_3724_inf__period_I3_J,axiom,
% 5.17/5.43 ! [D: int,D3: int,T: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ D @ D3 )
% 5.17/5.43 => ! [X5: int,K4: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.17/5.43 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(3)
% 5.17/5.43 thf(fact_3725_inf__period_I4_J,axiom,
% 5.17/5.43 ! [D: code_integer,D3: code_integer,T: code_integer] :
% 5.17/5.43 ( ( dvd_dvd_Code_integer @ D @ D3 )
% 5.17/5.43 => ! [X5: code_integer,K4: code_integer] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X5 @ T ) ) )
% 5.17/5.43 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(4)
% 5.17/5.43 thf(fact_3726_inf__period_I4_J,axiom,
% 5.17/5.43 ! [D: real,D3: real,T: real] :
% 5.17/5.43 ( ( dvd_dvd_real @ D @ D3 )
% 5.17/5.43 => ! [X5: real,K4: real] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 5.17/5.43 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(4)
% 5.17/5.43 thf(fact_3727_inf__period_I4_J,axiom,
% 5.17/5.43 ! [D: rat,D3: rat,T: rat] :
% 5.17/5.43 ( ( dvd_dvd_rat @ D @ D3 )
% 5.17/5.43 => ! [X5: rat,K4: rat] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 5.17/5.43 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(4)
% 5.17/5.43 thf(fact_3728_inf__period_I4_J,axiom,
% 5.17/5.43 ! [D: int,D3: int,T: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ D @ D3 )
% 5.17/5.43 => ! [X5: int,K4: int] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 5.17/5.43 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % inf_period(4)
% 5.17/5.43 thf(fact_3729_numeral__Bit1,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.17/5.43 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.17/5.43
% 5.17/5.43 % numeral_Bit1
% 5.17/5.43 thf(fact_3730_numeral__Bit1,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.17/5.43 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.17/5.43
% 5.17/5.43 % numeral_Bit1
% 5.17/5.43 thf(fact_3731_numeral__Bit1,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.17/5.43 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.17/5.43
% 5.17/5.43 % numeral_Bit1
% 5.17/5.43 thf(fact_3732_numeral__Bit1,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.17/5.43 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % numeral_Bit1
% 5.17/5.43 thf(fact_3733_numeral__Bit1,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.17/5.43 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % numeral_Bit1
% 5.17/5.43 thf(fact_3734_nat__diff__split__asm,axiom,
% 5.17/5.43 ! [P: nat > $o,A: nat,B: nat] :
% 5.17/5.43 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.17/5.43 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.17/5.43 & ~ ( P @ zero_zero_nat ) )
% 5.17/5.43 | ? [D4: nat] :
% 5.17/5.43 ( ( A
% 5.17/5.43 = ( plus_plus_nat @ B @ D4 ) )
% 5.17/5.43 & ~ ( P @ D4 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_diff_split_asm
% 5.17/5.43 thf(fact_3735_nat__diff__split,axiom,
% 5.17/5.43 ! [P: nat > $o,A: nat,B: nat] :
% 5.17/5.43 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.17/5.43 = ( ( ( ord_less_nat @ A @ B )
% 5.17/5.43 => ( P @ zero_zero_nat ) )
% 5.17/5.43 & ! [D4: nat] :
% 5.17/5.43 ( ( A
% 5.17/5.43 = ( plus_plus_nat @ B @ D4 ) )
% 5.17/5.43 => ( P @ D4 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_diff_split
% 5.17/5.43 thf(fact_3736_less__diff__conv2,axiom,
% 5.17/5.43 ! [K: nat,J: nat,I: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ K @ J )
% 5.17/5.43 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.17/5.43 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % less_diff_conv2
% 5.17/5.43 thf(fact_3737_nat__diff__add__eq2,axiom,
% 5.17/5.43 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.43 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_diff_add_eq2
% 5.17/5.43 thf(fact_3738_nat__diff__add__eq1,axiom,
% 5.17/5.43 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ J @ I )
% 5.17/5.43 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_diff_add_eq1
% 5.17/5.43 thf(fact_3739_nat__le__add__iff2,axiom,
% 5.17/5.43 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.43 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_le_add_iff2
% 5.17/5.43 thf(fact_3740_nat__le__add__iff1,axiom,
% 5.17/5.43 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ J @ I )
% 5.17/5.43 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_le_add_iff1
% 5.17/5.43 thf(fact_3741_nat__eq__add__iff2,axiom,
% 5.17/5.43 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.43 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( M
% 5.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_eq_add_iff2
% 5.17/5.43 thf(fact_3742_nat__eq__add__iff1,axiom,
% 5.17/5.43 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ J @ I )
% 5.17/5.43 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.17/5.43 = N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_eq_add_iff1
% 5.17/5.43 thf(fact_3743_bezout__add__strong__nat,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( A != zero_zero_nat )
% 5.17/5.43 => ? [D2: nat,X4: nat,Y: nat] :
% 5.17/5.43 ( ( dvd_dvd_nat @ D2 @ A )
% 5.17/5.43 & ( dvd_dvd_nat @ D2 @ B )
% 5.17/5.43 & ( ( times_times_nat @ A @ X4 )
% 5.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % bezout_add_strong_nat
% 5.17/5.43 thf(fact_3744_convex__bound__le,axiom,
% 5.17/5.43 ! [X: rat,A: rat,Y4: rat,U: rat,V: rat] :
% 5.17/5.43 ( ( ord_less_eq_rat @ X @ A )
% 5.17/5.43 => ( ( ord_less_eq_rat @ Y4 @ A )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.17/5.43 => ( ( ( plus_plus_rat @ U @ V )
% 5.17/5.43 = one_one_rat )
% 5.17/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % convex_bound_le
% 5.17/5.43 thf(fact_3745_convex__bound__le,axiom,
% 5.17/5.43 ! [X: int,A: int,Y4: int,U: int,V: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ X @ A )
% 5.17/5.43 => ( ( ord_less_eq_int @ Y4 @ A )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.17/5.43 => ( ( ( plus_plus_int @ U @ V )
% 5.17/5.43 = one_one_int )
% 5.17/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % convex_bound_le
% 5.17/5.43 thf(fact_3746_convex__bound__le,axiom,
% 5.17/5.43 ! [X: real,A: real,Y4: real,U: real,V: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ X @ A )
% 5.17/5.43 => ( ( ord_less_eq_real @ Y4 @ A )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.17/5.43 => ( ( ( plus_plus_real @ U @ V )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % convex_bound_le
% 5.17/5.43 thf(fact_3747_mult__2,axiom,
% 5.17/5.43 ! [Z: complex] :
% 5.17/5.43 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.17/5.43 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2
% 5.17/5.43 thf(fact_3748_mult__2,axiom,
% 5.17/5.43 ! [Z: real] :
% 5.17/5.43 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.17/5.43 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2
% 5.17/5.43 thf(fact_3749_mult__2,axiom,
% 5.17/5.43 ! [Z: rat] :
% 5.17/5.43 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.17/5.43 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2
% 5.17/5.43 thf(fact_3750_mult__2,axiom,
% 5.17/5.43 ! [Z: nat] :
% 5.17/5.43 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.17/5.43 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2
% 5.17/5.43 thf(fact_3751_mult__2,axiom,
% 5.17/5.43 ! [Z: int] :
% 5.17/5.43 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.17/5.43 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2
% 5.17/5.43 thf(fact_3752_mult__2__right,axiom,
% 5.17/5.43 ! [Z: complex] :
% 5.17/5.43 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2_right
% 5.17/5.43 thf(fact_3753_mult__2__right,axiom,
% 5.17/5.43 ! [Z: real] :
% 5.17/5.43 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2_right
% 5.17/5.43 thf(fact_3754_mult__2__right,axiom,
% 5.17/5.43 ! [Z: rat] :
% 5.17/5.43 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2_right
% 5.17/5.43 thf(fact_3755_mult__2__right,axiom,
% 5.17/5.43 ! [Z: nat] :
% 5.17/5.43 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2_right
% 5.17/5.43 thf(fact_3756_mult__2__right,axiom,
% 5.17/5.43 ! [Z: int] :
% 5.17/5.43 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_2_right
% 5.17/5.43 thf(fact_3757_left__add__twice,axiom,
% 5.17/5.43 ! [A: complex,B: complex] :
% 5.17/5.43 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.17/5.43 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % left_add_twice
% 5.17/5.43 thf(fact_3758_left__add__twice,axiom,
% 5.17/5.43 ! [A: real,B: real] :
% 5.17/5.43 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.17/5.43 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % left_add_twice
% 5.17/5.43 thf(fact_3759_left__add__twice,axiom,
% 5.17/5.43 ! [A: rat,B: rat] :
% 5.17/5.43 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.43 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % left_add_twice
% 5.17/5.43 thf(fact_3760_left__add__twice,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % left_add_twice
% 5.17/5.43 thf(fact_3761_left__add__twice,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % left_add_twice
% 5.17/5.43 thf(fact_3762_field__sum__of__halves,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.43 = X ) ).
% 5.17/5.43
% 5.17/5.43 % field_sum_of_halves
% 5.17/5.43 thf(fact_3763_field__sum__of__halves,axiom,
% 5.17/5.43 ! [X: rat] :
% 5.17/5.43 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.17/5.43 = X ) ).
% 5.17/5.43
% 5.17/5.43 % field_sum_of_halves
% 5.17/5.43 thf(fact_3764_odd__even__add,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.43 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.17/5.43 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % odd_even_add
% 5.17/5.43 thf(fact_3765_odd__even__add,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.43 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.43 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % odd_even_add
% 5.17/5.43 thf(fact_3766_odd__even__add,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.43 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.17/5.43 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % odd_even_add
% 5.17/5.43 thf(fact_3767_Suc3__eq__add__3,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.17/5.43 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc3_eq_add_3
% 5.17/5.43 thf(fact_3768_nat__1__add__1,axiom,
% 5.17/5.43 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.17/5.43 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_1_add_1
% 5.17/5.43 thf(fact_3769_add__eq__if,axiom,
% 5.17/5.43 ( plus_plus_nat
% 5.17/5.43 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % add_eq_if
% 5.17/5.43 thf(fact_3770_nat__less__add__iff2,axiom,
% 5.17/5.43 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.43 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_less_add_iff2
% 5.17/5.43 thf(fact_3771_nat__less__add__iff1,axiom,
% 5.17/5.43 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ J @ I )
% 5.17/5.43 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.17/5.43 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_less_add_iff1
% 5.17/5.43 thf(fact_3772_dividend__less__times__div,axiom,
% 5.17/5.43 ! [N: nat,M: nat] :
% 5.17/5.43 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dividend_less_times_div
% 5.17/5.43 thf(fact_3773_dividend__less__div__times,axiom,
% 5.17/5.43 ! [N: nat,M: nat] :
% 5.17/5.43 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dividend_less_div_times
% 5.17/5.43 thf(fact_3774_split__div,axiom,
% 5.17/5.43 ! [P: nat > $o,M: nat,N: nat] :
% 5.17/5.43 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.43 = ( ( ( N = zero_zero_nat )
% 5.17/5.43 => ( P @ zero_zero_nat ) )
% 5.17/5.43 & ( ( N != zero_zero_nat )
% 5.17/5.43 => ! [I2: nat,J3: nat] :
% 5.17/5.43 ( ( ord_less_nat @ J3 @ N )
% 5.17/5.43 => ( ( M
% 5.17/5.43 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 5.17/5.43 => ( P @ I2 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % split_div
% 5.17/5.43 thf(fact_3775_mult__eq__if,axiom,
% 5.17/5.43 ( times_times_nat
% 5.17/5.43 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_eq_if
% 5.17/5.43 thf(fact_3776_dvd__minus__add,axiom,
% 5.17/5.43 ! [Q2: nat,N: nat,R2: nat,M: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.17/5.43 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.17/5.43 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.17/5.43 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dvd_minus_add
% 5.17/5.43 thf(fact_3777_convex__bound__lt,axiom,
% 5.17/5.43 ! [X: rat,A: rat,Y4: rat,U: rat,V: rat] :
% 5.17/5.43 ( ( ord_less_rat @ X @ A )
% 5.17/5.43 => ( ( ord_less_rat @ Y4 @ A )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.17/5.43 => ( ( ( plus_plus_rat @ U @ V )
% 5.17/5.43 = one_one_rat )
% 5.17/5.43 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % convex_bound_lt
% 5.17/5.43 thf(fact_3778_convex__bound__lt,axiom,
% 5.17/5.43 ! [X: int,A: int,Y4: int,U: int,V: int] :
% 5.17/5.43 ( ( ord_less_int @ X @ A )
% 5.17/5.43 => ( ( ord_less_int @ Y4 @ A )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.17/5.43 => ( ( ( plus_plus_int @ U @ V )
% 5.17/5.43 = one_one_int )
% 5.17/5.43 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % convex_bound_lt
% 5.17/5.43 thf(fact_3779_convex__bound__lt,axiom,
% 5.17/5.43 ! [X: real,A: real,Y4: real,U: real,V: real] :
% 5.17/5.43 ( ( ord_less_real @ X @ A )
% 5.17/5.43 => ( ( ord_less_real @ Y4 @ A )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.17/5.43 => ( ( ( plus_plus_real @ U @ V )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % convex_bound_lt
% 5.17/5.43 thf(fact_3780_scaling__mono,axiom,
% 5.17/5.43 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.17/5.43 ( ( ord_less_eq_rat @ U @ V )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.17/5.43 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.17/5.43 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % scaling_mono
% 5.17/5.43 thf(fact_3781_scaling__mono,axiom,
% 5.17/5.43 ! [U: real,V: real,R2: real,S2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ U @ V )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.17/5.43 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % scaling_mono
% 5.17/5.43 thf(fact_3782_field__less__half__sum,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.43 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % field_less_half_sum
% 5.17/5.43 thf(fact_3783_field__less__half__sum,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_rat @ X @ Y4 )
% 5.17/5.43 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % field_less_half_sum
% 5.17/5.43 thf(fact_3784_exp__add__not__zero__imp__left,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.43 != zero_zero_nat )
% 5.17/5.43 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.17/5.43 != zero_zero_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % exp_add_not_zero_imp_left
% 5.17/5.43 thf(fact_3785_exp__add__not__zero__imp__left,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.43 != zero_zero_int )
% 5.17/5.43 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.17/5.43 != zero_zero_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % exp_add_not_zero_imp_left
% 5.17/5.43 thf(fact_3786_exp__add__not__zero__imp__right,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.43 != zero_zero_nat )
% 5.17/5.43 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.43 != zero_zero_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % exp_add_not_zero_imp_right
% 5.17/5.43 thf(fact_3787_exp__add__not__zero__imp__right,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.43 != zero_zero_int )
% 5.17/5.43 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.43 != zero_zero_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % exp_add_not_zero_imp_right
% 5.17/5.43 thf(fact_3788_div__exp__eq,axiom,
% 5.17/5.43 ! [A: nat,M: nat,N: nat] :
% 5.17/5.43 ( ( 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 ) )
% 5.17/5.43 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % div_exp_eq
% 5.17/5.43 thf(fact_3789_div__exp__eq,axiom,
% 5.17/5.43 ! [A: int,M: nat,N: nat] :
% 5.17/5.43 ( ( 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 ) )
% 5.17/5.43 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % div_exp_eq
% 5.17/5.43 thf(fact_3790_nat__induct2,axiom,
% 5.17/5.43 ! [P: nat > $o,N: nat] :
% 5.17/5.43 ( ( P @ zero_zero_nat )
% 5.17/5.43 => ( ( P @ one_one_nat )
% 5.17/5.43 => ( ! [N2: nat] :
% 5.17/5.43 ( ( P @ N2 )
% 5.17/5.43 => ( P @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.43 => ( P @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_induct2
% 5.17/5.43 thf(fact_3791_Suc__div__eq__add3__div,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.17/5.43 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_div_eq_add3_div
% 5.17/5.43 thf(fact_3792_sum__power2__ge__zero,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_ge_zero
% 5.17/5.43 thf(fact_3793_sum__power2__ge__zero,axiom,
% 5.17/5.43 ! [X: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_ge_zero
% 5.17/5.43 thf(fact_3794_sum__power2__ge__zero,axiom,
% 5.17/5.43 ! [X: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_ge_zero
% 5.17/5.43 thf(fact_3795_sum__power2__le__zero__iff,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.17/5.43 = ( ( X = zero_zero_rat )
% 5.17/5.43 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_le_zero_iff
% 5.17/5.43 thf(fact_3796_sum__power2__le__zero__iff,axiom,
% 5.17/5.43 ! [X: int,Y4: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.17/5.43 = ( ( X = zero_zero_int )
% 5.17/5.43 & ( Y4 = zero_zero_int ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_le_zero_iff
% 5.17/5.43 thf(fact_3797_sum__power2__le__zero__iff,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.17/5.43 = ( ( X = zero_zero_real )
% 5.17/5.43 & ( Y4 = zero_zero_real ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_le_zero_iff
% 5.17/5.43 thf(fact_3798_not__sum__power2__lt__zero,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % not_sum_power2_lt_zero
% 5.17/5.43 thf(fact_3799_not__sum__power2__lt__zero,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.17/5.43
% 5.17/5.43 % not_sum_power2_lt_zero
% 5.17/5.43 thf(fact_3800_not__sum__power2__lt__zero,axiom,
% 5.17/5.43 ! [X: int,Y4: int] :
% 5.17/5.43 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % not_sum_power2_lt_zero
% 5.17/5.43 thf(fact_3801_sum__power2__gt__zero__iff,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.43 = ( ( X != zero_zero_real )
% 5.17/5.43 | ( Y4 != zero_zero_real ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_gt_zero_iff
% 5.17/5.43 thf(fact_3802_sum__power2__gt__zero__iff,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.43 = ( ( X != zero_zero_rat )
% 5.17/5.43 | ( Y4 != zero_zero_rat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_gt_zero_iff
% 5.17/5.43 thf(fact_3803_sum__power2__gt__zero__iff,axiom,
% 5.17/5.43 ! [X: int,Y4: int] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.43 = ( ( X != zero_zero_int )
% 5.17/5.43 | ( Y4 != zero_zero_int ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_power2_gt_zero_iff
% 5.17/5.43 thf(fact_3804_oddE,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.43 => ~ ! [B3: code_integer] :
% 5.17/5.43 ( A
% 5.17/5.43 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % oddE
% 5.17/5.43 thf(fact_3805_oddE,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.43 => ~ ! [B3: nat] :
% 5.17/5.43 ( A
% 5.17/5.43 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % oddE
% 5.17/5.43 thf(fact_3806_oddE,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.43 => ~ ! [B3: int] :
% 5.17/5.43 ( A
% 5.17/5.43 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % oddE
% 5.17/5.43 thf(fact_3807_power2__sum,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex] :
% 5.17/5.43 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_sum
% 5.17/5.43 thf(fact_3808_power2__sum,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( power_power_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_sum
% 5.17/5.43 thf(fact_3809_power2__sum,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_sum
% 5.17/5.43 thf(fact_3810_power2__sum,axiom,
% 5.17/5.43 ! [X: nat,Y4: nat] :
% 5.17/5.43 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_sum
% 5.17/5.43 thf(fact_3811_power2__sum,axiom,
% 5.17/5.43 ! [X: int,Y4: int] :
% 5.17/5.43 ( ( power_power_int @ ( plus_plus_int @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_sum
% 5.17/5.43 thf(fact_3812_real__arch__simple,axiom,
% 5.17/5.43 ! [X: rat] :
% 5.17/5.43 ? [N2: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % real_arch_simple
% 5.17/5.43 thf(fact_3813_real__arch__simple,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % real_arch_simple
% 5.17/5.43 thf(fact_3814_reals__Archimedean2,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ? [N2: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % reals_Archimedean2
% 5.17/5.43 thf(fact_3815_reals__Archimedean2,axiom,
% 5.17/5.43 ! [X: rat] :
% 5.17/5.43 ? [N2: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % reals_Archimedean2
% 5.17/5.43 thf(fact_3816_exists__least__lemma,axiom,
% 5.17/5.43 ! [P: nat > $o] :
% 5.17/5.43 ( ~ ( P @ zero_zero_nat )
% 5.17/5.43 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.17/5.43 => ? [N2: nat] :
% 5.17/5.43 ( ~ ( P @ N2 )
% 5.17/5.43 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % exists_least_lemma
% 5.17/5.43 thf(fact_3817_sum__squares__bound,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y4 ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_squares_bound
% 5.17/5.43 thf(fact_3818_sum__squares__bound,axiom,
% 5.17/5.43 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y4 ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % sum_squares_bound
% 5.17/5.43 thf(fact_3819_power2__diff,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex] :
% 5.17/5.43 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_diff
% 5.17/5.43 thf(fact_3820_power2__diff,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( power_power_real @ ( minus_minus_real @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_diff
% 5.17/5.43 thf(fact_3821_power2__diff,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_diff
% 5.17/5.43 thf(fact_3822_power2__diff,axiom,
% 5.17/5.43 ! [X: int,Y4: int] :
% 5.17/5.43 ( ( power_power_int @ ( minus_minus_int @ X @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power2_diff
% 5.17/5.43 thf(fact_3823_ex__power__ivl1,axiom,
% 5.17/5.43 ! [B: nat,K: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.43 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.17/5.43 => ? [N2: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.17/5.43 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % ex_power_ivl1
% 5.17/5.43 thf(fact_3824_ex__power__ivl2,axiom,
% 5.17/5.43 ! [B: nat,K: nat] :
% 5.17/5.43 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.43 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.17/5.43 => ? [N2: nat] :
% 5.17/5.43 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.17/5.43 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % ex_power_ivl2
% 5.17/5.43 thf(fact_3825_arith__geo__mean,axiom,
% 5.17/5.43 ! [U: rat,X: rat,Y4: rat] :
% 5.17/5.43 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( times_times_rat @ X @ Y4 ) )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.43 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.43 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % arith_geo_mean
% 5.17/5.43 thf(fact_3826_arith__geo__mean,axiom,
% 5.17/5.43 ! [U: real,X: real,Y4: real] :
% 5.17/5.43 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( times_times_real @ X @ Y4 ) )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.43 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.43 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % arith_geo_mean
% 5.17/5.43 thf(fact_3827_ex__less__of__nat__mult,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.43 => ? [N2: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % ex_less_of_nat_mult
% 5.17/5.43 thf(fact_3828_ex__less__of__nat__mult,axiom,
% 5.17/5.43 ! [X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.43 => ? [N2: nat] : ( ord_less_rat @ Y4 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % ex_less_of_nat_mult
% 5.17/5.43 thf(fact_3829_low__inv,axiom,
% 5.17/5.43 ! [X: nat,N: nat,Y4: nat] :
% 5.17/5.43 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.17/5.43 = X ) ) ).
% 5.17/5.43
% 5.17/5.43 % low_inv
% 5.17/5.43 thf(fact_3830_Bolzano,axiom,
% 5.17/5.43 ! [A: real,B: real,P: real > real > $o] :
% 5.17/5.43 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.43 => ( ! [A4: real,B3: real,C3: real] :
% 5.17/5.43 ( ( P @ A4 @ B3 )
% 5.17/5.43 => ( ( P @ B3 @ C3 )
% 5.17/5.43 => ( ( ord_less_eq_real @ A4 @ B3 )
% 5.17/5.43 => ( ( ord_less_eq_real @ B3 @ C3 )
% 5.17/5.43 => ( P @ A4 @ C3 ) ) ) ) )
% 5.17/5.43 => ( ! [X4: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.43 => ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.43 => ? [D5: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.17/5.43 & ! [A4: real,B3: real] :
% 5.17/5.43 ( ( ( ord_less_eq_real @ A4 @ X4 )
% 5.17/5.43 & ( ord_less_eq_real @ X4 @ B3 )
% 5.17/5.43 & ( ord_less_real @ ( minus_minus_real @ B3 @ A4 ) @ D5 ) )
% 5.17/5.43 => ( P @ A4 @ B3 ) ) ) ) )
% 5.17/5.43 => ( P @ A @ B ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % Bolzano
% 5.17/5.43 thf(fact_3831_mult__le__cancel__iff1,axiom,
% 5.17/5.43 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.17/5.43 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y4 @ Z ) )
% 5.17/5.43 = ( ord_less_eq_rat @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_le_cancel_iff1
% 5.17/5.43 thf(fact_3832_mult__le__cancel__iff1,axiom,
% 5.17/5.43 ! [Z: int,X: int,Y4: int] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.43 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y4 @ Z ) )
% 5.17/5.43 = ( ord_less_eq_int @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_le_cancel_iff1
% 5.17/5.43 thf(fact_3833_mult__le__cancel__iff1,axiom,
% 5.17/5.43 ! [Z: real,X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y4 @ Z ) )
% 5.17/5.43 = ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_le_cancel_iff1
% 5.17/5.43 thf(fact_3834_mult__le__cancel__iff2,axiom,
% 5.17/5.43 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.17/5.43 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y4 ) )
% 5.17/5.43 = ( ord_less_eq_rat @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_le_cancel_iff2
% 5.17/5.43 thf(fact_3835_mult__le__cancel__iff2,axiom,
% 5.17/5.43 ! [Z: int,X: int,Y4: int] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.43 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y4 ) )
% 5.17/5.43 = ( ord_less_eq_int @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_le_cancel_iff2
% 5.17/5.43 thf(fact_3836_mult__le__cancel__iff2,axiom,
% 5.17/5.43 ! [Z: real,X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y4 ) )
% 5.17/5.43 = ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_le_cancel_iff2
% 5.17/5.43 thf(fact_3837_lemma__termdiff3,axiom,
% 5.17/5.43 ! [H: real,Z: real,K5: real,N: nat] :
% 5.17/5.43 ( ( H != zero_zero_real )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H ) ) @ K5 )
% 5.17/5.43 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % lemma_termdiff3
% 5.17/5.43 thf(fact_3838_lemma__termdiff3,axiom,
% 5.17/5.43 ! [H: complex,Z: complex,K5: real,N: nat] :
% 5.17/5.43 ( ( H != zero_zero_complex )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H ) ) @ K5 )
% 5.17/5.43 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % lemma_termdiff3
% 5.17/5.43 thf(fact_3839_dbl__inc__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.17/5.43 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(3)
% 5.17/5.43 thf(fact_3840_dbl__inc__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.17/5.43 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(3)
% 5.17/5.43 thf(fact_3841_dbl__inc__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.17/5.43 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(3)
% 5.17/5.43 thf(fact_3842_dbl__inc__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.17/5.43 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(3)
% 5.17/5.43 thf(fact_3843_dbl__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.17/5.43 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(3)
% 5.17/5.43 thf(fact_3844_dbl__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.17/5.43 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(3)
% 5.17/5.43 thf(fact_3845_dbl__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.17/5.43 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(3)
% 5.17/5.43 thf(fact_3846_dbl__simps_I3_J,axiom,
% 5.17/5.43 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.17/5.43 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(3)
% 5.17/5.43 thf(fact_3847_semiring__norm_I6_J,axiom,
% 5.17/5.43 ! [M: num,N: num] :
% 5.17/5.43 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.43 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(6)
% 5.17/5.43 thf(fact_3848_dbl__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.17/5.43 = zero_zero_complex ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(2)
% 5.17/5.43 thf(fact_3849_dbl__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(2)
% 5.17/5.43 thf(fact_3850_dbl__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.17/5.43 = zero_zero_rat ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(2)
% 5.17/5.43 thf(fact_3851_dbl__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(2)
% 5.17/5.43 thf(fact_3852_semiring__norm_I2_J,axiom,
% 5.17/5.43 ( ( plus_plus_num @ one @ one )
% 5.17/5.43 = ( bit0 @ one ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(2)
% 5.17/5.43 thf(fact_3853_zle__add1__eq__le,axiom,
% 5.17/5.43 ! [W: int,Z: int] :
% 5.17/5.43 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.17/5.43 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % zle_add1_eq_le
% 5.17/5.43 thf(fact_3854_semiring__norm_I7_J,axiom,
% 5.17/5.43 ! [M: num,N: num] :
% 5.17/5.43 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.43 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(7)
% 5.17/5.43 thf(fact_3855_semiring__norm_I9_J,axiom,
% 5.17/5.43 ! [M: num,N: num] :
% 5.17/5.43 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.43 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(9)
% 5.17/5.43 thf(fact_3856_dbl__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.17/5.43 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(5)
% 5.17/5.43 thf(fact_3857_dbl__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.17/5.43 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(5)
% 5.17/5.43 thf(fact_3858_dbl__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.17/5.43 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(5)
% 5.17/5.43 thf(fact_3859_dbl__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.17/5.43 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_simps(5)
% 5.17/5.43 thf(fact_3860_dbl__inc__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.17/5.43 = one_one_complex ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(2)
% 5.17/5.43 thf(fact_3861_dbl__inc__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.17/5.43 = one_one_real ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(2)
% 5.17/5.43 thf(fact_3862_dbl__inc__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.17/5.43 = one_one_rat ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(2)
% 5.17/5.43 thf(fact_3863_dbl__inc__simps_I2_J,axiom,
% 5.17/5.43 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.17/5.43 = one_one_int ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(2)
% 5.17/5.43 thf(fact_3864_dbl__inc__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.17/5.43 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(5)
% 5.17/5.43 thf(fact_3865_dbl__inc__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.17/5.43 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(5)
% 5.17/5.43 thf(fact_3866_dbl__inc__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.17/5.43 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(5)
% 5.17/5.43 thf(fact_3867_dbl__inc__simps_I5_J,axiom,
% 5.17/5.43 ! [K: num] :
% 5.17/5.43 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.17/5.43 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_simps(5)
% 5.17/5.43 thf(fact_3868_power__add__numeral2,axiom,
% 5.17/5.43 ! [A: complex,M: num,N: num,B: complex] :
% 5.17/5.43 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.17/5.43 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral2
% 5.17/5.43 thf(fact_3869_power__add__numeral2,axiom,
% 5.17/5.43 ! [A: real,M: num,N: num,B: real] :
% 5.17/5.43 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.17/5.43 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral2
% 5.17/5.43 thf(fact_3870_power__add__numeral2,axiom,
% 5.17/5.43 ! [A: rat,M: num,N: num,B: rat] :
% 5.17/5.43 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.17/5.43 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral2
% 5.17/5.43 thf(fact_3871_power__add__numeral2,axiom,
% 5.17/5.43 ! [A: nat,M: num,N: num,B: nat] :
% 5.17/5.43 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.17/5.43 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral2
% 5.17/5.43 thf(fact_3872_power__add__numeral2,axiom,
% 5.17/5.43 ! [A: int,M: num,N: num,B: int] :
% 5.17/5.43 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.17/5.43 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral2
% 5.17/5.43 thf(fact_3873_power__add__numeral,axiom,
% 5.17/5.43 ! [A: complex,M: num,N: num] :
% 5.17/5.43 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.17/5.43 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral
% 5.17/5.43 thf(fact_3874_power__add__numeral,axiom,
% 5.17/5.43 ! [A: real,M: num,N: num] :
% 5.17/5.43 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.17/5.43 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral
% 5.17/5.43 thf(fact_3875_power__add__numeral,axiom,
% 5.17/5.43 ! [A: rat,M: num,N: num] :
% 5.17/5.43 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.17/5.43 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral
% 5.17/5.43 thf(fact_3876_power__add__numeral,axiom,
% 5.17/5.43 ! [A: nat,M: num,N: num] :
% 5.17/5.43 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.17/5.43 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral
% 5.17/5.43 thf(fact_3877_power__add__numeral,axiom,
% 5.17/5.43 ! [A: int,M: num,N: num] :
% 5.17/5.43 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.17/5.43 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_add_numeral
% 5.17/5.43 thf(fact_3878_Suc__numeral,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.17/5.43 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_numeral
% 5.17/5.43 thf(fact_3879_semiring__norm_I3_J,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.17/5.43 = ( bit1 @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(3)
% 5.17/5.43 thf(fact_3880_semiring__norm_I4_J,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.17/5.43 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(4)
% 5.17/5.43 thf(fact_3881_semiring__norm_I5_J,axiom,
% 5.17/5.43 ! [M: num] :
% 5.17/5.43 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.17/5.43 = ( bit1 @ M ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(5)
% 5.17/5.43 thf(fact_3882_semiring__norm_I8_J,axiom,
% 5.17/5.43 ! [M: num] :
% 5.17/5.43 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.17/5.43 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(8)
% 5.17/5.43 thf(fact_3883_semiring__norm_I10_J,axiom,
% 5.17/5.43 ! [M: num,N: num] :
% 5.17/5.43 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.43 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(10)
% 5.17/5.43 thf(fact_3884_semiring__norm_I16_J,axiom,
% 5.17/5.43 ! [M: num,N: num] :
% 5.17/5.43 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.43 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % semiring_norm(16)
% 5.17/5.43 thf(fact_3885_add__One__commute,axiom,
% 5.17/5.43 ! [N: num] :
% 5.17/5.43 ( ( plus_plus_num @ one @ N )
% 5.17/5.43 = ( plus_plus_num @ N @ one ) ) ).
% 5.17/5.43
% 5.17/5.43 % add_One_commute
% 5.17/5.43 thf(fact_3886_plus__int__code_I1_J,axiom,
% 5.17/5.43 ! [K: int] :
% 5.17/5.43 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.17/5.43 = K ) ).
% 5.17/5.43
% 5.17/5.43 % plus_int_code(1)
% 5.17/5.43 thf(fact_3887_plus__int__code_I2_J,axiom,
% 5.17/5.43 ! [L: int] :
% 5.17/5.43 ( ( plus_plus_int @ zero_zero_int @ L )
% 5.17/5.43 = L ) ).
% 5.17/5.43
% 5.17/5.43 % plus_int_code(2)
% 5.17/5.43 thf(fact_3888_int__distrib_I1_J,axiom,
% 5.17/5.43 ! [Z1: int,Z22: int,W: int] :
% 5.17/5.43 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_distrib(1)
% 5.17/5.43 thf(fact_3889_int__distrib_I2_J,axiom,
% 5.17/5.43 ! [W: int,Z1: int,Z22: int] :
% 5.17/5.43 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_distrib(2)
% 5.17/5.43 thf(fact_3890_iadd__is__0,axiom,
% 5.17/5.43 ! [M: extended_enat,N: extended_enat] :
% 5.17/5.43 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.17/5.43 = zero_z5237406670263579293d_enat )
% 5.17/5.43 = ( ( M = zero_z5237406670263579293d_enat )
% 5.17/5.43 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % iadd_is_0
% 5.17/5.43 thf(fact_3891_dbl__def,axiom,
% 5.17/5.43 ( neg_numeral_dbl_real
% 5.17/5.43 = ( ^ [X3: real] : ( plus_plus_real @ X3 @ X3 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_def
% 5.17/5.43 thf(fact_3892_dbl__def,axiom,
% 5.17/5.43 ( neg_numeral_dbl_rat
% 5.17/5.43 = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_def
% 5.17/5.43 thf(fact_3893_dbl__def,axiom,
% 5.17/5.43 ( neg_numeral_dbl_int
% 5.17/5.43 = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_def
% 5.17/5.43 thf(fact_3894_odd__nonzero,axiom,
% 5.17/5.43 ! [Z: int] :
% 5.17/5.43 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.17/5.43 != zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % odd_nonzero
% 5.17/5.43 thf(fact_3895_int__plus,axiom,
% 5.17/5.43 ! [N: nat,M: nat] :
% 5.17/5.43 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.43 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_plus
% 5.17/5.43 thf(fact_3896_int__ops_I5_J,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.43 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_ops(5)
% 5.17/5.43 thf(fact_3897_zadd__int__left,axiom,
% 5.17/5.43 ! [M: nat,N: nat,Z: int] :
% 5.17/5.43 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.17/5.43 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % zadd_int_left
% 5.17/5.43 thf(fact_3898_int__ge__induct,axiom,
% 5.17/5.43 ! [K: int,I: int,P: int > $o] :
% 5.17/5.43 ( ( ord_less_eq_int @ K @ I )
% 5.17/5.43 => ( ( P @ K )
% 5.17/5.43 => ( ! [I3: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ K @ I3 )
% 5.17/5.43 => ( ( P @ I3 )
% 5.17/5.43 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.17/5.43 => ( P @ I ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_ge_induct
% 5.17/5.43 thf(fact_3899_zless__add1__eq,axiom,
% 5.17/5.43 ! [W: int,Z: int] :
% 5.17/5.43 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.17/5.43 = ( ( ord_less_int @ W @ Z )
% 5.17/5.43 | ( W = Z ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % zless_add1_eq
% 5.17/5.43 thf(fact_3900_int__gr__induct,axiom,
% 5.17/5.43 ! [K: int,I: int,P: int > $o] :
% 5.17/5.43 ( ( ord_less_int @ K @ I )
% 5.17/5.43 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.17/5.43 => ( ! [I3: int] :
% 5.17/5.43 ( ( ord_less_int @ K @ I3 )
% 5.17/5.43 => ( ( P @ I3 )
% 5.17/5.43 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.17/5.43 => ( P @ I ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_gr_induct
% 5.17/5.43 thf(fact_3901_zle__iff__zadd,axiom,
% 5.17/5.43 ( ord_less_eq_int
% 5.17/5.43 = ( ^ [W3: int,Z5: int] :
% 5.17/5.43 ? [N4: nat] :
% 5.17/5.43 ( Z5
% 5.17/5.43 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % zle_iff_zadd
% 5.17/5.43 thf(fact_3902_zdvd__period,axiom,
% 5.17/5.43 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ A @ D )
% 5.17/5.43 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.17/5.43 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % zdvd_period
% 5.17/5.43 thf(fact_3903_zdvd__reduce,axiom,
% 5.17/5.43 ! [K: int,N: int,M: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.17/5.43 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % zdvd_reduce
% 5.17/5.43 thf(fact_3904_add__diff__assoc__enat,axiom,
% 5.17/5.43 ! [Z: extended_enat,Y4: extended_enat,X: extended_enat] :
% 5.17/5.43 ( ( ord_le2932123472753598470d_enat @ Z @ Y4 )
% 5.17/5.43 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y4 @ Z ) )
% 5.17/5.43 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % add_diff_assoc_enat
% 5.17/5.43 thf(fact_3905_int__Suc,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.17/5.43 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_Suc
% 5.17/5.43 thf(fact_3906_int__ops_I4_J,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.17/5.43 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_ops(4)
% 5.17/5.43 thf(fact_3907_zless__iff__Suc__zadd,axiom,
% 5.17/5.43 ( ord_less_int
% 5.17/5.43 = ( ^ [W3: int,Z5: int] :
% 5.17/5.43 ? [N4: nat] :
% 5.17/5.43 ( Z5
% 5.17/5.43 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % zless_iff_Suc_zadd
% 5.17/5.43 thf(fact_3908_odd__less__0__iff,axiom,
% 5.17/5.43 ! [Z: int] :
% 5.17/5.43 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.17/5.43 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % odd_less_0_iff
% 5.17/5.43 thf(fact_3909_add1__zle__eq,axiom,
% 5.17/5.43 ! [W: int,Z: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.17/5.43 = ( ord_less_int @ W @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % add1_zle_eq
% 5.17/5.43 thf(fact_3910_zless__imp__add1__zle,axiom,
% 5.17/5.43 ! [W: int,Z: int] :
% 5.17/5.43 ( ( ord_less_int @ W @ Z )
% 5.17/5.43 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.17/5.43
% 5.17/5.43 % zless_imp_add1_zle
% 5.17/5.43 thf(fact_3911_int__induct,axiom,
% 5.17/5.43 ! [P: int > $o,K: int,I: int] :
% 5.17/5.43 ( ( P @ K )
% 5.17/5.43 => ( ! [I3: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ K @ I3 )
% 5.17/5.43 => ( ( P @ I3 )
% 5.17/5.43 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.17/5.43 => ( ! [I3: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ I3 @ K )
% 5.17/5.43 => ( ( P @ I3 )
% 5.17/5.43 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.17/5.43 => ( P @ I ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_induct
% 5.17/5.43 thf(fact_3912_Suc__nat__number__of__add,axiom,
% 5.17/5.43 ! [V: num,N: nat] :
% 5.17/5.43 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.17/5.43 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_nat_number_of_add
% 5.17/5.43 thf(fact_3913_dbl__inc__def,axiom,
% 5.17/5.43 ( neg_nu8557863876264182079omplex
% 5.17/5.43 = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_def
% 5.17/5.43 thf(fact_3914_dbl__inc__def,axiom,
% 5.17/5.43 ( neg_nu8295874005876285629c_real
% 5.17/5.43 = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_def
% 5.17/5.43 thf(fact_3915_dbl__inc__def,axiom,
% 5.17/5.43 ( neg_nu5219082963157363817nc_rat
% 5.17/5.43 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_def
% 5.17/5.43 thf(fact_3916_dbl__inc__def,axiom,
% 5.17/5.43 ( neg_nu5851722552734809277nc_int
% 5.17/5.43 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % dbl_inc_def
% 5.17/5.43 thf(fact_3917_nat__less__real__le,axiom,
% 5.17/5.43 ( ord_less_nat
% 5.17/5.43 = ( ^ [N4: nat,M5: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N4 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M5 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_less_real_le
% 5.17/5.43 thf(fact_3918_nat__le__real__less,axiom,
% 5.17/5.43 ( ord_less_eq_nat
% 5.17/5.43 = ( ^ [N4: nat,M5: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M5 ) @ one_one_real ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nat_le_real_less
% 5.17/5.43 thf(fact_3919_le__imp__0__less,axiom,
% 5.17/5.43 ! [Z: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.43 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % le_imp_0_less
% 5.17/5.43 thf(fact_3920_unique__quotient__lemma__neg,axiom,
% 5.17/5.43 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.17/5.43 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.17/5.43 => ( ( ord_less_int @ B @ R2 )
% 5.17/5.43 => ( ( ord_less_int @ B @ R4 )
% 5.17/5.43 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unique_quotient_lemma_neg
% 5.17/5.43 thf(fact_3921_unique__quotient__lemma,axiom,
% 5.17/5.43 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.17/5.43 => ( ( ord_less_int @ R4 @ B )
% 5.17/5.43 => ( ( ord_less_int @ R2 @ B )
% 5.17/5.43 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % unique_quotient_lemma
% 5.17/5.43 thf(fact_3922_zdiv__mono2__neg__lemma,axiom,
% 5.17/5.43 ! [B: int,Q2: int,R2: int,B6: int,Q5: int,R4: int] :
% 5.17/5.43 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.17/5.43 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.17/5.43 => ( ( ord_less_int @ R2 @ B )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.17/5.43 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.17/5.43 => ( ( ord_less_eq_int @ B6 @ B )
% 5.17/5.43 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % zdiv_mono2_neg_lemma
% 5.17/5.43 thf(fact_3923_zdiv__mono2__lemma,axiom,
% 5.17/5.43 ! [B: int,Q2: int,R2: int,B6: int,Q5: int,R4: int] :
% 5.17/5.43 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.17/5.43 => ( ( ord_less_int @ R4 @ B6 )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.17/5.43 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.17/5.43 => ( ( ord_less_eq_int @ B6 @ B )
% 5.17/5.43 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % zdiv_mono2_lemma
% 5.17/5.43 thf(fact_3924_q__pos__lemma,axiom,
% 5.17/5.43 ! [B6: int,Q5: int,R4: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B6 @ Q5 ) @ R4 ) )
% 5.17/5.43 => ( ( ord_less_int @ R4 @ B6 )
% 5.17/5.43 => ( ( ord_less_int @ zero_zero_int @ B6 )
% 5.17/5.43 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % q_pos_lemma
% 5.17/5.43 thf(fact_3925_incr__mult__lemma,axiom,
% 5.17/5.43 ! [D: int,P: int > $o,K: int] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.43 => ( ! [X4: int] :
% 5.17/5.43 ( ( P @ X4 )
% 5.17/5.43 => ( P @ ( plus_plus_int @ X4 @ D ) ) )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.43 => ! [X5: int] :
% 5.17/5.43 ( ( P @ X5 )
% 5.17/5.43 => ( P @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % incr_mult_lemma
% 5.17/5.43 thf(fact_3926_linear__plus__1__le__power,axiom,
% 5.17/5.43 ! [X: real,N: nat] :
% 5.17/5.43 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % linear_plus_1_le_power
% 5.17/5.43 thf(fact_3927_even__diff__iff,axiom,
% 5.17/5.43 ! [K: int,L: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.17/5.43 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % even_diff_iff
% 5.17/5.43 thf(fact_3928_int__div__pos__eq,axiom,
% 5.17/5.43 ! [A: int,B: int,Q2: int,R2: int] :
% 5.17/5.43 ( ( A
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.17/5.43 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.17/5.43 => ( ( ord_less_int @ R2 @ B )
% 5.17/5.43 => ( ( divide_divide_int @ A @ B )
% 5.17/5.43 = Q2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_div_pos_eq
% 5.17/5.43 thf(fact_3929_int__div__neg__eq,axiom,
% 5.17/5.43 ! [A: int,B: int,Q2: int,R2: int] :
% 5.17/5.43 ( ( A
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.17/5.43 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.17/5.43 => ( ( ord_less_int @ B @ R2 )
% 5.17/5.43 => ( ( divide_divide_int @ A @ B )
% 5.17/5.43 = Q2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % int_div_neg_eq
% 5.17/5.43 thf(fact_3930_split__zdiv,axiom,
% 5.17/5.43 ! [P: int > $o,N: int,K: int] :
% 5.17/5.43 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.17/5.43 = ( ( ( K = zero_zero_int )
% 5.17/5.43 => ( P @ zero_zero_int ) )
% 5.17/5.43 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.43 => ! [I2: int,J3: int] :
% 5.17/5.43 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.17/5.43 & ( ord_less_int @ J3 @ K )
% 5.17/5.43 & ( N
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.17/5.43 => ( P @ I2 ) ) )
% 5.17/5.43 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.43 => ! [I2: int,J3: int] :
% 5.17/5.43 ( ( ( ord_less_int @ K @ J3 )
% 5.17/5.43 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.17/5.43 & ( N
% 5.17/5.43 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.17/5.43 => ( P @ I2 ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % split_zdiv
% 5.17/5.43 thf(fact_3931_div__pos__geq,axiom,
% 5.17/5.43 ! [L: int,K: int] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.43 => ( ( ord_less_eq_int @ L @ K )
% 5.17/5.43 => ( ( divide_divide_int @ K @ L )
% 5.17/5.43 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % div_pos_geq
% 5.17/5.43 thf(fact_3932_L2__set__mult__ineq__lemma,axiom,
% 5.17/5.43 ! [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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % L2_set_mult_ineq_lemma
% 5.17/5.43 thf(fact_3933_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.17/5.43 ! [X: nat,N: nat,M: nat] :
% 5.17/5.43 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.17/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.43 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % VEBT_internal.exp_split_high_low(2)
% 5.17/5.43 thf(fact_3934_neg__zdiv__mult__2,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.43 => ( ( 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 ) )
% 5.17/5.43 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % neg_zdiv_mult_2
% 5.17/5.43 thf(fact_3935_pos__zdiv__mult__2,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.43 => ( ( 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 ) )
% 5.17/5.43 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % pos_zdiv_mult_2
% 5.17/5.43 thf(fact_3936_Bernoulli__inequality__even,axiom,
% 5.17/5.43 ! [N: nat,X: real] :
% 5.17/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.43 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % Bernoulli_inequality_even
% 5.17/5.43 thf(fact_3937_mult__less__iff1,axiom,
% 5.17/5.43 ! [Z: real,X: real,Y4: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.17/5.43 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y4 @ Z ) )
% 5.17/5.43 = ( ord_less_real @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_less_iff1
% 5.17/5.43 thf(fact_3938_mult__less__iff1,axiom,
% 5.17/5.43 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.43 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.17/5.43 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y4 @ Z ) )
% 5.17/5.43 = ( ord_less_rat @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_less_iff1
% 5.17/5.43 thf(fact_3939_mult__less__iff1,axiom,
% 5.17/5.43 ! [Z: int,X: int,Y4: int] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.43 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y4 @ Z ) )
% 5.17/5.43 = ( ord_less_int @ X @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mult_less_iff1
% 5.17/5.43 thf(fact_3940_real__average__minus__second,axiom,
% 5.17/5.43 ! [B: real,A: real] :
% 5.17/5.43 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.17/5.43 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % real_average_minus_second
% 5.17/5.43 thf(fact_3941_real__average__minus__first,axiom,
% 5.17/5.43 ! [A: real,B: real] :
% 5.17/5.43 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.17/5.43 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % real_average_minus_first
% 5.17/5.43 thf(fact_3942_norm__divide__numeral,axiom,
% 5.17/5.43 ! [A: real,W: num] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.43 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_divide_numeral
% 5.17/5.43 thf(fact_3943_norm__divide__numeral,axiom,
% 5.17/5.43 ! [A: complex,W: num] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.43 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_divide_numeral
% 5.17/5.43 thf(fact_3944_norm__mult__numeral2,axiom,
% 5.17/5.43 ! [A: real,W: num] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.43 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_numeral2
% 5.17/5.43 thf(fact_3945_norm__mult__numeral2,axiom,
% 5.17/5.43 ! [A: complex,W: num] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.43 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_numeral2
% 5.17/5.43 thf(fact_3946_norm__mult__numeral1,axiom,
% 5.17/5.43 ! [W: num,A: real] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.17/5.43 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_numeral1
% 5.17/5.43 thf(fact_3947_norm__mult__numeral1,axiom,
% 5.17/5.43 ! [W: num,A: complex] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.17/5.43 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_numeral1
% 5.17/5.43 thf(fact_3948_norm__le__zero__iff,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.17/5.43 = ( X = zero_zero_real ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_le_zero_iff
% 5.17/5.43 thf(fact_3949_norm__le__zero__iff,axiom,
% 5.17/5.43 ! [X: complex] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.17/5.43 = ( X = zero_zero_complex ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_le_zero_iff
% 5.17/5.43 thf(fact_3950_zero__less__norm__iff,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 5.17/5.43 = ( X != zero_zero_real ) ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_norm_iff
% 5.17/5.43 thf(fact_3951_zero__less__norm__iff,axiom,
% 5.17/5.43 ! [X: complex] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 5.17/5.43 = ( X != zero_zero_complex ) ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_norm_iff
% 5.17/5.43 thf(fact_3952_norm__of__nat,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.43 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_of_nat
% 5.17/5.43 thf(fact_3953_norm__of__nat,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( semiri8010041392384452111omplex @ N ) )
% 5.17/5.43 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_of_nat
% 5.17/5.43 thf(fact_3954_norm__eq__zero,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ( ( ( real_V7735802525324610683m_real @ X )
% 5.17/5.43 = zero_zero_real )
% 5.17/5.43 = ( X = zero_zero_real ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_eq_zero
% 5.17/5.43 thf(fact_3955_norm__eq__zero,axiom,
% 5.17/5.43 ! [X: complex] :
% 5.17/5.43 ( ( ( real_V1022390504157884413omplex @ X )
% 5.17/5.43 = zero_zero_real )
% 5.17/5.43 = ( X = zero_zero_complex ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_eq_zero
% 5.17/5.43 thf(fact_3956_norm__zero,axiom,
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % norm_zero
% 5.17/5.43 thf(fact_3957_norm__zero,axiom,
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % norm_zero
% 5.17/5.43 thf(fact_3958_norm__numeral,axiom,
% 5.17/5.43 ! [W: num] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.43 = ( numeral_numeral_real @ W ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_numeral
% 5.17/5.43 thf(fact_3959_norm__numeral,axiom,
% 5.17/5.43 ! [W: num] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.43 = ( numeral_numeral_real @ W ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_numeral
% 5.17/5.43 thf(fact_3960_norm__minus__commute,axiom,
% 5.17/5.43 ! [A: real,B: real] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 5.17/5.43 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_minus_commute
% 5.17/5.43 thf(fact_3961_norm__minus__commute,axiom,
% 5.17/5.43 ! [A: complex,B: complex] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.17/5.43 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_minus_commute
% 5.17/5.43 thf(fact_3962_norm__triangle__mono,axiom,
% 5.17/5.43 ! [A: real,R2: real,B: real,S2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_mono
% 5.17/5.43 thf(fact_3963_norm__triangle__mono,axiom,
% 5.17/5.43 ! [A: complex,R2: real,B: complex,S2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_mono
% 5.17/5.43 thf(fact_3964_norm__triangle__ineq,axiom,
% 5.17/5.43 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_ineq
% 5.17/5.43 thf(fact_3965_norm__triangle__ineq,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_ineq
% 5.17/5.43 thf(fact_3966_norm__triangle__le,axiom,
% 5.17/5.43 ! [X: real,Y4: real,E2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) @ E2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_le
% 5.17/5.43 thf(fact_3967_norm__triangle__le,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex,E2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) @ E2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_le
% 5.17/5.43 thf(fact_3968_norm__add__leD,axiom,
% 5.17/5.43 ! [A: real,B: real,C: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_add_leD
% 5.17/5.43 thf(fact_3969_norm__add__leD,axiom,
% 5.17/5.43 ! [A: complex,B: complex,C: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_add_leD
% 5.17/5.43 thf(fact_3970_norm__diff__triangle__less,axiom,
% 5.17/5.43 ! [X: real,Y4: real,E1: real,Z: real,E22: real] :
% 5.17/5.43 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) @ E1 )
% 5.17/5.43 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y4 @ Z ) ) @ E22 )
% 5.17/5.43 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_triangle_less
% 5.17/5.43 thf(fact_3971_norm__diff__triangle__less,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex,E1: real,Z: complex,E22: real] :
% 5.17/5.43 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) @ E1 )
% 5.17/5.43 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y4 @ Z ) ) @ E22 )
% 5.17/5.43 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_triangle_less
% 5.17/5.43 thf(fact_3972_norm__triangle__sub,axiom,
% 5.17/5.43 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y4 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_sub
% 5.17/5.43 thf(fact_3973_norm__triangle__sub,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y4 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_sub
% 5.17/5.43 thf(fact_3974_norm__triangle__ineq4,axiom,
% 5.17/5.43 ! [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 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_ineq4
% 5.17/5.43 thf(fact_3975_norm__triangle__ineq4,axiom,
% 5.17/5.43 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_ineq4
% 5.17/5.43 thf(fact_3976_norm__diff__triangle__le,axiom,
% 5.17/5.43 ! [X: real,Y4: real,E1: real,Z: real,E22: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) @ E1 )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y4 @ Z ) ) @ E22 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_triangle_le
% 5.17/5.43 thf(fact_3977_norm__diff__triangle__le,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex,E1: real,Z: complex,E22: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) @ E1 )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y4 @ Z ) ) @ E22 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_triangle_le
% 5.17/5.43 thf(fact_3978_norm__triangle__le__diff,axiom,
% 5.17/5.43 ! [X: real,Y4: real,E2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y4 ) ) @ E2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_le_diff
% 5.17/5.43 thf(fact_3979_norm__triangle__le__diff,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex,E2: real] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E2 )
% 5.17/5.43 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y4 ) ) @ E2 ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_le_diff
% 5.17/5.43 thf(fact_3980_norm__not__less__zero,axiom,
% 5.17/5.43 ! [X: complex] :
% 5.17/5.43 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % norm_not_less_zero
% 5.17/5.43 thf(fact_3981_norm__ge__zero,axiom,
% 5.17/5.43 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_ge_zero
% 5.17/5.43 thf(fact_3982_norm__mult,axiom,
% 5.17/5.43 ! [X: real,Y4: real] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.43 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult
% 5.17/5.43 thf(fact_3983_norm__mult,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y4 ) )
% 5.17/5.43 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult
% 5.17/5.43 thf(fact_3984_norm__divide,axiom,
% 5.17/5.43 ! [A: real,B: real] :
% 5.17/5.43 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.43 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_divide
% 5.17/5.43 thf(fact_3985_norm__divide,axiom,
% 5.17/5.43 ! [A: complex,B: complex] :
% 5.17/5.43 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.43 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_divide
% 5.17/5.43 thf(fact_3986_norm__diff__triangle__ineq,axiom,
% 5.17/5.43 ! [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 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_triangle_ineq
% 5.17/5.43 thf(fact_3987_norm__diff__triangle__ineq,axiom,
% 5.17/5.43 ! [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 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_triangle_ineq
% 5.17/5.43 thf(fact_3988_nonzero__norm__divide,axiom,
% 5.17/5.43 ! [B: real,A: real] :
% 5.17/5.43 ( ( B != zero_zero_real )
% 5.17/5.43 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.43 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nonzero_norm_divide
% 5.17/5.43 thf(fact_3989_nonzero__norm__divide,axiom,
% 5.17/5.43 ! [B: complex,A: complex] :
% 5.17/5.43 ( ( B != zero_zero_complex )
% 5.17/5.43 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.43 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % nonzero_norm_divide
% 5.17/5.43 thf(fact_3990_power__eq__imp__eq__norm,axiom,
% 5.17/5.43 ! [W: real,N: nat,Z: real] :
% 5.17/5.43 ( ( ( power_power_real @ W @ N )
% 5.17/5.43 = ( power_power_real @ Z @ N ) )
% 5.17/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( ( real_V7735802525324610683m_real @ W )
% 5.17/5.43 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_eq_imp_eq_norm
% 5.17/5.43 thf(fact_3991_power__eq__imp__eq__norm,axiom,
% 5.17/5.43 ! [W: complex,N: nat,Z: complex] :
% 5.17/5.43 ( ( ( power_power_complex @ W @ N )
% 5.17/5.43 = ( power_power_complex @ Z @ N ) )
% 5.17/5.43 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( ( real_V1022390504157884413omplex @ W )
% 5.17/5.43 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_eq_imp_eq_norm
% 5.17/5.43 thf(fact_3992_norm__mult__less,axiom,
% 5.17/5.43 ! [X: real,R2: real,Y4: real,S2: real] :
% 5.17/5.43 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R2 )
% 5.17/5.43 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y4 ) @ S2 )
% 5.17/5.43 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y4 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_less
% 5.17/5.43 thf(fact_3993_norm__mult__less,axiom,
% 5.17/5.43 ! [X: complex,R2: real,Y4: complex,S2: real] :
% 5.17/5.43 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R2 )
% 5.17/5.43 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y4 ) @ S2 )
% 5.17/5.43 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y4 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_less
% 5.17/5.43 thf(fact_3994_norm__mult__ineq,axiom,
% 5.17/5.43 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y4 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_ineq
% 5.17/5.43 thf(fact_3995_norm__mult__ineq,axiom,
% 5.17/5.43 ! [X: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y4 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_mult_ineq
% 5.17/5.43 thf(fact_3996_norm__power__ineq,axiom,
% 5.17/5.43 ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_power_ineq
% 5.17/5.43 thf(fact_3997_norm__power__ineq,axiom,
% 5.17/5.43 ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_power_ineq
% 5.17/5.43 thf(fact_3998_norm__diff__ineq,axiom,
% 5.17/5.43 ! [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 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_ineq
% 5.17/5.43 thf(fact_3999_norm__diff__ineq,axiom,
% 5.17/5.43 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_diff_ineq
% 5.17/5.43 thf(fact_4000_norm__triangle__ineq2,axiom,
% 5.17/5.43 ! [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 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_ineq2
% 5.17/5.43 thf(fact_4001_norm__triangle__ineq2,axiom,
% 5.17/5.43 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_triangle_ineq2
% 5.17/5.43 thf(fact_4002_power__eq__1__iff,axiom,
% 5.17/5.43 ! [W: real,N: nat] :
% 5.17/5.43 ( ( ( power_power_real @ W @ N )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_eq_1_iff
% 5.17/5.43 thf(fact_4003_power__eq__1__iff,axiom,
% 5.17/5.43 ! [W: complex,N: nat] :
% 5.17/5.43 ( ( ( power_power_complex @ W @ N )
% 5.17/5.43 = one_one_complex )
% 5.17/5.43 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % power_eq_1_iff
% 5.17/5.43 thf(fact_4004_square__norm__one,axiom,
% 5.17/5.43 ! [X: real] :
% 5.17/5.43 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 => ( ( real_V7735802525324610683m_real @ X )
% 5.17/5.43 = one_one_real ) ) ).
% 5.17/5.43
% 5.17/5.43 % square_norm_one
% 5.17/5.43 thf(fact_4005_square__norm__one,axiom,
% 5.17/5.43 ! [X: complex] :
% 5.17/5.43 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_complex )
% 5.17/5.43 => ( ( real_V1022390504157884413omplex @ X )
% 5.17/5.43 = one_one_real ) ) ).
% 5.17/5.43
% 5.17/5.43 % square_norm_one
% 5.17/5.43 thf(fact_4006_norm__power__diff,axiom,
% 5.17/5.43 ! [Z: real,W: real,M: nat] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.17/5.43 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_power_diff
% 5.17/5.43 thf(fact_4007_norm__power__diff,axiom,
% 5.17/5.43 ! [Z: complex,W: complex,M: nat] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.17/5.43 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.17/5.43 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % norm_power_diff
% 5.17/5.43 thf(fact_4008_arcosh__1,axiom,
% 5.17/5.43 ( ( arcosh_real @ one_one_real )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % arcosh_1
% 5.17/5.43 thf(fact_4009_artanh__0,axiom,
% 5.17/5.43 ( ( artanh_real @ zero_zero_real )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % artanh_0
% 5.17/5.43 thf(fact_4010_arsinh__0,axiom,
% 5.17/5.43 ( ( arsinh_real @ zero_zero_real )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % arsinh_0
% 5.17/5.43 thf(fact_4011_low__def,axiom,
% 5.17/5.43 ( vEBT_VEBT_low
% 5.17/5.43 = ( ^ [X3: nat,N4: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % low_def
% 5.17/5.43 thf(fact_4012_pochhammer__double,axiom,
% 5.17/5.43 ! [Z: complex,N: nat] :
% 5.17/5.43 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( 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 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_double
% 5.17/5.43 thf(fact_4013_pochhammer__double,axiom,
% 5.17/5.43 ! [Z: real,N: nat] :
% 5.17/5.43 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( 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 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_double
% 5.17/5.43 thf(fact_4014_pochhammer__double,axiom,
% 5.17/5.43 ! [Z: rat,N: nat] :
% 5.17/5.43 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( 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 ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_double
% 5.17/5.43 thf(fact_4015_central__binomial__lower__bound,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.43 => ( 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 ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % central_binomial_lower_bound
% 5.17/5.43 thf(fact_4016_flip__bit__0,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.17/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % flip_bit_0
% 5.17/5.43 thf(fact_4017_flip__bit__0,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.17/5.43 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % flip_bit_0
% 5.17/5.43 thf(fact_4018_flip__bit__0,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.17/5.43 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % flip_bit_0
% 5.17/5.43 thf(fact_4019_mod__mod__trivial,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mod_trivial
% 5.17/5.43 thf(fact_4020_mod__mod__trivial,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mod_trivial
% 5.17/5.43 thf(fact_4021_mod__mod__trivial,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mod_trivial
% 5.17/5.43 thf(fact_4022_mod__self,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ A @ A )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_self
% 5.17/5.43 thf(fact_4023_mod__self,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ A @ A )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % mod_self
% 5.17/5.43 thf(fact_4024_mod__self,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ A @ A )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % mod_self
% 5.17/5.43 thf(fact_4025_mod__by__0,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.17/5.43 = A ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_0
% 5.17/5.43 thf(fact_4026_mod__by__0,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.17/5.43 = A ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_0
% 5.17/5.43 thf(fact_4027_mod__by__0,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.17/5.43 = A ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_0
% 5.17/5.43 thf(fact_4028_mod__0,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_0
% 5.17/5.43 thf(fact_4029_mod__0,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % mod_0
% 5.17/5.43 thf(fact_4030_mod__0,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % mod_0
% 5.17/5.43 thf(fact_4031_bits__mod__0,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_0
% 5.17/5.43 thf(fact_4032_bits__mod__0,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_0
% 5.17/5.43 thf(fact_4033_bits__mod__0,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_0
% 5.17/5.43 thf(fact_4034_mod__add__self2,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_add_self2
% 5.17/5.43 thf(fact_4035_mod__add__self2,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_add_self2
% 5.17/5.43 thf(fact_4036_mod__add__self2,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_add_self2
% 5.17/5.43 thf(fact_4037_mod__add__self1,axiom,
% 5.17/5.43 ! [B: nat,A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_add_self1
% 5.17/5.43 thf(fact_4038_mod__add__self1,axiom,
% 5.17/5.43 ! [B: int,A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_add_self1
% 5.17/5.43 thf(fact_4039_mod__add__self1,axiom,
% 5.17/5.43 ! [B: code_integer,A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_add_self1
% 5.17/5.43 thf(fact_4040_minus__mod__self2,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % minus_mod_self2
% 5.17/5.43 thf(fact_4041_minus__mod__self2,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % minus_mod_self2
% 5.17/5.43 thf(fact_4042_of__bool__less__eq__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.17/5.43 = ( P
% 5.17/5.43 => Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_eq_iff
% 5.17/5.43 thf(fact_4043_of__bool__less__eq__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.17/5.43 = ( P
% 5.17/5.43 => Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_eq_iff
% 5.17/5.43 thf(fact_4044_of__bool__less__eq__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.17/5.43 = ( P
% 5.17/5.43 => Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_eq_iff
% 5.17/5.43 thf(fact_4045_of__bool__less__eq__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.17/5.43 = ( P
% 5.17/5.43 => Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_eq_iff
% 5.17/5.43 thf(fact_4046_of__bool__less__eq__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.17/5.43 = ( P
% 5.17/5.43 => Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_eq_iff
% 5.17/5.43 thf(fact_4047_of__bool__eq__0__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.17/5.43 = zero_zero_complex )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_0_iff
% 5.17/5.43 thf(fact_4048_of__bool__eq__0__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.17/5.43 = zero_zero_real )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_0_iff
% 5.17/5.43 thf(fact_4049_of__bool__eq__0__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.17/5.43 = zero_zero_rat )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_0_iff
% 5.17/5.43 thf(fact_4050_of__bool__eq__0__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.17/5.43 = zero_zero_nat )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_0_iff
% 5.17/5.43 thf(fact_4051_of__bool__eq__0__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.17/5.43 = zero_zero_int )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_0_iff
% 5.17/5.43 thf(fact_4052_of__bool__eq__0__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n356916108424825756nteger @ P )
% 5.17/5.43 = zero_z3403309356797280102nteger )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_0_iff
% 5.17/5.43 thf(fact_4053_of__bool__eq_I1_J,axiom,
% 5.17/5.43 ( ( zero_n1201886186963655149omplex @ $false )
% 5.17/5.43 = zero_zero_complex ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(1)
% 5.17/5.43 thf(fact_4054_of__bool__eq_I1_J,axiom,
% 5.17/5.43 ( ( zero_n3304061248610475627l_real @ $false )
% 5.17/5.43 = zero_zero_real ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(1)
% 5.17/5.43 thf(fact_4055_of__bool__eq_I1_J,axiom,
% 5.17/5.43 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.17/5.43 = zero_zero_rat ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(1)
% 5.17/5.43 thf(fact_4056_of__bool__eq_I1_J,axiom,
% 5.17/5.43 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(1)
% 5.17/5.43 thf(fact_4057_of__bool__eq_I1_J,axiom,
% 5.17/5.43 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(1)
% 5.17/5.43 thf(fact_4058_of__bool__eq_I1_J,axiom,
% 5.17/5.43 ( ( zero_n356916108424825756nteger @ $false )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(1)
% 5.17/5.43 thf(fact_4059_of__bool__less__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.17/5.43 = ( ~ P
% 5.17/5.43 & Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_iff
% 5.17/5.43 thf(fact_4060_of__bool__less__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.17/5.43 = ( ~ P
% 5.17/5.43 & Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_iff
% 5.17/5.43 thf(fact_4061_of__bool__less__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.17/5.43 = ( ~ P
% 5.17/5.43 & Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_iff
% 5.17/5.43 thf(fact_4062_of__bool__less__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.17/5.43 = ( ~ P
% 5.17/5.43 & Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_iff
% 5.17/5.43 thf(fact_4063_of__bool__less__iff,axiom,
% 5.17/5.43 ! [P: $o,Q: $o] :
% 5.17/5.43 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.17/5.43 = ( ~ P
% 5.17/5.43 & Q ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_iff
% 5.17/5.43 thf(fact_4064_of__bool__eq__1__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.17/5.43 = one_one_complex )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_1_iff
% 5.17/5.43 thf(fact_4065_of__bool__eq__1__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.17/5.43 = one_one_real )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_1_iff
% 5.17/5.43 thf(fact_4066_of__bool__eq__1__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.17/5.43 = one_one_rat )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_1_iff
% 5.17/5.43 thf(fact_4067_of__bool__eq__1__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.17/5.43 = one_one_nat )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_1_iff
% 5.17/5.43 thf(fact_4068_of__bool__eq__1__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.17/5.43 = one_one_int )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_1_iff
% 5.17/5.43 thf(fact_4069_of__bool__eq__1__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ( zero_n356916108424825756nteger @ P )
% 5.17/5.43 = one_one_Code_integer )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq_1_iff
% 5.17/5.43 thf(fact_4070_of__bool__eq_I2_J,axiom,
% 5.17/5.43 ( ( zero_n1201886186963655149omplex @ $true )
% 5.17/5.43 = one_one_complex ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(2)
% 5.17/5.43 thf(fact_4071_of__bool__eq_I2_J,axiom,
% 5.17/5.43 ( ( zero_n3304061248610475627l_real @ $true )
% 5.17/5.43 = one_one_real ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(2)
% 5.17/5.43 thf(fact_4072_of__bool__eq_I2_J,axiom,
% 5.17/5.43 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.17/5.43 = one_one_rat ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(2)
% 5.17/5.43 thf(fact_4073_of__bool__eq_I2_J,axiom,
% 5.17/5.43 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.17/5.43 = one_one_nat ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(2)
% 5.17/5.43 thf(fact_4074_of__bool__eq_I2_J,axiom,
% 5.17/5.43 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.17/5.43 = one_one_int ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(2)
% 5.17/5.43 thf(fact_4075_of__bool__eq_I2_J,axiom,
% 5.17/5.43 ( ( zero_n356916108424825756nteger @ $true )
% 5.17/5.43 = one_one_Code_integer ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_eq(2)
% 5.17/5.43 thf(fact_4076_mod__less,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( ord_less_nat @ M @ N )
% 5.17/5.43 => ( ( modulo_modulo_nat @ M @ N )
% 5.17/5.43 = M ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_less
% 5.17/5.43 thf(fact_4077_of__nat__of__bool,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_nat_of_bool
% 5.17/5.43 thf(fact_4078_of__nat__of__bool,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_nat_of_bool
% 5.17/5.43 thf(fact_4079_of__nat__of__bool,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_nat_of_bool
% 5.17/5.43 thf(fact_4080_of__nat__of__bool,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_nat_of_bool
% 5.17/5.43 thf(fact_4081_of__nat__of__bool,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_nat_of_bool
% 5.17/5.43 thf(fact_4082_of__nat__of__bool,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_nat_of_bool
% 5.17/5.43 thf(fact_4083_mod__mult__self1__is__0,axiom,
% 5.17/5.43 ! [B: nat,A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self1_is_0
% 5.17/5.43 thf(fact_4084_mod__mult__self1__is__0,axiom,
% 5.17/5.43 ! [B: int,A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self1_is_0
% 5.17/5.43 thf(fact_4085_mod__mult__self1__is__0,axiom,
% 5.17/5.43 ! [B: code_integer,A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self1_is_0
% 5.17/5.43 thf(fact_4086_mod__mult__self2__is__0,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self2_is_0
% 5.17/5.43 thf(fact_4087_mod__mult__self2__is__0,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self2_is_0
% 5.17/5.43 thf(fact_4088_mod__mult__self2__is__0,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self2_is_0
% 5.17/5.43 thf(fact_4089_mod__by__1,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_1
% 5.17/5.43 thf(fact_4090_mod__by__1,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_1
% 5.17/5.43 thf(fact_4091_mod__by__1,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_1
% 5.17/5.43 thf(fact_4092_bits__mod__by__1,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_by_1
% 5.17/5.43 thf(fact_4093_bits__mod__by__1,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_by_1
% 5.17/5.43 thf(fact_4094_bits__mod__by__1,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_by_1
% 5.17/5.43 thf(fact_4095_bits__mod__div__trivial,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_div_trivial
% 5.17/5.43 thf(fact_4096_bits__mod__div__trivial,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_div_trivial
% 5.17/5.43 thf(fact_4097_bits__mod__div__trivial,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % bits_mod_div_trivial
% 5.17/5.43 thf(fact_4098_mod__div__trivial,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_div_trivial
% 5.17/5.43 thf(fact_4099_mod__div__trivial,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % mod_div_trivial
% 5.17/5.43 thf(fact_4100_mod__div__trivial,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % mod_div_trivial
% 5.17/5.43 thf(fact_4101_mod__mult__self4,axiom,
% 5.17/5.43 ! [B: nat,C: nat,A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self4
% 5.17/5.43 thf(fact_4102_mod__mult__self4,axiom,
% 5.17/5.43 ! [B: int,C: int,A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self4
% 5.17/5.43 thf(fact_4103_mod__mult__self4,axiom,
% 5.17/5.43 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self4
% 5.17/5.43 thf(fact_4104_mod__mult__self3,axiom,
% 5.17/5.43 ! [C: nat,B: nat,A: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self3
% 5.17/5.43 thf(fact_4105_mod__mult__self3,axiom,
% 5.17/5.43 ! [C: int,B: int,A: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self3
% 5.17/5.43 thf(fact_4106_mod__mult__self3,axiom,
% 5.17/5.43 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self3
% 5.17/5.43 thf(fact_4107_mod__mult__self2,axiom,
% 5.17/5.43 ! [A: nat,B: nat,C: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self2
% 5.17/5.43 thf(fact_4108_mod__mult__self2,axiom,
% 5.17/5.43 ! [A: int,B: int,C: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self2
% 5.17/5.43 thf(fact_4109_mod__mult__self2,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self2
% 5.17/5.43 thf(fact_4110_mod__mult__self1,axiom,
% 5.17/5.43 ! [A: nat,C: nat,B: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.17/5.43 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self1
% 5.17/5.43 thf(fact_4111_mod__mult__self1,axiom,
% 5.17/5.43 ! [A: int,C: int,B: int] :
% 5.17/5.43 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.17/5.43 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self1
% 5.17/5.43 thf(fact_4112_mod__mult__self1,axiom,
% 5.17/5.43 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.17/5.43 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_mult_self1
% 5.17/5.43 thf(fact_4113_dvd__imp__mod__0,axiom,
% 5.17/5.43 ! [A: nat,B: nat] :
% 5.17/5.43 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.43 => ( ( modulo_modulo_nat @ B @ A )
% 5.17/5.43 = zero_zero_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % dvd_imp_mod_0
% 5.17/5.43 thf(fact_4114_dvd__imp__mod__0,axiom,
% 5.17/5.43 ! [A: int,B: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.43 => ( ( modulo_modulo_int @ B @ A )
% 5.17/5.43 = zero_zero_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % dvd_imp_mod_0
% 5.17/5.43 thf(fact_4115_dvd__imp__mod__0,axiom,
% 5.17/5.43 ! [A: code_integer,B: code_integer] :
% 5.17/5.43 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.17/5.43 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.43
% 5.17/5.43 % dvd_imp_mod_0
% 5.17/5.43 thf(fact_4116_zero__less__of__bool__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_of_bool_iff
% 5.17/5.43 thf(fact_4117_zero__less__of__bool__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_of_bool_iff
% 5.17/5.43 thf(fact_4118_zero__less__of__bool__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_of_bool_iff
% 5.17/5.43 thf(fact_4119_zero__less__of__bool__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_of_bool_iff
% 5.17/5.43 thf(fact_4120_zero__less__of__bool__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.17/5.43 = P ) ).
% 5.17/5.43
% 5.17/5.43 % zero_less_of_bool_iff
% 5.17/5.43 thf(fact_4121_of__bool__less__one__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_one_iff
% 5.17/5.43 thf(fact_4122_of__bool__less__one__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_one_iff
% 5.17/5.43 thf(fact_4123_of__bool__less__one__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_one_iff
% 5.17/5.43 thf(fact_4124_of__bool__less__one__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_one_iff
% 5.17/5.43 thf(fact_4125_of__bool__less__one__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.17/5.43 = ~ P ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_less_one_iff
% 5.17/5.43 thf(fact_4126_of__bool__not__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.17/5.43 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_not_iff
% 5.17/5.43 thf(fact_4127_of__bool__not__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.17/5.43 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_not_iff
% 5.17/5.43 thf(fact_4128_of__bool__not__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.17/5.43 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_not_iff
% 5.17/5.43 thf(fact_4129_of__bool__not__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.17/5.43 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_not_iff
% 5.17/5.43 thf(fact_4130_of__bool__not__iff,axiom,
% 5.17/5.43 ! [P: $o] :
% 5.17/5.43 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.17/5.43 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_not_iff
% 5.17/5.43 thf(fact_4131_Suc__0__mod__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.43 = ( zero_n2687167440665602831ol_nat
% 5.17/5.43 @ ( N
% 5.17/5.43 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_0_mod_eq
% 5.17/5.43 thf(fact_4132_mod__by__Suc__0,axiom,
% 5.17/5.43 ! [M: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % mod_by_Suc_0
% 5.17/5.43 thf(fact_4133_pochhammer__0,axiom,
% 5.17/5.43 ! [A: complex] :
% 5.17/5.43 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.17/5.43 = one_one_complex ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_0
% 5.17/5.43 thf(fact_4134_pochhammer__0,axiom,
% 5.17/5.43 ! [A: real] :
% 5.17/5.43 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.17/5.43 = one_one_real ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_0
% 5.17/5.43 thf(fact_4135_pochhammer__0,axiom,
% 5.17/5.43 ! [A: rat] :
% 5.17/5.43 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.17/5.43 = one_one_rat ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_0
% 5.17/5.43 thf(fact_4136_pochhammer__0,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.17/5.43 = one_one_nat ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_0
% 5.17/5.43 thf(fact_4137_pochhammer__0,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.17/5.43 = one_one_int ) ).
% 5.17/5.43
% 5.17/5.43 % pochhammer_0
% 5.17/5.43 thf(fact_4138_Suc__mod__mult__self1,axiom,
% 5.17/5.43 ! [M: nat,K: nat,N: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.17/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_mod_mult_self1
% 5.17/5.43 thf(fact_4139_Suc__mod__mult__self2,axiom,
% 5.17/5.43 ! [M: nat,N: nat,K: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.17/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_mod_mult_self2
% 5.17/5.43 thf(fact_4140_Suc__mod__mult__self3,axiom,
% 5.17/5.43 ! [K: nat,N: nat,M: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.17/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_mod_mult_self3
% 5.17/5.43 thf(fact_4141_Suc__mod__mult__self4,axiom,
% 5.17/5.43 ! [N: nat,K: nat,M: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.17/5.43 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_mod_mult_self4
% 5.17/5.43 thf(fact_4142_bits__one__mod__two__eq__one,axiom,
% 5.17/5.43 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_nat ) ).
% 5.17/5.43
% 5.17/5.43 % bits_one_mod_two_eq_one
% 5.17/5.43 thf(fact_4143_bits__one__mod__two__eq__one,axiom,
% 5.17/5.43 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_int ) ).
% 5.17/5.43
% 5.17/5.43 % bits_one_mod_two_eq_one
% 5.17/5.43 thf(fact_4144_bits__one__mod__two__eq__one,axiom,
% 5.17/5.43 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_Code_integer ) ).
% 5.17/5.43
% 5.17/5.43 % bits_one_mod_two_eq_one
% 5.17/5.43 thf(fact_4145_one__mod__two__eq__one,axiom,
% 5.17/5.43 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_nat ) ).
% 5.17/5.43
% 5.17/5.43 % one_mod_two_eq_one
% 5.17/5.43 thf(fact_4146_one__mod__two__eq__one,axiom,
% 5.17/5.43 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_int ) ).
% 5.17/5.43
% 5.17/5.43 % one_mod_two_eq_one
% 5.17/5.43 thf(fact_4147_one__mod__two__eq__one,axiom,
% 5.17/5.43 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_Code_integer ) ).
% 5.17/5.43
% 5.17/5.43 % one_mod_two_eq_one
% 5.17/5.43 thf(fact_4148_even__mod__2__iff,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.43 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.43
% 5.17/5.43 % even_mod_2_iff
% 5.17/5.43 thf(fact_4149_even__mod__2__iff,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.17/5.43 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.43
% 5.17/5.43 % even_mod_2_iff
% 5.17/5.43 thf(fact_4150_even__mod__2__iff,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.17/5.43 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.43
% 5.17/5.43 % even_mod_2_iff
% 5.17/5.43 thf(fact_4151_odd__of__bool__self,axiom,
% 5.17/5.43 ! [P5: $o] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P5 ) ) )
% 5.17/5.43 = P5 ) ).
% 5.17/5.43
% 5.17/5.43 % odd_of_bool_self
% 5.17/5.43 thf(fact_4152_odd__of__bool__self,axiom,
% 5.17/5.43 ! [P5: $o] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P5 ) ) )
% 5.17/5.43 = P5 ) ).
% 5.17/5.43
% 5.17/5.43 % odd_of_bool_self
% 5.17/5.43 thf(fact_4153_odd__of__bool__self,axiom,
% 5.17/5.43 ! [P5: $o] :
% 5.17/5.43 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P5 ) ) )
% 5.17/5.43 = P5 ) ).
% 5.17/5.43
% 5.17/5.43 % odd_of_bool_self
% 5.17/5.43 thf(fact_4154_mod2__Suc__Suc,axiom,
% 5.17/5.43 ! [M: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod2_Suc_Suc
% 5.17/5.43 thf(fact_4155_Suc__times__numeral__mod__eq,axiom,
% 5.17/5.43 ! [K: num,N: nat] :
% 5.17/5.43 ( ( ( numeral_numeral_nat @ K )
% 5.17/5.43 != one_one_nat )
% 5.17/5.43 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.43 = one_one_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_times_numeral_mod_eq
% 5.17/5.43 thf(fact_4156_not__mod__2__eq__1__eq__0,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 != one_one_nat )
% 5.17/5.43 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_zero_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod_2_eq_1_eq_0
% 5.17/5.43 thf(fact_4157_not__mod__2__eq__1__eq__0,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 != one_one_int )
% 5.17/5.43 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_zero_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod_2_eq_1_eq_0
% 5.17/5.43 thf(fact_4158_not__mod__2__eq__1__eq__0,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 != one_one_Code_integer )
% 5.17/5.43 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod_2_eq_1_eq_0
% 5.17/5.43 thf(fact_4159_not__mod__2__eq__0__eq__1,axiom,
% 5.17/5.43 ! [A: nat] :
% 5.17/5.43 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 != zero_zero_nat )
% 5.17/5.43 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod_2_eq_0_eq_1
% 5.17/5.43 thf(fact_4160_not__mod__2__eq__0__eq__1,axiom,
% 5.17/5.43 ! [A: int] :
% 5.17/5.43 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 != zero_zero_int )
% 5.17/5.43 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_int ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod_2_eq_0_eq_1
% 5.17/5.43 thf(fact_4161_not__mod__2__eq__0__eq__1,axiom,
% 5.17/5.43 ! [A: code_integer] :
% 5.17/5.43 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 != zero_z3403309356797280102nteger )
% 5.17/5.43 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_Code_integer ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod_2_eq_0_eq_1
% 5.17/5.43 thf(fact_4162_of__bool__half__eq__0,axiom,
% 5.17/5.43 ! [B: $o] :
% 5.17/5.43 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_half_eq_0
% 5.17/5.43 thf(fact_4163_of__bool__half__eq__0,axiom,
% 5.17/5.43 ! [B: $o] :
% 5.17/5.43 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_zero_int ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_half_eq_0
% 5.17/5.43 thf(fact_4164_of__bool__half__eq__0,axiom,
% 5.17/5.43 ! [B: $o] :
% 5.17/5.43 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_z3403309356797280102nteger ) ).
% 5.17/5.43
% 5.17/5.43 % of_bool_half_eq_0
% 5.17/5.43 thf(fact_4165_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 != ( suc @ zero_zero_nat ) )
% 5.17/5.43 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_zero_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % not_mod2_eq_Suc_0_eq_0
% 5.17/5.43 thf(fact_4166_add__self__mod__2,axiom,
% 5.17/5.43 ! [M: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = zero_zero_nat ) ).
% 5.17/5.43
% 5.17/5.43 % add_self_mod_2
% 5.17/5.43 thf(fact_4167_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.17/5.43 ! [M: nat,V: num] :
% 5.17/5.43 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.43 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % Suc_mod_eq_add3_mod_numeral
% 5.17/5.43 thf(fact_4168_mod__Suc__eq__mod__add3,axiom,
% 5.17/5.43 ! [M: nat,N: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.17/5.43 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod_Suc_eq_mod_add3
% 5.17/5.43 thf(fact_4169_mod2__gr__0,axiom,
% 5.17/5.43 ! [M: nat] :
% 5.17/5.43 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.43 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.43 = one_one_nat ) ) ).
% 5.17/5.43
% 5.17/5.43 % mod2_gr_0
% 5.17/5.43 thf(fact_4170_bits__1__div__exp,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % bits_1_div_exp
% 5.17/5.43 thf(fact_4171_bits__1__div__exp,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % bits_1_div_exp
% 5.17/5.43 thf(fact_4172_bits__1__div__exp,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % bits_1_div_exp
% 5.17/5.43 thf(fact_4173_one__div__2__pow__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % one_div_2_pow_eq
% 5.17/5.43 thf(fact_4174_one__div__2__pow__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % one_div_2_pow_eq
% 5.17/5.43 thf(fact_4175_one__div__2__pow__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % one_div_2_pow_eq
% 5.17/5.43 thf(fact_4176_one__mod__2__pow__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % one_mod_2_pow_eq
% 5.17/5.43 thf(fact_4177_one__mod__2__pow__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % one_mod_2_pow_eq
% 5.17/5.43 thf(fact_4178_one__mod__2__pow__eq,axiom,
% 5.17/5.43 ! [N: nat] :
% 5.17/5.43 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.43 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.43
% 5.17/5.43 % one_mod_2_pow_eq
% 5.17/5.43 thf(fact_4179_even__succ__mod__exp,axiom,
% 5.17/5.43 ! [A: nat,N: nat] :
% 5.17/5.43 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_succ_mod_exp
% 5.17/5.44 thf(fact_4180_even__succ__mod__exp,axiom,
% 5.17/5.44 ! [A: int,N: nat] :
% 5.17/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_succ_mod_exp
% 5.17/5.44 thf(fact_4181_even__succ__mod__exp,axiom,
% 5.17/5.44 ! [A: code_integer,N: nat] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_succ_mod_exp
% 5.17/5.44 thf(fact_4182_of__bool__eq__iff,axiom,
% 5.17/5.44 ! [P5: $o,Q2: $o] :
% 5.17/5.44 ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 5.17/5.44 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.17/5.44 = ( P5 = Q2 ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_eq_iff
% 5.17/5.44 thf(fact_4183_of__bool__eq__iff,axiom,
% 5.17/5.44 ! [P5: $o,Q2: $o] :
% 5.17/5.44 ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 5.17/5.44 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.17/5.44 = ( P5 = Q2 ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_eq_iff
% 5.17/5.44 thf(fact_4184_of__bool__eq__iff,axiom,
% 5.17/5.44 ! [P5: $o,Q2: $o] :
% 5.17/5.44 ( ( ( zero_n356916108424825756nteger @ P5 )
% 5.17/5.44 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.17/5.44 = ( P5 = Q2 ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_eq_iff
% 5.17/5.44 thf(fact_4185_of__nat__mod,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_nat_mod
% 5.17/5.44 thf(fact_4186_of__nat__mod,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_nat_mod
% 5.17/5.44 thf(fact_4187_of__nat__mod,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_nat_mod
% 5.17/5.44 thf(fact_4188_pochhammer__of__nat,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( comm_s2602460028002588243omplex @ ( semiri8010041392384452111omplex @ X ) @ N )
% 5.17/5.44 = ( semiri8010041392384452111omplex @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_of_nat
% 5.17/5.44 thf(fact_4189_pochhammer__of__nat,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( comm_s7457072308508201937r_real @ ( semiri5074537144036343181t_real @ X ) @ N )
% 5.17/5.44 = ( semiri5074537144036343181t_real @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_of_nat
% 5.17/5.44 thf(fact_4190_pochhammer__of__nat,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( comm_s4028243227959126397er_rat @ ( semiri681578069525770553at_rat @ X ) @ N )
% 5.17/5.44 = ( semiri681578069525770553at_rat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_of_nat
% 5.17/5.44 thf(fact_4191_pochhammer__of__nat,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( comm_s4663373288045622133er_nat @ ( semiri1316708129612266289at_nat @ X ) @ N )
% 5.17/5.44 = ( semiri1316708129612266289at_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_of_nat
% 5.17/5.44 thf(fact_4192_pochhammer__of__nat,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( comm_s4660882817536571857er_int @ ( semiri1314217659103216013at_int @ X ) @ N )
% 5.17/5.44 = ( semiri1314217659103216013at_int @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_of_nat
% 5.17/5.44 thf(fact_4193_mod__mult__right__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat,C: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_right_eq
% 5.17/5.44 thf(fact_4194_mod__mult__right__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,C: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_right_eq
% 5.17/5.44 thf(fact_4195_mod__mult__right__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_right_eq
% 5.17/5.44 thf(fact_4196_mod__mult__left__eq,axiom,
% 5.17/5.44 ! [A: nat,C: nat,B: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_left_eq
% 5.17/5.44 thf(fact_4197_mod__mult__left__eq,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_left_eq
% 5.17/5.44 thf(fact_4198_mod__mult__left__eq,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_left_eq
% 5.17/5.44 thf(fact_4199_mult__mod__right,axiom,
% 5.17/5.44 ! [C: nat,A: nat,B: nat] :
% 5.17/5.44 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mult_mod_right
% 5.17/5.44 thf(fact_4200_mult__mod__right,axiom,
% 5.17/5.44 ! [C: int,A: int,B: int] :
% 5.17/5.44 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mult_mod_right
% 5.17/5.44 thf(fact_4201_mult__mod__right,axiom,
% 5.17/5.44 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mult_mod_right
% 5.17/5.44 thf(fact_4202_mod__mult__mult2,axiom,
% 5.17/5.44 ! [A: nat,C: nat,B: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.17/5.44 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_mult2
% 5.17/5.44 thf(fact_4203_mod__mult__mult2,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.17/5.44 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_mult2
% 5.17/5.44 thf(fact_4204_mod__mult__mult2,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.44 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_mult2
% 5.17/5.44 thf(fact_4205_mod__mult__cong,axiom,
% 5.17/5.44 ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ A @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( times_times_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_cong
% 5.17/5.44 thf(fact_4206_mod__mult__cong,axiom,
% 5.17/5.44 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ C )
% 5.17/5.44 = ( modulo_modulo_int @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo_modulo_int @ B @ C )
% 5.17/5.44 = ( modulo_modulo_int @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( times_times_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_cong
% 5.17/5.44 thf(fact_4207_mod__mult__cong,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,A6: code_integer,B: code_integer,B6: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_cong
% 5.17/5.44 thf(fact_4208_mod__mult__eq,axiom,
% 5.17/5.44 ! [A: nat,C: nat,B: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_eq
% 5.17/5.44 thf(fact_4209_mod__mult__eq,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_eq
% 5.17/5.44 thf(fact_4210_mod__mult__eq,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_eq
% 5.17/5.44 thf(fact_4211_mod__add__right__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat,C: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_right_eq
% 5.17/5.44 thf(fact_4212_mod__add__right__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,C: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_right_eq
% 5.17/5.44 thf(fact_4213_mod__add__right__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_right_eq
% 5.17/5.44 thf(fact_4214_mod__add__left__eq,axiom,
% 5.17/5.44 ! [A: nat,C: nat,B: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_left_eq
% 5.17/5.44 thf(fact_4215_mod__add__left__eq,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_left_eq
% 5.17/5.44 thf(fact_4216_mod__add__left__eq,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_left_eq
% 5.17/5.44 thf(fact_4217_mod__add__cong,axiom,
% 5.17/5.44 ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ A @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_cong
% 5.17/5.44 thf(fact_4218_mod__add__cong,axiom,
% 5.17/5.44 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ C )
% 5.17/5.44 = ( modulo_modulo_int @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo_modulo_int @ B @ C )
% 5.17/5.44 = ( modulo_modulo_int @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_cong
% 5.17/5.44 thf(fact_4219_mod__add__cong,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,A6: code_integer,B: code_integer,B6: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_cong
% 5.17/5.44 thf(fact_4220_mod__add__eq,axiom,
% 5.17/5.44 ! [A: nat,C: nat,B: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_eq
% 5.17/5.44 thf(fact_4221_mod__add__eq,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_eq
% 5.17/5.44 thf(fact_4222_mod__add__eq,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_add_eq
% 5.17/5.44 thf(fact_4223_mod__diff__right__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,C: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_right_eq
% 5.17/5.44 thf(fact_4224_mod__diff__right__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_right_eq
% 5.17/5.44 thf(fact_4225_mod__diff__left__eq,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_left_eq
% 5.17/5.44 thf(fact_4226_mod__diff__left__eq,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_left_eq
% 5.17/5.44 thf(fact_4227_mod__diff__cong,axiom,
% 5.17/5.44 ! [A: int,C: int,A6: int,B: int,B6: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ C )
% 5.17/5.44 = ( modulo_modulo_int @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo_modulo_int @ B @ C )
% 5.17/5.44 = ( modulo_modulo_int @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( minus_minus_int @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_cong
% 5.17/5.44 thf(fact_4228_mod__diff__cong,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,A6: code_integer,B: code_integer,B6: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A6 @ C ) )
% 5.17/5.44 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ B6 @ C ) )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A6 @ B6 ) @ C ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_cong
% 5.17/5.44 thf(fact_4229_mod__diff__eq,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_eq
% 5.17/5.44 thf(fact_4230_mod__diff__eq,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_diff_eq
% 5.17/5.44 thf(fact_4231_of__bool__conj,axiom,
% 5.17/5.44 ! [P: $o,Q: $o] :
% 5.17/5.44 ( ( zero_n3304061248610475627l_real
% 5.17/5.44 @ ( P
% 5.17/5.44 & Q ) )
% 5.17/5.44 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_conj
% 5.17/5.44 thf(fact_4232_of__bool__conj,axiom,
% 5.17/5.44 ! [P: $o,Q: $o] :
% 5.17/5.44 ( ( zero_n2052037380579107095ol_rat
% 5.17/5.44 @ ( P
% 5.17/5.44 & Q ) )
% 5.17/5.44 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_conj
% 5.17/5.44 thf(fact_4233_of__bool__conj,axiom,
% 5.17/5.44 ! [P: $o,Q: $o] :
% 5.17/5.44 ( ( zero_n2687167440665602831ol_nat
% 5.17/5.44 @ ( P
% 5.17/5.44 & Q ) )
% 5.17/5.44 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_conj
% 5.17/5.44 thf(fact_4234_of__bool__conj,axiom,
% 5.17/5.44 ! [P: $o,Q: $o] :
% 5.17/5.44 ( ( zero_n2684676970156552555ol_int
% 5.17/5.44 @ ( P
% 5.17/5.44 & Q ) )
% 5.17/5.44 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_conj
% 5.17/5.44 thf(fact_4235_of__bool__conj,axiom,
% 5.17/5.44 ! [P: $o,Q: $o] :
% 5.17/5.44 ( ( zero_n356916108424825756nteger
% 5.17/5.44 @ ( P
% 5.17/5.44 & Q ) )
% 5.17/5.44 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_conj
% 5.17/5.44 thf(fact_4236_power__mod,axiom,
% 5.17/5.44 ! [A: nat,B: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.17/5.44 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % power_mod
% 5.17/5.44 thf(fact_4237_power__mod,axiom,
% 5.17/5.44 ! [A: int,B: int,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.17/5.44 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % power_mod
% 5.17/5.44 thf(fact_4238_power__mod,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,N: nat] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % power_mod
% 5.17/5.44 thf(fact_4239_dvd__mod,axiom,
% 5.17/5.44 ! [K: nat,M: nat,N: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ K @ M )
% 5.17/5.44 => ( ( dvd_dvd_nat @ K @ N )
% 5.17/5.44 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod
% 5.17/5.44 thf(fact_4240_dvd__mod,axiom,
% 5.17/5.44 ! [K: int,M: int,N: int] :
% 5.17/5.44 ( ( dvd_dvd_int @ K @ M )
% 5.17/5.44 => ( ( dvd_dvd_int @ K @ N )
% 5.17/5.44 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod
% 5.17/5.44 thf(fact_4241_dvd__mod,axiom,
% 5.17/5.44 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.17/5.44 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.17/5.44 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod
% 5.17/5.44 thf(fact_4242_mod__mod__cancel,axiom,
% 5.17/5.44 ! [C: nat,B: nat,A: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mod_cancel
% 5.17/5.44 thf(fact_4243_mod__mod__cancel,axiom,
% 5.17/5.44 ! [C: int,B: int,A: int] :
% 5.17/5.44 ( ( dvd_dvd_int @ C @ B )
% 5.17/5.44 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.17/5.44 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mod_cancel
% 5.17/5.44 thf(fact_4244_mod__mod__cancel,axiom,
% 5.17/5.44 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mod_cancel
% 5.17/5.44 thf(fact_4245_dvd__mod__iff,axiom,
% 5.17/5.44 ! [C: nat,B: nat,A: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.44 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod_iff
% 5.17/5.44 thf(fact_4246_dvd__mod__iff,axiom,
% 5.17/5.44 ! [C: int,B: int,A: int] :
% 5.17/5.44 ( ( dvd_dvd_int @ C @ B )
% 5.17/5.44 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod_iff
% 5.17/5.44 thf(fact_4247_dvd__mod__iff,axiom,
% 5.17/5.44 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.44 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod_iff
% 5.17/5.44 thf(fact_4248_dvd__mod__imp__dvd,axiom,
% 5.17/5.44 ! [C: nat,A: nat,B: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 => ( ( dvd_dvd_nat @ C @ B )
% 5.17/5.44 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod_imp_dvd
% 5.17/5.44 thf(fact_4249_dvd__mod__imp__dvd,axiom,
% 5.17/5.44 ! [C: int,A: int,B: int] :
% 5.17/5.44 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 => ( ( dvd_dvd_int @ C @ B )
% 5.17/5.44 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod_imp_dvd
% 5.17/5.44 thf(fact_4250_dvd__mod__imp__dvd,axiom,
% 5.17/5.44 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.17/5.44 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_mod_imp_dvd
% 5.17/5.44 thf(fact_4251_mod__Suc__Suc__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_Suc_Suc_eq
% 5.17/5.44 thf(fact_4252_mod__Suc__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_Suc_eq
% 5.17/5.44 thf(fact_4253_mod__less__eq__dividend,axiom,
% 5.17/5.44 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.17/5.44
% 5.17/5.44 % mod_less_eq_dividend
% 5.17/5.44 thf(fact_4254_of__bool__odd__eq__mod__2,axiom,
% 5.17/5.44 ! [A: nat] :
% 5.17/5.44 ( ( zero_n2687167440665602831ol_nat
% 5.17/5.44 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.44 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_odd_eq_mod_2
% 5.17/5.44 thf(fact_4255_of__bool__odd__eq__mod__2,axiom,
% 5.17/5.44 ! [A: int] :
% 5.17/5.44 ( ( zero_n2684676970156552555ol_int
% 5.17/5.44 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.44 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_odd_eq_mod_2
% 5.17/5.44 thf(fact_4256_of__bool__odd__eq__mod__2,axiom,
% 5.17/5.44 ! [A: code_integer] :
% 5.17/5.44 ( ( zero_n356916108424825756nteger
% 5.17/5.44 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_odd_eq_mod_2
% 5.17/5.44 thf(fact_4257_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.44 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.17/5.44 thf(fact_4258_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.44 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.17/5.44 thf(fact_4259_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.44 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.17/5.44 thf(fact_4260_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.17/5.44 ! [B: nat,A: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.44 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.17/5.44 thf(fact_4261_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.17/5.44 thf(fact_4262_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.44 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.17/5.44 thf(fact_4263_zero__less__eq__of__bool,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_eq_of_bool
% 5.17/5.44 thf(fact_4264_zero__less__eq__of__bool,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_eq_of_bool
% 5.17/5.44 thf(fact_4265_zero__less__eq__of__bool,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_eq_of_bool
% 5.17/5.44 thf(fact_4266_zero__less__eq__of__bool,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_eq_of_bool
% 5.17/5.44 thf(fact_4267_zero__less__eq__of__bool,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_eq_of_bool
% 5.17/5.44 thf(fact_4268_mod__eq__self__iff__div__eq__0,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ A @ B )
% 5.17/5.44 = A )
% 5.17/5.44 = ( ( divide_divide_nat @ A @ B )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_self_iff_div_eq_0
% 5.17/5.44 thf(fact_4269_mod__eq__self__iff__div__eq__0,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = A )
% 5.17/5.44 = ( ( divide_divide_int @ A @ B )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_self_iff_div_eq_0
% 5.17/5.44 thf(fact_4270_mod__eq__self__iff__div__eq__0,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.17/5.44 = A )
% 5.17/5.44 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_self_iff_div_eq_0
% 5.17/5.44 thf(fact_4271_cong__exp__iff__simps_I9_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(9)
% 5.17/5.44 thf(fact_4272_cong__exp__iff__simps_I9_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(9)
% 5.17/5.44 thf(fact_4273_cong__exp__iff__simps_I9_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(9)
% 5.17/5.44 thf(fact_4274_cong__exp__iff__simps_I4_J,axiom,
% 5.17/5.44 ! [M: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(4)
% 5.17/5.44 thf(fact_4275_cong__exp__iff__simps_I4_J,axiom,
% 5.17/5.44 ! [M: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(4)
% 5.17/5.44 thf(fact_4276_cong__exp__iff__simps_I4_J,axiom,
% 5.17/5.44 ! [M: num,N: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(4)
% 5.17/5.44 thf(fact_4277_mod__eqE,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ C )
% 5.17/5.44 = ( modulo_modulo_int @ B @ C ) )
% 5.17/5.44 => ~ ! [D2: int] :
% 5.17/5.44 ( B
% 5.17/5.44 != ( plus_plus_int @ A @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eqE
% 5.17/5.44 thf(fact_4278_mod__eqE,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.17/5.44 => ~ ! [D2: code_integer] :
% 5.17/5.44 ( B
% 5.17/5.44 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eqE
% 5.17/5.44 thf(fact_4279_mod__eq__0__iff__dvd,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ A @ B )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_0_iff_dvd
% 5.17/5.44 thf(fact_4280_mod__eq__0__iff__dvd,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_0_iff_dvd
% 5.17/5.44 thf(fact_4281_mod__eq__0__iff__dvd,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.17/5.44 = zero_z3403309356797280102nteger )
% 5.17/5.44 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_0_iff_dvd
% 5.17/5.44 thf(fact_4282_dvd__eq__mod__eq__0,axiom,
% 5.17/5.44 ( dvd_dvd_nat
% 5.17/5.44 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ B2 @ A3 )
% 5.17/5.44 = zero_zero_nat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_eq_mod_eq_0
% 5.17/5.44 thf(fact_4283_dvd__eq__mod__eq__0,axiom,
% 5.17/5.44 ( dvd_dvd_int
% 5.17/5.44 = ( ^ [A3: int,B2: int] :
% 5.17/5.44 ( ( modulo_modulo_int @ B2 @ A3 )
% 5.17/5.44 = zero_zero_int ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_eq_mod_eq_0
% 5.17/5.44 thf(fact_4284_dvd__eq__mod__eq__0,axiom,
% 5.17/5.44 ( dvd_dvd_Code_integer
% 5.17/5.44 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_eq_mod_eq_0
% 5.17/5.44 thf(fact_4285_mod__0__imp__dvd,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ A @ B )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_0_imp_dvd
% 5.17/5.44 thf(fact_4286_mod__0__imp__dvd,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_0_imp_dvd
% 5.17/5.44 thf(fact_4287_mod__0__imp__dvd,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.17/5.44 = zero_z3403309356797280102nteger )
% 5.17/5.44 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_0_imp_dvd
% 5.17/5.44 thf(fact_4288_div__add1__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat,C: nat] :
% 5.17/5.44 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_add1_eq
% 5.17/5.44 thf(fact_4289_div__add1__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,C: int] :
% 5.17/5.44 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_add1_eq
% 5.17/5.44 thf(fact_4290_div__add1__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.44 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_add1_eq
% 5.17/5.44 thf(fact_4291_of__bool__less__eq__one,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_less_eq_one
% 5.17/5.44 thf(fact_4292_of__bool__less__eq__one,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_less_eq_one
% 5.17/5.44 thf(fact_4293_of__bool__less__eq__one,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_less_eq_one
% 5.17/5.44 thf(fact_4294_of__bool__less__eq__one,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_less_eq_one
% 5.17/5.44 thf(fact_4295_of__bool__less__eq__one,axiom,
% 5.17/5.44 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_less_eq_one
% 5.17/5.44 thf(fact_4296_split__of__bool__asm,axiom,
% 5.17/5.44 ! [P: complex > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 5.17/5.44 = ( ~ ( ( P5
% 5.17/5.44 & ~ ( P @ one_one_complex ) )
% 5.17/5.44 | ( ~ P5
% 5.17/5.44 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool_asm
% 5.17/5.44 thf(fact_4297_split__of__bool__asm,axiom,
% 5.17/5.44 ! [P: real > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 5.17/5.44 = ( ~ ( ( P5
% 5.17/5.44 & ~ ( P @ one_one_real ) )
% 5.17/5.44 | ( ~ P5
% 5.17/5.44 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool_asm
% 5.17/5.44 thf(fact_4298_split__of__bool__asm,axiom,
% 5.17/5.44 ! [P: rat > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 5.17/5.44 = ( ~ ( ( P5
% 5.17/5.44 & ~ ( P @ one_one_rat ) )
% 5.17/5.44 | ( ~ P5
% 5.17/5.44 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool_asm
% 5.17/5.44 thf(fact_4299_split__of__bool__asm,axiom,
% 5.17/5.44 ! [P: nat > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 5.17/5.44 = ( ~ ( ( P5
% 5.17/5.44 & ~ ( P @ one_one_nat ) )
% 5.17/5.44 | ( ~ P5
% 5.17/5.44 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool_asm
% 5.17/5.44 thf(fact_4300_split__of__bool__asm,axiom,
% 5.17/5.44 ! [P: int > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 5.17/5.44 = ( ~ ( ( P5
% 5.17/5.44 & ~ ( P @ one_one_int ) )
% 5.17/5.44 | ( ~ P5
% 5.17/5.44 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool_asm
% 5.17/5.44 thf(fact_4301_split__of__bool__asm,axiom,
% 5.17/5.44 ! [P: code_integer > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 5.17/5.44 = ( ~ ( ( P5
% 5.17/5.44 & ~ ( P @ one_one_Code_integer ) )
% 5.17/5.44 | ( ~ P5
% 5.17/5.44 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool_asm
% 5.17/5.44 thf(fact_4302_split__of__bool,axiom,
% 5.17/5.44 ! [P: complex > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 5.17/5.44 = ( ( P5
% 5.17/5.44 => ( P @ one_one_complex ) )
% 5.17/5.44 & ( ~ P5
% 5.17/5.44 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool
% 5.17/5.44 thf(fact_4303_split__of__bool,axiom,
% 5.17/5.44 ! [P: real > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 5.17/5.44 = ( ( P5
% 5.17/5.44 => ( P @ one_one_real ) )
% 5.17/5.44 & ( ~ P5
% 5.17/5.44 => ( P @ zero_zero_real ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool
% 5.17/5.44 thf(fact_4304_split__of__bool,axiom,
% 5.17/5.44 ! [P: rat > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 5.17/5.44 = ( ( P5
% 5.17/5.44 => ( P @ one_one_rat ) )
% 5.17/5.44 & ( ~ P5
% 5.17/5.44 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool
% 5.17/5.44 thf(fact_4305_split__of__bool,axiom,
% 5.17/5.44 ! [P: nat > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 5.17/5.44 = ( ( P5
% 5.17/5.44 => ( P @ one_one_nat ) )
% 5.17/5.44 & ( ~ P5
% 5.17/5.44 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool
% 5.17/5.44 thf(fact_4306_split__of__bool,axiom,
% 5.17/5.44 ! [P: int > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 5.17/5.44 = ( ( P5
% 5.17/5.44 => ( P @ one_one_int ) )
% 5.17/5.44 & ( ~ P5
% 5.17/5.44 => ( P @ zero_zero_int ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool
% 5.17/5.44 thf(fact_4307_split__of__bool,axiom,
% 5.17/5.44 ! [P: code_integer > $o,P5: $o] :
% 5.17/5.44 ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 5.17/5.44 = ( ( P5
% 5.17/5.44 => ( P @ one_one_Code_integer ) )
% 5.17/5.44 & ( ~ P5
% 5.17/5.44 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_of_bool
% 5.17/5.44 thf(fact_4308_of__bool__def,axiom,
% 5.17/5.44 ( zero_n1201886186963655149omplex
% 5.17/5.44 = ( ^ [P6: $o] : ( if_complex @ P6 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_def
% 5.17/5.44 thf(fact_4309_of__bool__def,axiom,
% 5.17/5.44 ( zero_n3304061248610475627l_real
% 5.17/5.44 = ( ^ [P6: $o] : ( if_real @ P6 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_def
% 5.17/5.44 thf(fact_4310_of__bool__def,axiom,
% 5.17/5.44 ( zero_n2052037380579107095ol_rat
% 5.17/5.44 = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_def
% 5.17/5.44 thf(fact_4311_of__bool__def,axiom,
% 5.17/5.44 ( zero_n2687167440665602831ol_nat
% 5.17/5.44 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_def
% 5.17/5.44 thf(fact_4312_of__bool__def,axiom,
% 5.17/5.44 ( zero_n2684676970156552555ol_int
% 5.17/5.44 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_def
% 5.17/5.44 thf(fact_4313_of__bool__def,axiom,
% 5.17/5.44 ( zero_n356916108424825756nteger
% 5.17/5.44 = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_bool_def
% 5.17/5.44 thf(fact_4314_mod__eq__dvd__iff,axiom,
% 5.17/5.44 ! [A: int,C: int,B: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ A @ C )
% 5.17/5.44 = ( modulo_modulo_int @ B @ C ) )
% 5.17/5.44 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_dvd_iff
% 5.17/5.44 thf(fact_4315_mod__eq__dvd__iff,axiom,
% 5.17/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.17/5.44 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.17/5.44 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_dvd_iff
% 5.17/5.44 thf(fact_4316_dvd__minus__mod,axiom,
% 5.17/5.44 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_minus_mod
% 5.17/5.44 thf(fact_4317_dvd__minus__mod,axiom,
% 5.17/5.44 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_minus_mod
% 5.17/5.44 thf(fact_4318_dvd__minus__mod,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % dvd_minus_mod
% 5.17/5.44 thf(fact_4319_mod__Suc,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 = N )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.17/5.44 = zero_zero_nat ) )
% 5.17/5.44 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 != N )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.17/5.44 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_Suc
% 5.17/5.44 thf(fact_4320_mod__induct,axiom,
% 5.17/5.44 ! [P: nat > $o,N: nat,P5: nat,M: nat] :
% 5.17/5.44 ( ( P @ N )
% 5.17/5.44 => ( ( ord_less_nat @ N @ P5 )
% 5.17/5.44 => ( ( ord_less_nat @ M @ P5 )
% 5.17/5.44 => ( ! [N2: nat] :
% 5.17/5.44 ( ( ord_less_nat @ N2 @ P5 )
% 5.17/5.44 => ( ( P @ N2 )
% 5.17/5.44 => ( P @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P5 ) ) ) )
% 5.17/5.44 => ( P @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_induct
% 5.17/5.44 thf(fact_4321_mod__less__divisor,axiom,
% 5.17/5.44 ! [N: nat,M: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_less_divisor
% 5.17/5.44 thf(fact_4322_gcd__nat__induct,axiom,
% 5.17/5.44 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.17/5.44 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.17/5.44 => ( ! [M4: nat,N2: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.44 => ( ( P @ N2 @ ( modulo_modulo_nat @ M4 @ N2 ) )
% 5.17/5.44 => ( P @ M4 @ N2 ) ) )
% 5.17/5.44 => ( P @ M @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % gcd_nat_induct
% 5.17/5.44 thf(fact_4323_mod__Suc__le__divisor,axiom,
% 5.17/5.44 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.17/5.44
% 5.17/5.44 % mod_Suc_le_divisor
% 5.17/5.44 thf(fact_4324_mod__eq__0D,axiom,
% 5.17/5.44 ! [M: nat,D: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ M @ D )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 => ? [Q4: nat] :
% 5.17/5.44 ( M
% 5.17/5.44 = ( times_times_nat @ D @ Q4 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_0D
% 5.17/5.44 thf(fact_4325_mod__if,axiom,
% 5.17/5.44 ( modulo_modulo_nat
% 5.17/5.44 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( ord_less_nat @ M5 @ N4 ) @ M5 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_if
% 5.17/5.44 thf(fact_4326_mod__geq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ~ ( ord_less_nat @ M @ N )
% 5.17/5.44 => ( ( modulo_modulo_nat @ M @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_geq
% 5.17/5.44 thf(fact_4327_le__mod__geq,axiom,
% 5.17/5.44 ! [N: nat,M: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( modulo_modulo_nat @ M @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % le_mod_geq
% 5.17/5.44 thf(fact_4328_nat__mod__eq__iff,axiom,
% 5.17/5.44 ! [X: nat,N: nat,Y4: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ X @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ Y4 @ N ) )
% 5.17/5.44 = ( ? [Q1: nat,Q22: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 5.17/5.44 = ( plus_plus_nat @ Y4 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % nat_mod_eq_iff
% 5.17/5.44 thf(fact_4329_pochhammer__pos,axiom,
% 5.17/5.44 ! [X: real,N: nat] :
% 5.17/5.44 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.44 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_pos
% 5.17/5.44 thf(fact_4330_pochhammer__pos,axiom,
% 5.17/5.44 ! [X: rat,N: nat] :
% 5.17/5.44 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.44 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_pos
% 5.17/5.44 thf(fact_4331_pochhammer__pos,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.44 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_pos
% 5.17/5.44 thf(fact_4332_pochhammer__pos,axiom,
% 5.17/5.44 ! [X: int,N: nat] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ X )
% 5.17/5.44 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_pos
% 5.17/5.44 thf(fact_4333_pochhammer__eq__0__mono,axiom,
% 5.17/5.44 ! [A: complex,N: nat,M: nat] :
% 5.17/5.44 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.17/5.44 = zero_zero_complex )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.17/5.44 = zero_zero_complex ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_eq_0_mono
% 5.17/5.44 thf(fact_4334_pochhammer__eq__0__mono,axiom,
% 5.17/5.44 ! [A: real,N: nat,M: nat] :
% 5.17/5.44 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.17/5.44 = zero_zero_real )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.17/5.44 = zero_zero_real ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_eq_0_mono
% 5.17/5.44 thf(fact_4335_pochhammer__eq__0__mono,axiom,
% 5.17/5.44 ! [A: rat,N: nat,M: nat] :
% 5.17/5.44 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.17/5.44 = zero_zero_rat )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.17/5.44 = zero_zero_rat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_eq_0_mono
% 5.17/5.44 thf(fact_4336_pochhammer__neq__0__mono,axiom,
% 5.17/5.44 ! [A: complex,M: nat,N: nat] :
% 5.17/5.44 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.17/5.44 != zero_zero_complex )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.17/5.44 != zero_zero_complex ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_neq_0_mono
% 5.17/5.44 thf(fact_4337_pochhammer__neq__0__mono,axiom,
% 5.17/5.44 ! [A: real,M: nat,N: nat] :
% 5.17/5.44 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.17/5.44 != zero_zero_real )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.17/5.44 != zero_zero_real ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_neq_0_mono
% 5.17/5.44 thf(fact_4338_pochhammer__neq__0__mono,axiom,
% 5.17/5.44 ! [A: rat,M: nat,N: nat] :
% 5.17/5.44 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.17/5.44 != zero_zero_rat )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.17/5.44 != zero_zero_rat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_neq_0_mono
% 5.17/5.44 thf(fact_4339_exp__mod__exp,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % exp_mod_exp
% 5.17/5.44 thf(fact_4340_exp__mod__exp,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % exp_mod_exp
% 5.17/5.44 thf(fact_4341_exp__mod__exp,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % exp_mod_exp
% 5.17/5.44 thf(fact_4342_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.44 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.17/5.44 thf(fact_4343_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.17/5.44 ! [B: nat,A: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.17/5.44 thf(fact_4344_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.17/5.44 thf(fact_4345_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.44 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.17/5.44 = A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_less
% 5.17/5.44 thf(fact_4346_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.44 => ( ( ord_less_nat @ A @ B )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ B )
% 5.17/5.44 = A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_less
% 5.17/5.44 thf(fact_4347_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.44 => ( ( ord_less_int @ A @ B )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_less
% 5.17/5.44 thf(fact_4348_cong__exp__iff__simps_I2_J,axiom,
% 5.17/5.44 ! [N: num,Q2: num] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(2)
% 5.17/5.44 thf(fact_4349_cong__exp__iff__simps_I2_J,axiom,
% 5.17/5.44 ! [N: num,Q2: num] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(2)
% 5.17/5.44 thf(fact_4350_cong__exp__iff__simps_I2_J,axiom,
% 5.17/5.44 ! [N: num,Q2: num] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = zero_z3403309356797280102nteger )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(2)
% 5.17/5.44 thf(fact_4351_cong__exp__iff__simps_I1_J,axiom,
% 5.17/5.44 ! [N: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.17/5.44 = zero_zero_nat ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(1)
% 5.17/5.44 thf(fact_4352_cong__exp__iff__simps_I1_J,axiom,
% 5.17/5.44 ! [N: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.17/5.44 = zero_zero_int ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(1)
% 5.17/5.44 thf(fact_4353_cong__exp__iff__simps_I1_J,axiom,
% 5.17/5.44 ! [N: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(1)
% 5.17/5.44 thf(fact_4354_cong__exp__iff__simps_I6_J,axiom,
% 5.17/5.44 ! [Q2: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(6)
% 5.17/5.44 thf(fact_4355_cong__exp__iff__simps_I6_J,axiom,
% 5.17/5.44 ! [Q2: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(6)
% 5.17/5.44 thf(fact_4356_cong__exp__iff__simps_I6_J,axiom,
% 5.17/5.44 ! [Q2: num,N: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(6)
% 5.17/5.44 thf(fact_4357_cong__exp__iff__simps_I8_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(8)
% 5.17/5.44 thf(fact_4358_cong__exp__iff__simps_I8_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(8)
% 5.17/5.44 thf(fact_4359_cong__exp__iff__simps_I8_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(8)
% 5.17/5.44 thf(fact_4360_div__mult1__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat,C: nat] :
% 5.17/5.44 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_mult1_eq
% 5.17/5.44 thf(fact_4361_div__mult1__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,C: int] :
% 5.17/5.44 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_mult1_eq
% 5.17/5.44 thf(fact_4362_div__mult1__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.44 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_mult1_eq
% 5.17/5.44 thf(fact_4363_mult__div__mod__eq,axiom,
% 5.17/5.44 ! [B: nat,A: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mult_div_mod_eq
% 5.17/5.44 thf(fact_4364_mult__div__mod__eq,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mult_div_mod_eq
% 5.17/5.44 thf(fact_4365_mult__div__mod__eq,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mult_div_mod_eq
% 5.17/5.44 thf(fact_4366_mod__mult__div__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_div_eq
% 5.17/5.44 thf(fact_4367_mod__mult__div__eq,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_div_eq
% 5.17/5.44 thf(fact_4368_mod__mult__div__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult_div_eq
% 5.17/5.44 thf(fact_4369_mod__div__mult__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mod_div_mult_eq
% 5.17/5.44 thf(fact_4370_mod__div__mult__eq,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mod_div_mult_eq
% 5.17/5.44 thf(fact_4371_mod__div__mult__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % mod_div_mult_eq
% 5.17/5.44 thf(fact_4372_div__mult__mod__eq,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % div_mult_mod_eq
% 5.17/5.44 thf(fact_4373_div__mult__mod__eq,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % div_mult_mod_eq
% 5.17/5.44 thf(fact_4374_div__mult__mod__eq,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 = A ) ).
% 5.17/5.44
% 5.17/5.44 % div_mult_mod_eq
% 5.17/5.44 thf(fact_4375_mod__div__decomp,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( A
% 5.17/5.44 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_div_decomp
% 5.17/5.44 thf(fact_4376_mod__div__decomp,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( A
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_div_decomp
% 5.17/5.44 thf(fact_4377_mod__div__decomp,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( A
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_div_decomp
% 5.17/5.44 thf(fact_4378_cancel__div__mod__rules_I1_J,axiom,
% 5.17/5.44 ! [A: nat,B: nat,C: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.17/5.44 = ( plus_plus_nat @ A @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % cancel_div_mod_rules(1)
% 5.17/5.44 thf(fact_4379_cancel__div__mod__rules_I1_J,axiom,
% 5.17/5.44 ! [A: int,B: int,C: int] :
% 5.17/5.44 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.17/5.44 = ( plus_plus_int @ A @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % cancel_div_mod_rules(1)
% 5.17/5.44 thf(fact_4380_cancel__div__mod__rules_I1_J,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.17/5.44 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % cancel_div_mod_rules(1)
% 5.17/5.44 thf(fact_4381_cancel__div__mod__rules_I2_J,axiom,
% 5.17/5.44 ! [B: nat,A: nat,C: nat] :
% 5.17/5.44 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.17/5.44 = ( plus_plus_nat @ A @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % cancel_div_mod_rules(2)
% 5.17/5.44 thf(fact_4382_cancel__div__mod__rules_I2_J,axiom,
% 5.17/5.44 ! [B: int,A: int,C: int] :
% 5.17/5.44 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.17/5.44 = ( plus_plus_int @ A @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % cancel_div_mod_rules(2)
% 5.17/5.44 thf(fact_4383_cancel__div__mod__rules_I2_J,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.17/5.44 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % cancel_div_mod_rules(2)
% 5.17/5.44 thf(fact_4384_unit__imp__mod__eq__0,axiom,
% 5.17/5.44 ! [B: nat,A: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ B )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % unit_imp_mod_eq_0
% 5.17/5.44 thf(fact_4385_unit__imp__mod__eq__0,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % unit_imp_mod_eq_0
% 5.17/5.44 thf(fact_4386_unit__imp__mod__eq__0,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % unit_imp_mod_eq_0
% 5.17/5.44 thf(fact_4387_minus__mult__div__eq__mod,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.17/5.44 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mult_div_eq_mod
% 5.17/5.44 thf(fact_4388_minus__mult__div__eq__mod,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.17/5.44 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mult_div_eq_mod
% 5.17/5.44 thf(fact_4389_minus__mult__div__eq__mod,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mult_div_eq_mod
% 5.17/5.44 thf(fact_4390_minus__mod__eq__mult__div,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mod_eq_mult_div
% 5.17/5.44 thf(fact_4391_minus__mod__eq__mult__div,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mod_eq_mult_div
% 5.17/5.44 thf(fact_4392_minus__mod__eq__mult__div,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mod_eq_mult_div
% 5.17/5.44 thf(fact_4393_minus__mod__eq__div__mult,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mod_eq_div_mult
% 5.17/5.44 thf(fact_4394_minus__mod__eq__div__mult,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mod_eq_div_mult
% 5.17/5.44 thf(fact_4395_minus__mod__eq__div__mult,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.17/5.44 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_mod_eq_div_mult
% 5.17/5.44 thf(fact_4396_minus__div__mult__eq__mod,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.17/5.44 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_div_mult_eq_mod
% 5.17/5.44 thf(fact_4397_minus__div__mult__eq__mod,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.17/5.44 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_div_mult_eq_mod
% 5.17/5.44 thf(fact_4398_minus__div__mult__eq__mod,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.17/5.44
% 5.17/5.44 % minus_div_mult_eq_mod
% 5.17/5.44 thf(fact_4399_cong__exp__iff__simps_I10_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(10)
% 5.17/5.44 thf(fact_4400_cong__exp__iff__simps_I10_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(10)
% 5.17/5.44 thf(fact_4401_cong__exp__iff__simps_I10_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(10)
% 5.17/5.44 thf(fact_4402_cong__exp__iff__simps_I12_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(12)
% 5.17/5.44 thf(fact_4403_cong__exp__iff__simps_I12_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(12)
% 5.17/5.44 thf(fact_4404_cong__exp__iff__simps_I12_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(12)
% 5.17/5.44 thf(fact_4405_cong__exp__iff__simps_I13_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(13)
% 5.17/5.44 thf(fact_4406_cong__exp__iff__simps_I13_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(13)
% 5.17/5.44 thf(fact_4407_cong__exp__iff__simps_I13_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(13)
% 5.17/5.44 thf(fact_4408_mod__le__divisor,axiom,
% 5.17/5.44 ! [N: nat,M: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_le_divisor
% 5.17/5.44 thf(fact_4409_mod__greater__zero__iff__not__dvd,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_greater_zero_iff_not_dvd
% 5.17/5.44 thf(fact_4410_div__less__mono,axiom,
% 5.17/5.44 ! [A2: nat,B4: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ A2 @ B4 )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_less_mono
% 5.17/5.44 thf(fact_4411_mod__eq__nat1E,axiom,
% 5.17/5.44 ! [M: nat,Q2: nat,N: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.17/5.44 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ~ ! [S3: nat] :
% 5.17/5.44 ( M
% 5.17/5.44 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_nat1E
% 5.17/5.44 thf(fact_4412_mod__eq__nat2E,axiom,
% 5.17/5.44 ! [M: nat,Q2: nat,N: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.17/5.44 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.17/5.44 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ~ ! [S3: nat] :
% 5.17/5.44 ( N
% 5.17/5.44 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_nat2E
% 5.17/5.44 thf(fact_4413_nat__mod__eq__lemma,axiom,
% 5.17/5.44 ! [X: nat,N: nat,Y4: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ X @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ Y4 @ N ) )
% 5.17/5.44 => ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.44 => ? [Q4: nat] :
% 5.17/5.44 ( X
% 5.17/5.44 = ( plus_plus_nat @ Y4 @ ( times_times_nat @ N @ Q4 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % nat_mod_eq_lemma
% 5.17/5.44 thf(fact_4414_pochhammer__nonneg,axiom,
% 5.17/5.44 ! [X: rat,N: nat] :
% 5.17/5.44 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.44 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_nonneg
% 5.17/5.44 thf(fact_4415_pochhammer__nonneg,axiom,
% 5.17/5.44 ! [X: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.17/5.44 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_nonneg
% 5.17/5.44 thf(fact_4416_pochhammer__nonneg,axiom,
% 5.17/5.44 ! [X: int,N: nat] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ X )
% 5.17/5.44 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_nonneg
% 5.17/5.44 thf(fact_4417_pochhammer__nonneg,axiom,
% 5.17/5.44 ! [X: real,N: nat] :
% 5.17/5.44 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.44 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_nonneg
% 5.17/5.44 thf(fact_4418_mod__eq__dvd__iff__nat,axiom,
% 5.17/5.44 ! [N: nat,M: nat,Q2: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.44 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.17/5.44 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.17/5.44 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_eq_dvd_iff_nat
% 5.17/5.44 thf(fact_4419_mod__mult2__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.17/5.44 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult2_eq
% 5.17/5.44 thf(fact_4420_div__mod__decomp,axiom,
% 5.17/5.44 ! [A2: nat,N: nat] :
% 5.17/5.44 ( A2
% 5.17/5.44 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_mod_decomp
% 5.17/5.44 thf(fact_4421_modulo__nat__def,axiom,
% 5.17/5.44 ( modulo_modulo_nat
% 5.17/5.44 = ( ^ [M5: nat,N4: nat] : ( minus_minus_nat @ M5 @ ( times_times_nat @ ( divide_divide_nat @ M5 @ N4 ) @ N4 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % modulo_nat_def
% 5.17/5.44 thf(fact_4422_pochhammer__0__left,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( N = zero_zero_nat )
% 5.17/5.44 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.17/5.44 = one_one_complex ) )
% 5.17/5.44 & ( ( N != zero_zero_nat )
% 5.17/5.44 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.17/5.44 = zero_zero_complex ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_0_left
% 5.17/5.44 thf(fact_4423_pochhammer__0__left,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( N = zero_zero_nat )
% 5.17/5.44 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.17/5.44 = one_one_real ) )
% 5.17/5.44 & ( ( N != zero_zero_nat )
% 5.17/5.44 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.17/5.44 = zero_zero_real ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_0_left
% 5.17/5.44 thf(fact_4424_pochhammer__0__left,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( N = zero_zero_nat )
% 5.17/5.44 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.17/5.44 = one_one_rat ) )
% 5.17/5.44 & ( ( N != zero_zero_nat )
% 5.17/5.44 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.17/5.44 = zero_zero_rat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_0_left
% 5.17/5.44 thf(fact_4425_pochhammer__0__left,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( N = zero_zero_nat )
% 5.17/5.44 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.17/5.44 = one_one_nat ) )
% 5.17/5.44 & ( ( N != zero_zero_nat )
% 5.17/5.44 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.17/5.44 = zero_zero_nat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_0_left
% 5.17/5.44 thf(fact_4426_pochhammer__0__left,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( N = zero_zero_nat )
% 5.17/5.44 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.17/5.44 = one_one_int ) )
% 5.17/5.44 & ( ( N != zero_zero_nat )
% 5.17/5.44 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.17/5.44 = zero_zero_int ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_0_left
% 5.17/5.44 thf(fact_4427_cong__exp__iff__simps_I3_J,axiom,
% 5.17/5.44 ! [N: num,Q2: num] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != zero_zero_nat ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(3)
% 5.17/5.44 thf(fact_4428_cong__exp__iff__simps_I3_J,axiom,
% 5.17/5.44 ! [N: num,Q2: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != zero_zero_int ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(3)
% 5.17/5.44 thf(fact_4429_cong__exp__iff__simps_I3_J,axiom,
% 5.17/5.44 ! [N: num,Q2: num] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 != zero_z3403309356797280102nteger ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(3)
% 5.17/5.44 thf(fact_4430_mod__mult2__eq_H,axiom,
% 5.17/5.44 ! [A: code_integer,M: nat,N: nat] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult2_eq'
% 5.17/5.44 thf(fact_4431_mod__mult2__eq_H,axiom,
% 5.17/5.44 ! [A: nat,M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.17/5.44 = ( 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 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult2_eq'
% 5.17/5.44 thf(fact_4432_mod__mult2__eq_H,axiom,
% 5.17/5.44 ! [A: int,M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.44 = ( 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 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_mult2_eq'
% 5.17/5.44 thf(fact_4433_even__even__mod__4__iff,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.44 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_even_mod_4_iff
% 5.17/5.44 thf(fact_4434_field__char__0__class_Oof__nat__div,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.44 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % field_char_0_class.of_nat_div
% 5.17/5.44 thf(fact_4435_field__char__0__class_Oof__nat__div,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.44 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % field_char_0_class.of_nat_div
% 5.17/5.44 thf(fact_4436_field__char__0__class_Oof__nat__div,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.17/5.44 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % field_char_0_class.of_nat_div
% 5.17/5.44 thf(fact_4437_split__mod,axiom,
% 5.17/5.44 ! [P: nat > $o,M: nat,N: nat] :
% 5.17/5.44 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.17/5.44 = ( ( ( N = zero_zero_nat )
% 5.17/5.44 => ( P @ M ) )
% 5.17/5.44 & ( ( N != zero_zero_nat )
% 5.17/5.44 => ! [I2: nat,J3: nat] :
% 5.17/5.44 ( ( ord_less_nat @ J3 @ N )
% 5.17/5.44 => ( ( M
% 5.17/5.44 = ( plus_plus_nat @ ( times_times_nat @ N @ I2 ) @ J3 ) )
% 5.17/5.44 => ( P @ J3 ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_mod
% 5.17/5.44 thf(fact_4438_mod__nat__eqI,axiom,
% 5.17/5.44 ! [R2: nat,N: nat,M: nat] :
% 5.17/5.44 ( ( ord_less_nat @ R2 @ N )
% 5.17/5.44 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.17/5.44 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.17/5.44 => ( ( modulo_modulo_nat @ M @ N )
% 5.17/5.44 = R2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_nat_eqI
% 5.17/5.44 thf(fact_4439_pochhammer__rec,axiom,
% 5.17/5.44 ! [A: complex,N: nat] :
% 5.17/5.44 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec
% 5.17/5.44 thf(fact_4440_pochhammer__rec,axiom,
% 5.17/5.44 ! [A: real,N: nat] :
% 5.17/5.44 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec
% 5.17/5.44 thf(fact_4441_pochhammer__rec,axiom,
% 5.17/5.44 ! [A: rat,N: nat] :
% 5.17/5.44 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec
% 5.17/5.44 thf(fact_4442_pochhammer__rec,axiom,
% 5.17/5.44 ! [A: nat,N: nat] :
% 5.17/5.44 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec
% 5.17/5.44 thf(fact_4443_pochhammer__rec,axiom,
% 5.17/5.44 ! [A: int,N: nat] :
% 5.17/5.44 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec
% 5.17/5.44 thf(fact_4444_pochhammer__rec_H,axiom,
% 5.17/5.44 ! [Z: complex,N: nat] :
% 5.17/5.44 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec'
% 5.17/5.44 thf(fact_4445_pochhammer__rec_H,axiom,
% 5.17/5.44 ! [Z: real,N: nat] :
% 5.17/5.44 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec'
% 5.17/5.44 thf(fact_4446_pochhammer__rec_H,axiom,
% 5.17/5.44 ! [Z: rat,N: nat] :
% 5.17/5.44 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec'
% 5.17/5.44 thf(fact_4447_pochhammer__rec_H,axiom,
% 5.17/5.44 ! [Z: nat,N: nat] :
% 5.17/5.44 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec'
% 5.17/5.44 thf(fact_4448_pochhammer__rec_H,axiom,
% 5.17/5.44 ! [Z: int,N: nat] :
% 5.17/5.44 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_rec'
% 5.17/5.44 thf(fact_4449_pochhammer__Suc,axiom,
% 5.17/5.44 ! [A: complex,N: nat] :
% 5.17/5.44 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_Suc
% 5.17/5.44 thf(fact_4450_pochhammer__Suc,axiom,
% 5.17/5.44 ! [A: real,N: nat] :
% 5.17/5.44 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_Suc
% 5.17/5.44 thf(fact_4451_pochhammer__Suc,axiom,
% 5.17/5.44 ! [A: rat,N: nat] :
% 5.17/5.44 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_Suc
% 5.17/5.44 thf(fact_4452_pochhammer__Suc,axiom,
% 5.17/5.44 ! [A: nat,N: nat] :
% 5.17/5.44 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_Suc
% 5.17/5.44 thf(fact_4453_pochhammer__Suc,axiom,
% 5.17/5.44 ! [A: int,N: nat] :
% 5.17/5.44 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.17/5.44 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_Suc
% 5.17/5.44 thf(fact_4454_real__of__nat__div__aux,axiom,
% 5.17/5.44 ! [X: nat,D: nat] :
% 5.17/5.44 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.17/5.44 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % real_of_nat_div_aux
% 5.17/5.44 thf(fact_4455_pochhammer__product_H,axiom,
% 5.17/5.44 ! [Z: complex,N: nat,M: nat] :
% 5.17/5.44 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.44 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product'
% 5.17/5.44 thf(fact_4456_pochhammer__product_H,axiom,
% 5.17/5.44 ! [Z: real,N: nat,M: nat] :
% 5.17/5.44 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.44 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product'
% 5.17/5.44 thf(fact_4457_pochhammer__product_H,axiom,
% 5.17/5.44 ! [Z: rat,N: nat,M: nat] :
% 5.17/5.44 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.44 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product'
% 5.17/5.44 thf(fact_4458_pochhammer__product_H,axiom,
% 5.17/5.44 ! [Z: nat,N: nat,M: nat] :
% 5.17/5.44 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.44 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product'
% 5.17/5.44 thf(fact_4459_pochhammer__product_H,axiom,
% 5.17/5.44 ! [Z: int,N: nat,M: nat] :
% 5.17/5.44 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.17/5.44 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product'
% 5.17/5.44 thf(fact_4460_binomial__maximum_H,axiom,
% 5.17/5.44 ! [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 ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_maximum'
% 5.17/5.44 thf(fact_4461_binomial__mono,axiom,
% 5.17/5.44 ! [K: nat,K6: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ K6 )
% 5.17/5.44 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.17/5.44 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_mono
% 5.17/5.44 thf(fact_4462_binomial__antimono,axiom,
% 5.17/5.44 ! [K: nat,K6: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ K6 )
% 5.17/5.44 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.17/5.44 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.17/5.44 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_antimono
% 5.17/5.44 thf(fact_4463_binomial__maximum,axiom,
% 5.17/5.44 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_maximum
% 5.17/5.44 thf(fact_4464_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.17/5.44 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.17/5.44 thf(fact_4465_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.17/5.44 ! [C: nat,A: nat,B: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.17/5.44 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.17/5.44 thf(fact_4466_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.17/5.44 ! [C: int,A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.17/5.44 thf(fact_4467_even__iff__mod__2__eq__zero,axiom,
% 5.17/5.44 ! [A: nat] :
% 5.17/5.44 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_iff_mod_2_eq_zero
% 5.17/5.44 thf(fact_4468_even__iff__mod__2__eq__zero,axiom,
% 5.17/5.44 ! [A: int] :
% 5.17/5.44 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_iff_mod_2_eq_zero
% 5.17/5.44 thf(fact_4469_even__iff__mod__2__eq__zero,axiom,
% 5.17/5.44 ! [A: code_integer] :
% 5.17/5.44 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_iff_mod_2_eq_zero
% 5.17/5.44 thf(fact_4470_cong__exp__iff__simps_I7_J,axiom,
% 5.17/5.44 ! [Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(7)
% 5.17/5.44 thf(fact_4471_cong__exp__iff__simps_I7_J,axiom,
% 5.17/5.44 ! [Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(7)
% 5.17/5.44 thf(fact_4472_cong__exp__iff__simps_I7_J,axiom,
% 5.17/5.44 ! [Q2: num,N: num] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(7)
% 5.17/5.44 thf(fact_4473_cong__exp__iff__simps_I11_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(11)
% 5.17/5.44 thf(fact_4474_cong__exp__iff__simps_I11_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(11)
% 5.17/5.44 thf(fact_4475_cong__exp__iff__simps_I11_J,axiom,
% 5.17/5.44 ! [M: num,Q2: num] :
% 5.17/5.44 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % cong_exp_iff_simps(11)
% 5.17/5.44 thf(fact_4476_odd__iff__mod__2__eq__one,axiom,
% 5.17/5.44 ! [A: nat] :
% 5.17/5.44 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.44 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = one_one_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % odd_iff_mod_2_eq_one
% 5.17/5.44 thf(fact_4477_odd__iff__mod__2__eq__one,axiom,
% 5.17/5.44 ! [A: int] :
% 5.17/5.44 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.44 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = one_one_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % odd_iff_mod_2_eq_one
% 5.17/5.44 thf(fact_4478_odd__iff__mod__2__eq__one,axiom,
% 5.17/5.44 ! [A: code_integer] :
% 5.17/5.44 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.44 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = one_one_Code_integer ) ) ).
% 5.17/5.44
% 5.17/5.44 % odd_iff_mod_2_eq_one
% 5.17/5.44 thf(fact_4479_Suc__mod__eq__add3__mod,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.17/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % Suc_mod_eq_add3_mod
% 5.17/5.44 thf(fact_4480_Suc__times__mod__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.17/5.44 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.17/5.44 = one_one_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % Suc_times_mod_eq
% 5.17/5.44 thf(fact_4481_pochhammer__product,axiom,
% 5.17/5.44 ! [M: nat,N: nat,Z: complex] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 5.17/5.44 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product
% 5.17/5.44 thf(fact_4482_pochhammer__product,axiom,
% 5.17/5.44 ! [M: nat,N: nat,Z: real] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.17/5.44 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product
% 5.17/5.44 thf(fact_4483_pochhammer__product,axiom,
% 5.17/5.44 ! [M: nat,N: nat,Z: rat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.17/5.44 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product
% 5.17/5.44 thf(fact_4484_pochhammer__product,axiom,
% 5.17/5.44 ! [M: nat,N: nat,Z: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.17/5.44 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product
% 5.17/5.44 thf(fact_4485_pochhammer__product,axiom,
% 5.17/5.44 ! [M: nat,N: nat,Z: int] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.17/5.44 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pochhammer_product
% 5.17/5.44 thf(fact_4486_binomial__strict__antimono,axiom,
% 5.17/5.44 ! [K: nat,K6: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ K @ K6 )
% 5.17/5.44 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.17/5.44 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.17/5.44 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_strict_antimono
% 5.17/5.44 thf(fact_4487_binomial__strict__mono,axiom,
% 5.17/5.44 ! [K: nat,K6: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ K @ K6 )
% 5.17/5.44 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.17/5.44 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_strict_mono
% 5.17/5.44 thf(fact_4488_binomial__less__binomial__Suc,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.44 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_less_binomial_Suc
% 5.17/5.44 thf(fact_4489_central__binomial__odd,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.44 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.44 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % central_binomial_odd
% 5.17/5.44 thf(fact_4490_divmod__digit__0_I2_J,axiom,
% 5.17/5.44 ! [B: nat,A: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.44 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.17/5.44 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_0(2)
% 5.17/5.44 thf(fact_4491_divmod__digit__0_I2_J,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.17/5.44 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_0(2)
% 5.17/5.44 thf(fact_4492_divmod__digit__0_I2_J,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.44 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_0(2)
% 5.17/5.44 thf(fact_4493_bits__stable__imp__add__self,axiom,
% 5.17/5.44 ! [A: nat] :
% 5.17/5.44 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = A )
% 5.17/5.44 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % bits_stable_imp_add_self
% 5.17/5.44 thf(fact_4494_bits__stable__imp__add__self,axiom,
% 5.17/5.44 ! [A: int] :
% 5.17/5.44 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = A )
% 5.17/5.44 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % bits_stable_imp_add_self
% 5.17/5.44 thf(fact_4495_bits__stable__imp__add__self,axiom,
% 5.17/5.44 ! [A: code_integer] :
% 5.17/5.44 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = A )
% 5.17/5.44 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.44
% 5.17/5.44 % bits_stable_imp_add_self
% 5.17/5.44 thf(fact_4496_parity__cases,axiom,
% 5.17/5.44 ! [A: nat] :
% 5.17/5.44 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 != zero_zero_nat ) )
% 5.17/5.44 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 != one_one_nat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % parity_cases
% 5.17/5.44 thf(fact_4497_parity__cases,axiom,
% 5.17/5.44 ! [A: int] :
% 5.17/5.44 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 != zero_zero_int ) )
% 5.17/5.44 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 != one_one_int ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % parity_cases
% 5.17/5.44 thf(fact_4498_parity__cases,axiom,
% 5.17/5.44 ! [A: code_integer] :
% 5.17/5.44 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 != zero_z3403309356797280102nteger ) )
% 5.17/5.44 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 != one_one_Code_integer ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % parity_cases
% 5.17/5.44 thf(fact_4499_mod2__eq__if,axiom,
% 5.17/5.44 ! [A: nat] :
% 5.17/5.44 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = zero_zero_nat ) )
% 5.17/5.44 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = one_one_nat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod2_eq_if
% 5.17/5.44 thf(fact_4500_mod2__eq__if,axiom,
% 5.17/5.44 ! [A: int] :
% 5.17/5.44 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = zero_zero_int ) )
% 5.17/5.44 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = one_one_int ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod2_eq_if
% 5.17/5.44 thf(fact_4501_mod2__eq__if,axiom,
% 5.17/5.44 ! [A: code_integer] :
% 5.17/5.44 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = zero_z3403309356797280102nteger ) )
% 5.17/5.44 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = one_one_Code_integer ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod2_eq_if
% 5.17/5.44 thf(fact_4502_div__exp__mod__exp__eq,axiom,
% 5.17/5.44 ! [A: nat,N: nat,M: nat] :
% 5.17/5.44 ( ( 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 ) )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_exp_mod_exp_eq
% 5.17/5.44 thf(fact_4503_div__exp__mod__exp__eq,axiom,
% 5.17/5.44 ! [A: int,N: nat,M: nat] :
% 5.17/5.44 ( ( 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 ) )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_exp_mod_exp_eq
% 5.17/5.44 thf(fact_4504_div__exp__mod__exp__eq,axiom,
% 5.17/5.44 ! [A: code_integer,N: nat,M: nat] :
% 5.17/5.44 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_exp_mod_exp_eq
% 5.17/5.44 thf(fact_4505_bits__induct,axiom,
% 5.17/5.44 ! [P: nat > $o,A: nat] :
% 5.17/5.44 ( ! [A4: nat] :
% 5.17/5.44 ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = A4 )
% 5.17/5.44 => ( P @ A4 ) )
% 5.17/5.44 => ( ! [A4: nat,B3: $o] :
% 5.17/5.44 ( ( P @ A4 )
% 5.17/5.44 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = A4 )
% 5.17/5.44 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.17/5.44 => ( P @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % bits_induct
% 5.17/5.44 thf(fact_4506_bits__induct,axiom,
% 5.17/5.44 ! [P: int > $o,A: int] :
% 5.17/5.44 ( ! [A4: int] :
% 5.17/5.44 ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = A4 )
% 5.17/5.44 => ( P @ A4 ) )
% 5.17/5.44 => ( ! [A4: int,B3: $o] :
% 5.17/5.44 ( ( P @ A4 )
% 5.17/5.44 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.44 = A4 )
% 5.17/5.44 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.17/5.44 => ( P @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % bits_induct
% 5.17/5.44 thf(fact_4507_bits__induct,axiom,
% 5.17/5.44 ! [P: code_integer > $o,A: code_integer] :
% 5.17/5.44 ( ! [A4: code_integer] :
% 5.17/5.44 ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = A4 )
% 5.17/5.44 => ( P @ A4 ) )
% 5.17/5.44 => ( ! [A4: code_integer,B3: $o] :
% 5.17/5.44 ( ( P @ A4 )
% 5.17/5.44 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.44 = A4 )
% 5.17/5.44 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.17/5.44 => ( P @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % bits_induct
% 5.17/5.44 thf(fact_4508_verit__le__mono__div,axiom,
% 5.17/5.44 ! [A2: nat,B4: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ A2 @ B4 )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ord_less_eq_nat
% 5.17/5.44 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.17/5.44 @ ( if_nat
% 5.17/5.44 @ ( ( modulo_modulo_nat @ B4 @ N )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 @ one_one_nat
% 5.17/5.44 @ zero_zero_nat ) )
% 5.17/5.44 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % verit_le_mono_div
% 5.17/5.44 thf(fact_4509_divmod__digit__0_I1_J,axiom,
% 5.17/5.44 ! [B: nat,A: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.44 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_0(1)
% 5.17/5.44 thf(fact_4510_divmod__digit__0_I1_J,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_0(1)
% 5.17/5.44 thf(fact_4511_divmod__digit__0_I1_J,axiom,
% 5.17/5.44 ! [B: code_integer,A: code_integer] :
% 5.17/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.44 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_0(1)
% 5.17/5.44 thf(fact_4512_mult__exp__mod__exp__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat,A: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( 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 ) )
% 5.17/5.44 = ( 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 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mult_exp_mod_exp_eq
% 5.17/5.44 thf(fact_4513_mult__exp__mod__exp__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat,A: int] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( 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 ) )
% 5.17/5.44 = ( 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 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mult_exp_mod_exp_eq
% 5.17/5.44 thf(fact_4514_mult__exp__mod__exp__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat,A: code_integer] :
% 5.17/5.44 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mult_exp_mod_exp_eq
% 5.17/5.44 thf(fact_4515_mod__double__modulus,axiom,
% 5.17/5.44 ! [M: code_integer,X: code_integer] :
% 5.17/5.44 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.17/5.44 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.17/5.44 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.17/5.44 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_double_modulus
% 5.17/5.44 thf(fact_4516_mod__double__modulus,axiom,
% 5.17/5.44 ! [M: nat,X: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.44 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.17/5.44 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( modulo_modulo_nat @ X @ M ) )
% 5.17/5.44 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_double_modulus
% 5.17/5.44 thf(fact_4517_mod__double__modulus,axiom,
% 5.17/5.44 ! [M: int,X: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ M )
% 5.17/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.44 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( modulo_modulo_int @ X @ M ) )
% 5.17/5.44 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.44 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_double_modulus
% 5.17/5.44 thf(fact_4518_divmod__digit__1_I2_J,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.44 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.44 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_1(2)
% 5.17/5.44 thf(fact_4519_divmod__digit__1_I2_J,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.44 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_1(2)
% 5.17/5.44 thf(fact_4520_divmod__digit__1_I2_J,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.44 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.17/5.44 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_1(2)
% 5.17/5.44 thf(fact_4521_unset__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: int] :
% 5.17/5.44 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unset_bit_Suc
% 5.17/5.44 thf(fact_4522_unset__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: nat] :
% 5.17/5.44 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unset_bit_Suc
% 5.17/5.44 thf(fact_4523_unset__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: code_integer] :
% 5.17/5.44 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % unset_bit_Suc
% 5.17/5.44 thf(fact_4524_set__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: int] :
% 5.17/5.44 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % set_bit_Suc
% 5.17/5.44 thf(fact_4525_set__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: nat] :
% 5.17/5.44 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % set_bit_Suc
% 5.17/5.44 thf(fact_4526_set__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: code_integer] :
% 5.17/5.44 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % set_bit_Suc
% 5.17/5.44 thf(fact_4527_flip__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: int] :
% 5.17/5.44 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % flip_bit_Suc
% 5.17/5.44 thf(fact_4528_flip__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: nat] :
% 5.17/5.44 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % flip_bit_Suc
% 5.17/5.44 thf(fact_4529_flip__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: code_integer] :
% 5.17/5.44 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % flip_bit_Suc
% 5.17/5.44 thf(fact_4530_even__mod__4__div__2,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = ( suc @ zero_zero_nat ) )
% 5.17/5.44 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % even_mod_4_div_2
% 5.17/5.44 thf(fact_4531_exp__div__exp__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_times_nat
% 5.17/5.44 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.44 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.17/5.44 != zero_zero_nat )
% 5.17/5.44 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.17/5.44 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % exp_div_exp_eq
% 5.17/5.44 thf(fact_4532_exp__div__exp__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_times_int
% 5.17/5.44 @ ( zero_n2684676970156552555ol_int
% 5.17/5.44 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.17/5.44 != zero_zero_int )
% 5.17/5.44 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.17/5.44 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % exp_div_exp_eq
% 5.17/5.44 thf(fact_4533_exp__div__exp__eq,axiom,
% 5.17/5.44 ! [M: nat,N: nat] :
% 5.17/5.44 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( times_3573771949741848930nteger
% 5.17/5.44 @ ( zero_n356916108424825756nteger
% 5.17/5.44 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.17/5.44 != zero_z3403309356797280102nteger )
% 5.17/5.44 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.17/5.44 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % exp_div_exp_eq
% 5.17/5.44 thf(fact_4534_odd__mod__4__div__2,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.44 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % odd_mod_4_div_2
% 5.17/5.44 thf(fact_4535_divmod__digit__1_I1_J,axiom,
% 5.17/5.44 ! [A: code_integer,B: code_integer] :
% 5.17/5.44 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.44 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.44 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.17/5.44 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_1(1)
% 5.17/5.44 thf(fact_4536_divmod__digit__1_I1_J,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.17/5.44 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 => ( ( 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 )
% 5.17/5.44 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_1(1)
% 5.17/5.44 thf(fact_4537_divmod__digit__1_I1_J,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.44 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.17/5.44 => ( ( 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 )
% 5.17/5.44 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % divmod_digit_1(1)
% 5.17/5.44 thf(fact_4538_zero__less__binomial__iff,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.17/5.44 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_binomial_iff
% 5.17/5.44 thf(fact_4539_choose__two,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % choose_two
% 5.17/5.44 thf(fact_4540_binomial__n__0,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( binomial @ N @ zero_zero_nat )
% 5.17/5.44 = one_one_nat ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_n_0
% 5.17/5.44 thf(fact_4541_binomial__Suc__Suc,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.17/5.44 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_Suc_Suc
% 5.17/5.44 thf(fact_4542_binomial__eq__0__iff,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( ( binomial @ N @ K )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 = ( ord_less_nat @ N @ K ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_eq_0_iff
% 5.17/5.44 thf(fact_4543_binomial__1,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.44 = N ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_1
% 5.17/5.44 thf(fact_4544_binomial__0__Suc,axiom,
% 5.17/5.44 ! [K: nat] :
% 5.17/5.44 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.17/5.44 = zero_zero_nat ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_0_Suc
% 5.17/5.44 thf(fact_4545_binomial__addition__formula,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ( binomial @ N @ ( suc @ K ) )
% 5.17/5.44 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_addition_formula
% 5.17/5.44 thf(fact_4546_binomial__Suc__n,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( binomial @ ( suc @ N ) @ N )
% 5.17/5.44 = ( suc @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_Suc_n
% 5.17/5.44 thf(fact_4547_mod__neg__neg__trivial,axiom,
% 5.17/5.44 ! [K: int,L: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.17/5.44 => ( ( ord_less_int @ L @ K )
% 5.17/5.44 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.44 = K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_neg_neg_trivial
% 5.17/5.44 thf(fact_4548_mod__pos__pos__trivial,axiom,
% 5.17/5.44 ! [K: int,L: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.44 => ( ( ord_less_int @ K @ L )
% 5.17/5.44 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.44 = K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_pos_pos_trivial
% 5.17/5.44 thf(fact_4549_zmod__numeral__Bit0,axiom,
% 5.17/5.44 ! [V: num,W: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.17/5.44 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_numeral_Bit0
% 5.17/5.44 thf(fact_4550_zmod__numeral__Bit1,axiom,
% 5.17/5.44 ! [V: num,W: num] :
% 5.17/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.17/5.44 = ( 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 ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_numeral_Bit1
% 5.17/5.44 thf(fact_4551_zmod__le__nonneg__dividend,axiom,
% 5.17/5.44 ! [M: int,K: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.17/5.44 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_le_nonneg_dividend
% 5.17/5.44 thf(fact_4552_neg__mod__bound,axiom,
% 5.17/5.44 ! [L: int,K: int] :
% 5.17/5.44 ( ( ord_less_int @ L @ zero_zero_int )
% 5.17/5.44 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % neg_mod_bound
% 5.17/5.44 thf(fact_4553_Euclidean__Division_Opos__mod__bound,axiom,
% 5.17/5.44 ! [L: int,K: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.44 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.17/5.44
% 5.17/5.44 % Euclidean_Division.pos_mod_bound
% 5.17/5.44 thf(fact_4554_zmod__eq__0D,axiom,
% 5.17/5.44 ! [M: int,D: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ M @ D )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 => ? [Q4: int] :
% 5.17/5.44 ( M
% 5.17/5.44 = ( times_times_int @ D @ Q4 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_eq_0D
% 5.17/5.44 thf(fact_4555_zmod__eq__0__iff,axiom,
% 5.17/5.44 ! [M: int,D: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ M @ D )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 = ( ? [Q3: int] :
% 5.17/5.44 ( M
% 5.17/5.44 = ( times_times_int @ D @ Q3 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_eq_0_iff
% 5.17/5.44 thf(fact_4556_zmod__int,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.17/5.44 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_int
% 5.17/5.44 thf(fact_4557_neg__mod__sign,axiom,
% 5.17/5.44 ! [L: int,K: int] :
% 5.17/5.44 ( ( ord_less_int @ L @ zero_zero_int )
% 5.17/5.44 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.17/5.44
% 5.17/5.44 % neg_mod_sign
% 5.17/5.44 thf(fact_4558_Euclidean__Division_Opos__mod__sign,axiom,
% 5.17/5.44 ! [L: int,K: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.44 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % Euclidean_Division.pos_mod_sign
% 5.17/5.44 thf(fact_4559_zmod__trivial__iff,axiom,
% 5.17/5.44 ! [I: int,K: int] :
% 5.17/5.44 ( ( ( modulo_modulo_int @ I @ K )
% 5.17/5.44 = I )
% 5.17/5.44 = ( ( K = zero_zero_int )
% 5.17/5.44 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.17/5.44 & ( ord_less_int @ I @ K ) )
% 5.17/5.44 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.17/5.44 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_trivial_iff
% 5.17/5.44 thf(fact_4560_pos__mod__conj,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.17/5.44 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pos_mod_conj
% 5.17/5.44 thf(fact_4561_neg__mod__conj,axiom,
% 5.17/5.44 ! [B: int,A: int] :
% 5.17/5.44 ( ( ord_less_int @ B @ zero_zero_int )
% 5.17/5.44 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.17/5.44 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % neg_mod_conj
% 5.17/5.44 thf(fact_4562_zdiv__mono__strict,axiom,
% 5.17/5.44 ! [A2: int,B4: int,N: int] :
% 5.17/5.44 ( ( ord_less_int @ A2 @ B4 )
% 5.17/5.44 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.17/5.44 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 => ( ( ( modulo_modulo_int @ B4 @ N )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zdiv_mono_strict
% 5.17/5.44 thf(fact_4563_div__mod__decomp__int,axiom,
% 5.17/5.44 ! [A2: int,N: int] :
% 5.17/5.44 ( A2
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % div_mod_decomp_int
% 5.17/5.44 thf(fact_4564_mod__pos__neg__trivial,axiom,
% 5.17/5.44 ! [K: int,L: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.44 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.17/5.44 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.44 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_pos_neg_trivial
% 5.17/5.44 thf(fact_4565_mod__pos__geq,axiom,
% 5.17/5.44 ! [L: int,K: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.44 => ( ( ord_less_eq_int @ L @ K )
% 5.17/5.44 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.44 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_pos_geq
% 5.17/5.44 thf(fact_4566_mod__int__pos__iff,axiom,
% 5.17/5.44 ! [K: int,L: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.17/5.44 = ( ( dvd_dvd_int @ L @ K )
% 5.17/5.44 | ( ( L = zero_zero_int )
% 5.17/5.44 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.17/5.44 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_int_pos_iff
% 5.17/5.44 thf(fact_4567_split__zmod,axiom,
% 5.17/5.44 ! [P: int > $o,N: int,K: int] :
% 5.17/5.44 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.17/5.44 = ( ( ( K = zero_zero_int )
% 5.17/5.44 => ( P @ N ) )
% 5.17/5.44 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.44 => ! [I2: int,J3: int] :
% 5.17/5.44 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.17/5.44 & ( ord_less_int @ J3 @ K )
% 5.17/5.44 & ( N
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.17/5.44 => ( P @ J3 ) ) )
% 5.17/5.44 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.44 => ! [I2: int,J3: int] :
% 5.17/5.44 ( ( ( ord_less_int @ K @ J3 )
% 5.17/5.44 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.17/5.44 & ( N
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.17/5.44 => ( P @ J3 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_zmod
% 5.17/5.44 thf(fact_4568_int__mod__neg__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,Q2: int,R2: int] :
% 5.17/5.44 ( ( A
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.17/5.44 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.17/5.44 => ( ( ord_less_int @ B @ R2 )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = R2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % int_mod_neg_eq
% 5.17/5.44 thf(fact_4569_int__mod__pos__eq,axiom,
% 5.17/5.44 ! [A: int,B: int,Q2: int,R2: int] :
% 5.17/5.44 ( ( A
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 5.17/5.44 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.17/5.44 => ( ( ord_less_int @ R2 @ B )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ B )
% 5.17/5.44 = R2 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % int_mod_pos_eq
% 5.17/5.44 thf(fact_4570_zmod__zmult2__eq,axiom,
% 5.17/5.44 ! [C: int,A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.17/5.44 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zmod_zmult2_eq
% 5.17/5.44 thf(fact_4571_verit__le__mono__div__int,axiom,
% 5.17/5.44 ! [A2: int,B4: int,N: int] :
% 5.17/5.44 ( ( ord_less_int @ A2 @ B4 )
% 5.17/5.44 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.17/5.44 => ( ord_less_eq_int
% 5.17/5.44 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.17/5.44 @ ( if_int
% 5.17/5.44 @ ( ( modulo_modulo_int @ B4 @ N )
% 5.17/5.44 = zero_zero_int )
% 5.17/5.44 @ one_one_int
% 5.17/5.44 @ zero_zero_int ) )
% 5.17/5.44 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % verit_le_mono_div_int
% 5.17/5.44 thf(fact_4572_split__neg__lemma,axiom,
% 5.17/5.44 ! [K: int,P: int > int > $o,N: int] :
% 5.17/5.44 ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.44 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.17/5.44 = ( ! [I2: int,J3: int] :
% 5.17/5.44 ( ( ( ord_less_int @ K @ J3 )
% 5.17/5.44 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.17/5.44 & ( N
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.17/5.44 => ( P @ I2 @ J3 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_neg_lemma
% 5.17/5.44 thf(fact_4573_split__pos__lemma,axiom,
% 5.17/5.44 ! [K: int,P: int > int > $o,N: int] :
% 5.17/5.44 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.44 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.17/5.44 = ( ! [I2: int,J3: int] :
% 5.17/5.44 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.17/5.44 & ( ord_less_int @ J3 @ K )
% 5.17/5.44 & ( N
% 5.17/5.44 = ( plus_plus_int @ ( times_times_int @ K @ I2 ) @ J3 ) ) )
% 5.17/5.44 => ( P @ I2 @ J3 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % split_pos_lemma
% 5.17/5.44 thf(fact_4574_pos__zmod__mult__2,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.44 => ( ( 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 ) )
% 5.17/5.44 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % pos_zmod_mult_2
% 5.17/5.44 thf(fact_4575_neg__zmod__mult__2,axiom,
% 5.17/5.44 ! [A: int,B: int] :
% 5.17/5.44 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.44 => ( ( 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 ) )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % neg_zmod_mult_2
% 5.17/5.44 thf(fact_4576_binomial__eq__0,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( ord_less_nat @ N @ K )
% 5.17/5.44 => ( ( binomial @ N @ K )
% 5.17/5.44 = zero_zero_nat ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_eq_0
% 5.17/5.44 thf(fact_4577_Suc__times__binomial__eq,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.17/5.44 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % Suc_times_binomial_eq
% 5.17/5.44 thf(fact_4578_Suc__times__binomial,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.17/5.44 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % Suc_times_binomial
% 5.17/5.44 thf(fact_4579_binomial__symmetric,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.44 => ( ( binomial @ N @ K )
% 5.17/5.44 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_symmetric
% 5.17/5.44 thf(fact_4580_choose__mult__lemma,axiom,
% 5.17/5.44 ! [M: nat,R2: nat,K: nat] :
% 5.17/5.44 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.17/5.44 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % choose_mult_lemma
% 5.17/5.44 thf(fact_4581_binomial__le__pow,axiom,
% 5.17/5.44 ! [R2: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ R2 @ N )
% 5.17/5.44 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_le_pow
% 5.17/5.44 thf(fact_4582_zero__less__binomial,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.44 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % zero_less_binomial
% 5.17/5.44 thf(fact_4583_Suc__times__binomial__add,axiom,
% 5.17/5.44 ! [A: nat,B: nat] :
% 5.17/5.44 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.17/5.44 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % Suc_times_binomial_add
% 5.17/5.44 thf(fact_4584_choose__mult,axiom,
% 5.17/5.44 ! [K: nat,M: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.44 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.44 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.17/5.44 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % choose_mult
% 5.17/5.44 thf(fact_4585_binomial__Suc__Suc__eq__times,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.17/5.44 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_Suc_Suc_eq_times
% 5.17/5.44 thf(fact_4586_binomial__absorb__comp,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.17/5.44 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_absorb_comp
% 5.17/5.44 thf(fact_4587_binomial__absorption,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.17/5.44 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_absorption
% 5.17/5.44 thf(fact_4588_binomial__ge__n__over__k__pow__k,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.44 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_ge_n_over_k_pow_k
% 5.17/5.44 thf(fact_4589_binomial__ge__n__over__k__pow__k,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.44 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_ge_n_over_k_pow_k
% 5.17/5.44 thf(fact_4590_binomial__le__pow2,axiom,
% 5.17/5.44 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % binomial_le_pow2
% 5.17/5.44 thf(fact_4591_choose__reduce__nat,axiom,
% 5.17/5.44 ! [N: nat,K: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.44 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.44 => ( ( binomial @ N @ K )
% 5.17/5.44 = ( 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 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % choose_reduce_nat
% 5.17/5.44 thf(fact_4592_times__binomial__minus1__eq,axiom,
% 5.17/5.44 ! [K: nat,N: nat] :
% 5.17/5.44 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.44 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.17/5.44 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % times_binomial_minus1_eq
% 5.17/5.44 thf(fact_4593_mod__exhaust__less__4,axiom,
% 5.17/5.44 ! [M: nat] :
% 5.17/5.44 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = zero_zero_nat )
% 5.17/5.44 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = one_one_nat )
% 5.17/5.44 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.44 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.44 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % mod_exhaust_less_4
% 5.17/5.44 thf(fact_4594_artanh__def,axiom,
% 5.17/5.44 ( artanh_real
% 5.17/5.44 = ( ^ [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 ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % artanh_def
% 5.17/5.44 thf(fact_4595_signed__take__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: code_integer] :
% 5.17/5.44 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.17/5.44 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % signed_take_bit_Suc
% 5.17/5.44 thf(fact_4596_signed__take__bit__Suc,axiom,
% 5.17/5.44 ! [N: nat,A: int] :
% 5.17/5.44 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.17/5.44 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % signed_take_bit_Suc
% 5.17/5.44 thf(fact_4597__C10_C,axiom,
% 5.17/5.44 ! [L: nat] :
% 5.17/5.44 ( ( foldr_real_real @ plus_plus_real @ ( replicate_real @ L @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ zero_zero_real )
% 5.17/5.44 = ( times_times_real @ ( semiri5074537144036343181t_real @ L ) @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % "10"
% 5.17/5.44 thf(fact_4598_add__scale__eq__noteq,axiom,
% 5.17/5.44 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.17/5.44 ( ( R2 != zero_zero_complex )
% 5.17/5.44 => ( ( ( A = B )
% 5.17/5.44 & ( C != D ) )
% 5.17/5.44 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.17/5.44 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % add_scale_eq_noteq
% 5.17/5.44 thf(fact_4599_add__scale__eq__noteq,axiom,
% 5.17/5.44 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.17/5.44 ( ( R2 != zero_zero_real )
% 5.17/5.44 => ( ( ( A = B )
% 5.17/5.44 & ( C != D ) )
% 5.17/5.44 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.17/5.44 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % add_scale_eq_noteq
% 5.17/5.44 thf(fact_4600_add__scale__eq__noteq,axiom,
% 5.17/5.44 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.44 ( ( R2 != zero_zero_rat )
% 5.17/5.44 => ( ( ( A = B )
% 5.17/5.44 & ( C != D ) )
% 5.17/5.44 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.17/5.44 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % add_scale_eq_noteq
% 5.17/5.44 thf(fact_4601_add__scale__eq__noteq,axiom,
% 5.17/5.44 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.44 ( ( R2 != zero_zero_nat )
% 5.17/5.44 => ( ( ( A = B )
% 5.17/5.44 & ( C != D ) )
% 5.17/5.44 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.17/5.44 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % add_scale_eq_noteq
% 5.17/5.44 thf(fact_4602_add__scale__eq__noteq,axiom,
% 5.17/5.44 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.17/5.44 ( ( R2 != zero_zero_int )
% 5.17/5.44 => ( ( ( A = B )
% 5.17/5.44 & ( C != D ) )
% 5.17/5.44 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.17/5.44 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % add_scale_eq_noteq
% 5.17/5.44 thf(fact_4603_fact__double,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % fact_double
% 5.17/5.44 thf(fact_4604_fact__double,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % fact_double
% 5.17/5.44 thf(fact_4605_fact__double,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.44 = ( 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 ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % fact_double
% 5.17/5.44 thf(fact_4606_num_Osize__gen_I3_J,axiom,
% 5.17/5.44 ! [X33: num] :
% 5.17/5.44 ( ( size_num @ ( bit1 @ X33 ) )
% 5.17/5.44 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % num.size_gen(3)
% 5.17/5.44 thf(fact_4607_foldr0,axiom,
% 5.17/5.44 ! [Xs: list_real,C: real,D: real] :
% 5.17/5.44 ( ( foldr_real_real @ plus_plus_real @ Xs @ ( plus_plus_real @ C @ D ) )
% 5.17/5.44 = ( plus_plus_real @ ( foldr_real_real @ plus_plus_real @ Xs @ D ) @ C ) ) ).
% 5.17/5.44
% 5.17/5.44 % foldr0
% 5.17/5.44 thf(fact_4608_ln__less__cancel__iff,axiom,
% 5.17/5.44 ! [X: real,Y4: real] :
% 5.17/5.44 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.44 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.44 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y4 ) )
% 5.17/5.44 = ( ord_less_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % ln_less_cancel_iff
% 5.17/5.44 thf(fact_4609_ln__inj__iff,axiom,
% 5.17/5.44 ! [X: real,Y4: real] :
% 5.17/5.44 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.44 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.44 => ( ( ( ln_ln_real @ X )
% 5.17/5.44 = ( ln_ln_real @ Y4 ) )
% 5.17/5.44 = ( X = Y4 ) ) ) ) ).
% 5.17/5.44
% 5.17/5.44 % ln_inj_iff
% 5.17/5.44 thf(fact_4610_of__nat__fact,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri681578069525770553at_rat @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.17/5.44 = ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_nat_fact
% 5.17/5.44 thf(fact_4611_of__nat__fact,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri1314217659103216013at_int @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.17/5.44 = ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_nat_fact
% 5.17/5.44 thf(fact_4612_of__nat__fact,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri1316708129612266289at_nat @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.17/5.44 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.44
% 5.17/5.44 % of_nat_fact
% 5.17/5.44 thf(fact_4613_of__nat__fact,axiom,
% 5.17/5.44 ! [N: nat] :
% 5.17/5.44 ( ( semiri5074537144036343181t_real @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.17/5.44 = ( semiri2265585572941072030t_real @ N ) ) ).
% 5.17/5.44
% 5.17/5.45 % of_nat_fact
% 5.17/5.45 thf(fact_4614_of__nat__fact,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri8010041392384452111omplex @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.17/5.45 = ( semiri5044797733671781792omplex @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % of_nat_fact
% 5.17/5.45 thf(fact_4615_signed__take__bit__of__0,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_of_0
% 5.17/5.45 thf(fact_4616_replicate__eq__replicate,axiom,
% 5.17/5.45 ! [M: nat,X: real,N: nat,Y4: real] :
% 5.17/5.45 ( ( ( replicate_real @ M @ X )
% 5.17/5.45 = ( replicate_real @ N @ Y4 ) )
% 5.17/5.45 = ( ( M = N )
% 5.17/5.45 & ( ( M != zero_zero_nat )
% 5.17/5.45 => ( X = Y4 ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % replicate_eq_replicate
% 5.17/5.45 thf(fact_4617_replicate__eq__replicate,axiom,
% 5.17/5.45 ! [M: nat,X: vEBT_VEBT,N: nat,Y4: vEBT_VEBT] :
% 5.17/5.45 ( ( ( replicate_VEBT_VEBT @ M @ X )
% 5.17/5.45 = ( replicate_VEBT_VEBT @ N @ Y4 ) )
% 5.17/5.45 = ( ( M = N )
% 5.17/5.45 & ( ( M != zero_zero_nat )
% 5.17/5.45 => ( X = Y4 ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % replicate_eq_replicate
% 5.17/5.45 thf(fact_4618_ln__le__cancel__iff,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.45 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y4 ) )
% 5.17/5.45 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_le_cancel_iff
% 5.17/5.45 thf(fact_4619_ln__less__zero__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.17/5.45 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_less_zero_iff
% 5.17/5.45 thf(fact_4620_ln__gt__zero__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.17/5.45 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_gt_zero_iff
% 5.17/5.45 thf(fact_4621_ln__eq__zero__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ( ln_ln_real @ X )
% 5.17/5.45 = zero_zero_real )
% 5.17/5.45 = ( X = one_one_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_eq_zero_iff
% 5.17/5.45 thf(fact_4622_ln__one,axiom,
% 5.17/5.45 ( ( ln_ln_real @ one_one_real )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % ln_one
% 5.17/5.45 thf(fact_4623_fact__0,axiom,
% 5.17/5.45 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.17/5.45 = one_one_rat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_0
% 5.17/5.45 thf(fact_4624_fact__0,axiom,
% 5.17/5.45 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % fact_0
% 5.17/5.45 thf(fact_4625_fact__0,axiom,
% 5.17/5.45 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.17/5.45 = one_one_nat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_0
% 5.17/5.45 thf(fact_4626_fact__0,axiom,
% 5.17/5.45 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.17/5.45 = one_one_real ) ).
% 5.17/5.45
% 5.17/5.45 % fact_0
% 5.17/5.45 thf(fact_4627_fact__0,axiom,
% 5.17/5.45 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.17/5.45 = one_one_complex ) ).
% 5.17/5.45
% 5.17/5.45 % fact_0
% 5.17/5.45 thf(fact_4628_signed__take__bit__Suc__1,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_Suc_1
% 5.17/5.45 thf(fact_4629_signed__take__bit__numeral__of__1,axiom,
% 5.17/5.45 ! [K: num] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_numeral_of_1
% 5.17/5.45 thf(fact_4630_ln__ge__zero__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.17/5.45 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_ge_zero_iff
% 5.17/5.45 thf(fact_4631_ln__le__zero__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.17/5.45 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_le_zero_iff
% 5.17/5.45 thf(fact_4632_fact__Suc__0,axiom,
% 5.17/5.45 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.17/5.45 = one_one_rat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc_0
% 5.17/5.45 thf(fact_4633_fact__Suc__0,axiom,
% 5.17/5.45 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc_0
% 5.17/5.45 thf(fact_4634_fact__Suc__0,axiom,
% 5.17/5.45 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.17/5.45 = one_one_nat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc_0
% 5.17/5.45 thf(fact_4635_fact__Suc__0,axiom,
% 5.17/5.45 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.17/5.45 = one_one_real ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc_0
% 5.17/5.45 thf(fact_4636_fact__Suc__0,axiom,
% 5.17/5.45 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.17/5.45 = one_one_complex ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc_0
% 5.17/5.45 thf(fact_4637_fact__Suc,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.17/5.45 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc
% 5.17/5.45 thf(fact_4638_fact__Suc,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.17/5.45 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc
% 5.17/5.45 thf(fact_4639_fact__Suc,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.17/5.45 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc
% 5.17/5.45 thf(fact_4640_fact__Suc,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.17/5.45 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc
% 5.17/5.45 thf(fact_4641_fact__Suc,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 5.17/5.45 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_Suc
% 5.17/5.45 thf(fact_4642_fact__2,axiom,
% 5.17/5.45 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.45 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_2
% 5.17/5.45 thf(fact_4643_fact__2,axiom,
% 5.17/5.45 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.45 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_2
% 5.17/5.45 thf(fact_4644_fact__2,axiom,
% 5.17/5.45 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.45 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_2
% 5.17/5.45 thf(fact_4645_fact__2,axiom,
% 5.17/5.45 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.45 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_2
% 5.17/5.45 thf(fact_4646_fact__2,axiom,
% 5.17/5.45 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.45 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_2
% 5.17/5.45 thf(fact_4647_signed__take__bit__Suc__bit0,axiom,
% 5.17/5.45 ! [N: nat,K: num] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.17/5.45 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_Suc_bit0
% 5.17/5.45 thf(fact_4648_signed__take__bit__Suc__bit1,axiom,
% 5.17/5.45 ! [N: nat,K: num] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.17/5.45 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_Suc_bit1
% 5.17/5.45 thf(fact_4649_fact__mono__nat,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mono_nat
% 5.17/5.45 thf(fact_4650_fact__ge__self,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_self
% 5.17/5.45 thf(fact_4651_fact__nonzero,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri773545260158071498ct_rat @ N )
% 5.17/5.45 != zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_nonzero
% 5.17/5.45 thf(fact_4652_fact__nonzero,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri1406184849735516958ct_int @ N )
% 5.17/5.45 != zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % fact_nonzero
% 5.17/5.45 thf(fact_4653_fact__nonzero,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri1408675320244567234ct_nat @ N )
% 5.17/5.45 != zero_zero_nat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_nonzero
% 5.17/5.45 thf(fact_4654_fact__nonzero,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri2265585572941072030t_real @ N )
% 5.17/5.45 != zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % fact_nonzero
% 5.17/5.45 thf(fact_4655_fact__nonzero,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( semiri5044797733671781792omplex @ N )
% 5.17/5.45 != zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % fact_nonzero
% 5.17/5.45 thf(fact_4656_signed__take__bit__mult,axiom,
% 5.17/5.45 ! [N: nat,K: int,L: int] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.17/5.45 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_mult
% 5.17/5.45 thf(fact_4657_signed__take__bit__add,axiom,
% 5.17/5.45 ! [N: nat,K: int,L: int] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.17/5.45 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_add
% 5.17/5.45 thf(fact_4658_signed__take__bit__diff,axiom,
% 5.17/5.45 ! [N: nat,K: int,L: int] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.17/5.45 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_diff
% 5.17/5.45 thf(fact_4659_ln__less__self,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_less_self
% 5.17/5.45 thf(fact_4660_fact__less__mono__nat,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.45 => ( ( ord_less_nat @ M @ N )
% 5.17/5.45 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_less_mono_nat
% 5.17/5.45 thf(fact_4661_fact__ge__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_zero
% 5.17/5.45 thf(fact_4662_fact__ge__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_zero
% 5.17/5.45 thf(fact_4663_fact__ge__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_zero
% 5.17/5.45 thf(fact_4664_fact__ge__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_zero
% 5.17/5.45 thf(fact_4665_fact__gt__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_gt_zero
% 5.17/5.45 thf(fact_4666_fact__gt__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_gt_zero
% 5.17/5.45 thf(fact_4667_fact__gt__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_gt_zero
% 5.17/5.45 thf(fact_4668_fact__gt__zero,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_gt_zero
% 5.17/5.45 thf(fact_4669_fact__not__neg,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_not_neg
% 5.17/5.45 thf(fact_4670_fact__not__neg,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % fact_not_neg
% 5.17/5.45 thf(fact_4671_fact__not__neg,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.17/5.45
% 5.17/5.45 % fact_not_neg
% 5.17/5.45 thf(fact_4672_fact__not__neg,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % fact_not_neg
% 5.17/5.45 thf(fact_4673_fact__ge__1,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_1
% 5.17/5.45 thf(fact_4674_fact__ge__1,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_1
% 5.17/5.45 thf(fact_4675_fact__ge__1,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_1
% 5.17/5.45 thf(fact_4676_fact__ge__1,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_1
% 5.17/5.45 thf(fact_4677_fact__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mono
% 5.17/5.45 thf(fact_4678_fact__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mono
% 5.17/5.45 thf(fact_4679_fact__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mono
% 5.17/5.45 thf(fact_4680_fact__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mono
% 5.17/5.45 thf(fact_4681_fact__dvd,axiom,
% 5.17/5.45 ! [N: nat,M: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.45 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_dvd
% 5.17/5.45 thf(fact_4682_fact__dvd,axiom,
% 5.17/5.45 ! [N: nat,M: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.45 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_dvd
% 5.17/5.45 thf(fact_4683_fact__dvd,axiom,
% 5.17/5.45 ! [N: nat,M: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.45 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_dvd
% 5.17/5.45 thf(fact_4684_fact__dvd,axiom,
% 5.17/5.45 ! [N: nat,M: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.45 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_dvd
% 5.17/5.45 thf(fact_4685_fact__diff__Suc,axiom,
% 5.17/5.45 ! [N: nat,M: nat] :
% 5.17/5.45 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.17/5.45 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.17/5.45 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_diff_Suc
% 5.17/5.45 thf(fact_4686_ln__bound,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_bound
% 5.17/5.45 thf(fact_4687_ln__gt__zero,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.45 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_gt_zero
% 5.17/5.45 thf(fact_4688_ln__less__zero,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.45 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_less_zero
% 5.17/5.45 thf(fact_4689_ln__gt__zero__imp__gt__one,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_gt_zero_imp_gt_one
% 5.17/5.45 thf(fact_4690_ln__ge__zero,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.45 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_ge_zero
% 5.17/5.45 thf(fact_4691_fact__ge__Suc__0__nat,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_ge_Suc_0_nat
% 5.17/5.45 thf(fact_4692_dvd__fact,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.17/5.45 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_fact
% 5.17/5.45 thf(fact_4693_fact__less__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.45 => ( ( ord_less_nat @ M @ N )
% 5.17/5.45 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_less_mono
% 5.17/5.45 thf(fact_4694_fact__less__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.45 => ( ( ord_less_nat @ M @ N )
% 5.17/5.45 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_less_mono
% 5.17/5.45 thf(fact_4695_fact__less__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.45 => ( ( ord_less_nat @ M @ N )
% 5.17/5.45 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_less_mono
% 5.17/5.45 thf(fact_4696_fact__less__mono,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.45 => ( ( ord_less_nat @ M @ N )
% 5.17/5.45 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_less_mono
% 5.17/5.45 thf(fact_4697_fact__fact__dvd__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_fact_dvd_fact
% 5.17/5.45 thf(fact_4698_fact__fact__dvd__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_fact_dvd_fact
% 5.17/5.45 thf(fact_4699_fact__fact__dvd__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_fact_dvd_fact
% 5.17/5.45 thf(fact_4700_fact__fact__dvd__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_fact_dvd_fact
% 5.17/5.45 thf(fact_4701_fact__fact__dvd__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_fact_dvd_fact
% 5.17/5.45 thf(fact_4702_fact__mod,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.17/5.45 = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mod
% 5.17/5.45 thf(fact_4703_fact__mod,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mod
% 5.17/5.45 thf(fact_4704_fact__mod,axiom,
% 5.17/5.45 ! [M: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.45 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.17/5.45 = zero_zero_nat ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_mod
% 5.17/5.45 thf(fact_4705_fact__le__power,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_le_power
% 5.17/5.45 thf(fact_4706_fact__le__power,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_le_power
% 5.17/5.45 thf(fact_4707_fact__le__power,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_le_power
% 5.17/5.45 thf(fact_4708_fact__le__power,axiom,
% 5.17/5.45 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_le_power
% 5.17/5.45 thf(fact_4709_ln__2__less__1,axiom,
% 5.17/5.45 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.17/5.45
% 5.17/5.45 % ln_2_less_1
% 5.17/5.45 thf(fact_4710_ln__ge__zero__imp__ge__one,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_ge_zero_imp_ge_one
% 5.17/5.45 thf(fact_4711_ln__add__one__self__le__self,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_add_one_self_le_self
% 5.17/5.45 thf(fact_4712_ln__mult,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.45 => ( ( ln_ln_real @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.45 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y4 ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_mult
% 5.17/5.45 thf(fact_4713_ln__eq__minus__one,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ( ln_ln_real @ X )
% 5.17/5.45 = ( minus_minus_real @ X @ one_one_real ) )
% 5.17/5.45 => ( X = one_one_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_eq_minus_one
% 5.17/5.45 thf(fact_4714_ln__div,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.45 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.45 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y4 ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_div
% 5.17/5.45 thf(fact_4715_fact__div__fact__le__pow,axiom,
% 5.17/5.45 ! [R2: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ R2 @ N )
% 5.17/5.45 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_div_fact_le_pow
% 5.17/5.45 thf(fact_4716_binomial__fact__lemma,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.17/5.45 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % binomial_fact_lemma
% 5.17/5.45 thf(fact_4717_choose__dvd,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % choose_dvd
% 5.17/5.45 thf(fact_4718_choose__dvd,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % choose_dvd
% 5.17/5.45 thf(fact_4719_choose__dvd,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % choose_dvd
% 5.17/5.45 thf(fact_4720_choose__dvd,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % choose_dvd
% 5.17/5.45 thf(fact_4721_choose__dvd,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % choose_dvd
% 5.17/5.45 thf(fact_4722_ln__le__minus__one,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_le_minus_one
% 5.17/5.45 thf(fact_4723_ln__diff__le,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.45 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y4 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y4 ) @ Y4 ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_diff_le
% 5.17/5.45 thf(fact_4724_ln__realpow,axiom,
% 5.17/5.45 ! [X: real,N: nat] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 5.17/5.45 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_realpow
% 5.17/5.45 thf(fact_4725_binomial__altdef__nat,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( binomial @ N @ K )
% 5.17/5.45 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % binomial_altdef_nat
% 5.17/5.45 thf(fact_4726_signed__take__bit__int__less__exp,axiom,
% 5.17/5.45 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_int_less_exp
% 5.17/5.45 thf(fact_4727_num_Osize__gen_I1_J,axiom,
% 5.17/5.45 ( ( size_num @ one )
% 5.17/5.45 = zero_zero_nat ) ).
% 5.17/5.45
% 5.17/5.45 % num.size_gen(1)
% 5.17/5.45 thf(fact_4728_even__signed__take__bit__iff,axiom,
% 5.17/5.45 ! [M: nat,A: code_integer] :
% 5.17/5.45 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.17/5.45 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % even_signed_take_bit_iff
% 5.17/5.45 thf(fact_4729_even__signed__take__bit__iff,axiom,
% 5.17/5.45 ! [M: nat,A: int] :
% 5.17/5.45 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.17/5.45 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % even_signed_take_bit_iff
% 5.17/5.45 thf(fact_4730_square__fact__le__2__fact,axiom,
% 5.17/5.45 ! [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 ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % square_fact_le_2_fact
% 5.17/5.45 thf(fact_4731_fact__num__eq__if,axiom,
% 5.17/5.45 ( semiri773545260158071498ct_rat
% 5.17/5.45 = ( ^ [M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M5 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_num_eq_if
% 5.17/5.45 thf(fact_4732_fact__num__eq__if,axiom,
% 5.17/5.45 ( semiri1406184849735516958ct_int
% 5.17/5.45 = ( ^ [M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_num_eq_if
% 5.17/5.45 thf(fact_4733_fact__num__eq__if,axiom,
% 5.17/5.45 ( semiri1408675320244567234ct_nat
% 5.17/5.45 = ( ^ [M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M5 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_num_eq_if
% 5.17/5.45 thf(fact_4734_fact__num__eq__if,axiom,
% 5.17/5.45 ( semiri2265585572941072030t_real
% 5.17/5.45 = ( ^ [M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_num_eq_if
% 5.17/5.45 thf(fact_4735_fact__num__eq__if,axiom,
% 5.17/5.45 ( semiri5044797733671781792omplex
% 5.17/5.45 = ( ^ [M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M5 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_num_eq_if
% 5.17/5.45 thf(fact_4736_fact__reduce,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.45 => ( ( semiri773545260158071498ct_rat @ N )
% 5.17/5.45 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_reduce
% 5.17/5.45 thf(fact_4737_fact__reduce,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.45 => ( ( semiri1406184849735516958ct_int @ N )
% 5.17/5.45 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_reduce
% 5.17/5.45 thf(fact_4738_fact__reduce,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.45 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.17/5.45 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_reduce
% 5.17/5.45 thf(fact_4739_fact__reduce,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.45 => ( ( semiri2265585572941072030t_real @ N )
% 5.17/5.45 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_reduce
% 5.17/5.45 thf(fact_4740_fact__reduce,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.45 => ( ( semiri5044797733671781792omplex @ N )
% 5.17/5.45 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_reduce
% 5.17/5.45 thf(fact_4741_signed__take__bit__int__less__self__iff,axiom,
% 5.17/5.45 ! [N: nat,K: int] :
% 5.17/5.45 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.17/5.45 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_int_less_self_iff
% 5.17/5.45 thf(fact_4742_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.17/5.45 ! [K: int,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.17/5.45 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_int_greater_eq_self_iff
% 5.17/5.45 thf(fact_4743_fact__binomial,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.17/5.45 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_binomial
% 5.17/5.45 thf(fact_4744_fact__binomial,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.17/5.45 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_binomial
% 5.17/5.45 thf(fact_4745_fact__binomial,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.17/5.45 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % fact_binomial
% 5.17/5.45 thf(fact_4746_binomial__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.17/5.45 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % binomial_fact
% 5.17/5.45 thf(fact_4747_binomial__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.17/5.45 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % binomial_fact
% 5.17/5.45 thf(fact_4748_binomial__fact,axiom,
% 5.17/5.45 ! [K: nat,N: nat] :
% 5.17/5.45 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.45 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.17/5.45 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % binomial_fact
% 5.17/5.45 thf(fact_4749_add__0__iff,axiom,
% 5.17/5.45 ! [B: complex,A: complex] :
% 5.17/5.45 ( ( B
% 5.17/5.45 = ( plus_plus_complex @ B @ A ) )
% 5.17/5.45 = ( A = zero_zero_complex ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_0_iff
% 5.17/5.45 thf(fact_4750_add__0__iff,axiom,
% 5.17/5.45 ! [B: real,A: real] :
% 5.17/5.45 ( ( B
% 5.17/5.45 = ( plus_plus_real @ B @ A ) )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_0_iff
% 5.17/5.45 thf(fact_4751_add__0__iff,axiom,
% 5.17/5.45 ! [B: rat,A: rat] :
% 5.17/5.45 ( ( B
% 5.17/5.45 = ( plus_plus_rat @ B @ A ) )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_0_iff
% 5.17/5.45 thf(fact_4752_add__0__iff,axiom,
% 5.17/5.45 ! [B: nat,A: nat] :
% 5.17/5.45 ( ( B
% 5.17/5.45 = ( plus_plus_nat @ B @ A ) )
% 5.17/5.45 = ( A = zero_zero_nat ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_0_iff
% 5.17/5.45 thf(fact_4753_add__0__iff,axiom,
% 5.17/5.45 ! [B: int,A: int] :
% 5.17/5.45 ( ( B
% 5.17/5.45 = ( plus_plus_int @ B @ A ) )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_0_iff
% 5.17/5.45 thf(fact_4754_crossproduct__eq,axiom,
% 5.17/5.45 ! [W: real,Y4: real,X: real,Z: real] :
% 5.17/5.45 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y4 ) @ ( times_times_real @ X @ Z ) )
% 5.17/5.45 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y4 ) ) )
% 5.17/5.45 = ( ( W = X )
% 5.17/5.45 | ( Y4 = Z ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_eq
% 5.17/5.45 thf(fact_4755_crossproduct__eq,axiom,
% 5.17/5.45 ! [W: rat,Y4: rat,X: rat,Z: rat] :
% 5.17/5.45 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y4 ) @ ( times_times_rat @ X @ Z ) )
% 5.17/5.45 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y4 ) ) )
% 5.17/5.45 = ( ( W = X )
% 5.17/5.45 | ( Y4 = Z ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_eq
% 5.17/5.45 thf(fact_4756_crossproduct__eq,axiom,
% 5.17/5.45 ! [W: nat,Y4: nat,X: nat,Z: nat] :
% 5.17/5.45 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y4 ) @ ( times_times_nat @ X @ Z ) )
% 5.17/5.45 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y4 ) ) )
% 5.17/5.45 = ( ( W = X )
% 5.17/5.45 | ( Y4 = Z ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_eq
% 5.17/5.45 thf(fact_4757_crossproduct__eq,axiom,
% 5.17/5.45 ! [W: int,Y4: int,X: int,Z: int] :
% 5.17/5.45 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y4 ) @ ( times_times_int @ X @ Z ) )
% 5.17/5.45 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y4 ) ) )
% 5.17/5.45 = ( ( W = X )
% 5.17/5.45 | ( Y4 = Z ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_eq
% 5.17/5.45 thf(fact_4758_crossproduct__noteq,axiom,
% 5.17/5.45 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.45 ( ( ( A != B )
% 5.17/5.45 & ( C != D ) )
% 5.17/5.45 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.17/5.45 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_noteq
% 5.17/5.45 thf(fact_4759_crossproduct__noteq,axiom,
% 5.17/5.45 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.17/5.45 ( ( ( A != B )
% 5.17/5.45 & ( C != D ) )
% 5.17/5.45 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.17/5.45 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_noteq
% 5.17/5.45 thf(fact_4760_crossproduct__noteq,axiom,
% 5.17/5.45 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.17/5.45 ( ( ( A != B )
% 5.17/5.45 & ( C != D ) )
% 5.17/5.45 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.17/5.45 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_noteq
% 5.17/5.45 thf(fact_4761_crossproduct__noteq,axiom,
% 5.17/5.45 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.45 ( ( ( A != B )
% 5.17/5.45 & ( C != D ) )
% 5.17/5.45 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.17/5.45 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % crossproduct_noteq
% 5.17/5.45 thf(fact_4762_signed__take__bit__int__less__eq,axiom,
% 5.17/5.45 ! [N: nat,K: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.17/5.45 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_int_less_eq
% 5.17/5.45 thf(fact_4763_eq__diff__eq_H,axiom,
% 5.17/5.45 ! [X: real,Y4: real,Z: real] :
% 5.17/5.45 ( ( X
% 5.17/5.45 = ( minus_minus_real @ Y4 @ Z ) )
% 5.17/5.45 = ( Y4
% 5.17/5.45 = ( plus_plus_real @ X @ Z ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % eq_diff_eq'
% 5.17/5.45 thf(fact_4764_ln__one__plus__pos__lower__bound,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.45 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_one_plus_pos_lower_bound
% 5.17/5.45 thf(fact_4765_num_Osize__gen_I2_J,axiom,
% 5.17/5.45 ! [X2: num] :
% 5.17/5.45 ( ( size_num @ ( bit0 @ X2 ) )
% 5.17/5.45 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % num.size_gen(2)
% 5.17/5.45 thf(fact_4766_binomial__code,axiom,
% 5.17/5.45 ( binomial
% 5.17/5.45 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % binomial_code
% 5.17/5.45 thf(fact_4767_tanh__ln__real,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.17/5.45 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_ln_real
% 5.17/5.45 thf(fact_4768_ln__one__minus__pos__lower__bound,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.45 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.45 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % ln_one_minus_pos_lower_bound
% 5.17/5.45 thf(fact_4769_signed__take__bit__Suc__minus__bit1,axiom,
% 5.17/5.45 ! [N: nat,K: num] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.17/5.45 = ( 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 ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_Suc_minus_bit1
% 5.17/5.45 thf(fact_4770_signed__take__bit__rec,axiom,
% 5.17/5.45 ( bit_ri6519982836138164636nteger
% 5.17/5.45 = ( ^ [N4: nat,A3: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_rec
% 5.17/5.45 thf(fact_4771_signed__take__bit__rec,axiom,
% 5.17/5.45 ( bit_ri631733984087533419it_int
% 5.17/5.45 = ( ^ [N4: nat,A3: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( 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 @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_rec
% 5.17/5.45 thf(fact_4772_map__cnt,axiom,
% 5.17/5.45 ( ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ zero_zero_real )
% 5.17/5.45 = ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % map_cnt
% 5.17/5.45 thf(fact_4773_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.45 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_ln_one_plus_x_minus_x_bound
% 5.17/5.45 thf(fact_4774_add_Oinverse__inverse,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_inverse
% 5.17/5.45 thf(fact_4775_add_Oinverse__inverse,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_inverse
% 5.17/5.45 thf(fact_4776_add_Oinverse__inverse,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_inverse
% 5.17/5.45 thf(fact_4777_add_Oinverse__inverse,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_inverse
% 5.17/5.45 thf(fact_4778_add_Oinverse__inverse,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_inverse
% 5.17/5.45 thf(fact_4779_neg__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( ( uminus_uminus_real @ A )
% 5.17/5.45 = ( uminus_uminus_real @ B ) )
% 5.17/5.45 = ( A = B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_iff_equal
% 5.17/5.45 thf(fact_4780_neg__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ A )
% 5.17/5.45 = ( uminus_uminus_int @ B ) )
% 5.17/5.45 = ( A = B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_iff_equal
% 5.17/5.45 thf(fact_4781_neg__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( ( uminus1482373934393186551omplex @ A )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.45 = ( A = B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_iff_equal
% 5.17/5.45 thf(fact_4782_neg__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = ( A = B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_iff_equal
% 5.17/5.45 thf(fact_4783_neg__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( ( uminus_uminus_rat @ A )
% 5.17/5.45 = ( uminus_uminus_rat @ B ) )
% 5.17/5.45 = ( A = B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_iff_equal
% 5.17/5.45 thf(fact_4784_verit__minus__simplify_I4_J,axiom,
% 5.17/5.45 ! [B: real] :
% 5.17/5.45 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(4)
% 5.17/5.45 thf(fact_4785_verit__minus__simplify_I4_J,axiom,
% 5.17/5.45 ! [B: int] :
% 5.17/5.45 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(4)
% 5.17/5.45 thf(fact_4786_verit__minus__simplify_I4_J,axiom,
% 5.17/5.45 ! [B: complex] :
% 5.17/5.45 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(4)
% 5.17/5.45 thf(fact_4787_verit__minus__simplify_I4_J,axiom,
% 5.17/5.45 ! [B: code_integer] :
% 5.17/5.45 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(4)
% 5.17/5.45 thf(fact_4788_verit__minus__simplify_I4_J,axiom,
% 5.17/5.45 ! [B: rat] :
% 5.17/5.45 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(4)
% 5.17/5.45 thf(fact_4789_Compl__subset__Compl__iff,axiom,
% 5.17/5.45 ! [A2: set_int,B4: set_int] :
% 5.17/5.45 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B4 ) )
% 5.17/5.45 = ( ord_less_eq_set_int @ B4 @ A2 ) ) ).
% 5.17/5.45
% 5.17/5.45 % Compl_subset_Compl_iff
% 5.17/5.45 thf(fact_4790_Compl__anti__mono,axiom,
% 5.17/5.45 ! [A2: set_int,B4: set_int] :
% 5.17/5.45 ( ( ord_less_eq_set_int @ A2 @ B4 )
% 5.17/5.45 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B4 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % Compl_anti_mono
% 5.17/5.45 thf(fact_4791_abs__idempotent,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.17/5.45 = ( abs_abs_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_idempotent
% 5.17/5.45 thf(fact_4792_abs__idempotent,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.17/5.45 = ( abs_abs_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_idempotent
% 5.17/5.45 thf(fact_4793_abs__idempotent,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.17/5.45 = ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_idempotent
% 5.17/5.45 thf(fact_4794_abs__idempotent,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.17/5.45 = ( abs_abs_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_idempotent
% 5.17/5.45 thf(fact_4795_abs__abs,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.17/5.45 = ( abs_abs_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_abs
% 5.17/5.45 thf(fact_4796_abs__abs,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.17/5.45 = ( abs_abs_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_abs
% 5.17/5.45 thf(fact_4797_abs__abs,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.17/5.45 = ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_abs
% 5.17/5.45 thf(fact_4798_abs__abs,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.17/5.45 = ( abs_abs_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_abs
% 5.17/5.45 thf(fact_4799_neg__le__iff__le,axiom,
% 5.17/5.45 ! [B: code_integer,A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_iff_le
% 5.17/5.45 thf(fact_4800_neg__le__iff__le,axiom,
% 5.17/5.45 ! [B: rat,A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_iff_le
% 5.17/5.45 thf(fact_4801_neg__le__iff__le,axiom,
% 5.17/5.45 ! [B: int,A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_iff_le
% 5.17/5.45 thf(fact_4802_neg__le__iff__le,axiom,
% 5.17/5.45 ! [B: real,A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_iff_le
% 5.17/5.45 thf(fact_4803_neg__equal__zero,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ( uminus_uminus_real @ A )
% 5.17/5.45 = A )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_zero
% 5.17/5.45 thf(fact_4804_neg__equal__zero,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ A )
% 5.17/5.45 = A )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_zero
% 5.17/5.45 thf(fact_4805_neg__equal__zero,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.45 = A )
% 5.17/5.45 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_zero
% 5.17/5.45 thf(fact_4806_neg__equal__zero,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ( uminus_uminus_rat @ A )
% 5.17/5.45 = A )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_zero
% 5.17/5.45 thf(fact_4807_equal__neg__zero,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( A
% 5.17/5.45 = ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % equal_neg_zero
% 5.17/5.45 thf(fact_4808_equal__neg__zero,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( A
% 5.17/5.45 = ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % equal_neg_zero
% 5.17/5.45 thf(fact_4809_equal__neg__zero,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( A
% 5.17/5.45 = ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % equal_neg_zero
% 5.17/5.45 thf(fact_4810_equal__neg__zero,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( A
% 5.17/5.45 = ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % equal_neg_zero
% 5.17/5.45 thf(fact_4811_neg__equal__0__iff__equal,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ( uminus_uminus_real @ A )
% 5.17/5.45 = zero_zero_real )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_0_iff_equal
% 5.17/5.45 thf(fact_4812_neg__equal__0__iff__equal,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ A )
% 5.17/5.45 = zero_zero_int )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_0_iff_equal
% 5.17/5.45 thf(fact_4813_neg__equal__0__iff__equal,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( ( uminus1482373934393186551omplex @ A )
% 5.17/5.45 = zero_zero_complex )
% 5.17/5.45 = ( A = zero_zero_complex ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_0_iff_equal
% 5.17/5.45 thf(fact_4814_neg__equal__0__iff__equal,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.45 = zero_z3403309356797280102nteger )
% 5.17/5.45 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_0_iff_equal
% 5.17/5.45 thf(fact_4815_neg__equal__0__iff__equal,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ( uminus_uminus_rat @ A )
% 5.17/5.45 = zero_zero_rat )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_equal_0_iff_equal
% 5.17/5.45 thf(fact_4816_neg__0__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( zero_zero_real
% 5.17/5.45 = ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( zero_zero_real = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_equal_iff_equal
% 5.17/5.45 thf(fact_4817_neg__0__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( zero_zero_int
% 5.17/5.45 = ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( zero_zero_int = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_equal_iff_equal
% 5.17/5.45 thf(fact_4818_neg__0__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( zero_zero_complex
% 5.17/5.45 = ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.45 = ( zero_zero_complex = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_equal_iff_equal
% 5.17/5.45 thf(fact_4819_neg__0__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( zero_z3403309356797280102nteger
% 5.17/5.45 = ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_equal_iff_equal
% 5.17/5.45 thf(fact_4820_neg__0__equal__iff__equal,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( zero_zero_rat
% 5.17/5.45 = ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( zero_zero_rat = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_equal_iff_equal
% 5.17/5.45 thf(fact_4821_add_Oinverse__neutral,axiom,
% 5.17/5.45 ( ( uminus_uminus_real @ zero_zero_real )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_neutral
% 5.17/5.45 thf(fact_4822_add_Oinverse__neutral,axiom,
% 5.17/5.45 ( ( uminus_uminus_int @ zero_zero_int )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_neutral
% 5.17/5.45 thf(fact_4823_add_Oinverse__neutral,axiom,
% 5.17/5.45 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_neutral
% 5.17/5.45 thf(fact_4824_add_Oinverse__neutral,axiom,
% 5.17/5.45 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_neutral
% 5.17/5.45 thf(fact_4825_add_Oinverse__neutral,axiom,
% 5.17/5.45 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % add.inverse_neutral
% 5.17/5.45 thf(fact_4826_neg__less__iff__less,axiom,
% 5.17/5.45 ! [B: real,A: real] :
% 5.17/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( ord_less_real @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_iff_less
% 5.17/5.45 thf(fact_4827_neg__less__iff__less,axiom,
% 5.17/5.45 ! [B: int,A: int] :
% 5.17/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( ord_less_int @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_iff_less
% 5.17/5.45 thf(fact_4828_neg__less__iff__less,axiom,
% 5.17/5.45 ! [B: code_integer,A: code_integer] :
% 5.17/5.45 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_iff_less
% 5.17/5.45 thf(fact_4829_neg__less__iff__less,axiom,
% 5.17/5.45 ! [B: rat,A: rat] :
% 5.17/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( ord_less_rat @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_iff_less
% 5.17/5.45 thf(fact_4830_neg__numeral__eq__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( M = N ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_eq_iff
% 5.17/5.45 thf(fact_4831_neg__numeral__eq__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( M = N ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_eq_iff
% 5.17/5.45 thf(fact_4832_neg__numeral__eq__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.45 = ( M = N ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_eq_iff
% 5.17/5.45 thf(fact_4833_neg__numeral__eq__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( M = N ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_eq_iff
% 5.17/5.45 thf(fact_4834_neg__numeral__eq__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( M = N ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_eq_iff
% 5.17/5.45 thf(fact_4835_mult__minus__left,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.45 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_left
% 5.17/5.45 thf(fact_4836_mult__minus__left,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.45 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_left
% 5.17/5.45 thf(fact_4837_mult__minus__left,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_left
% 5.17/5.45 thf(fact_4838_mult__minus__left,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_left
% 5.17/5.45 thf(fact_4839_mult__minus__left,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.45 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_left
% 5.17/5.45 thf(fact_4840_minus__mult__minus,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.17/5.45 = ( times_times_real @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mult_minus
% 5.17/5.45 thf(fact_4841_minus__mult__minus,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.17/5.45 = ( times_times_int @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mult_minus
% 5.17/5.45 thf(fact_4842_minus__mult__minus,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.45 = ( times_times_complex @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mult_minus
% 5.17/5.45 thf(fact_4843_minus__mult__minus,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mult_minus
% 5.17/5.45 thf(fact_4844_minus__mult__minus,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.17/5.45 = ( times_times_rat @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mult_minus
% 5.17/5.45 thf(fact_4845_mult__minus__right,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_right
% 5.17/5.45 thf(fact_4846_mult__minus__right,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_right
% 5.17/5.45 thf(fact_4847_mult__minus__right,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_right
% 5.17/5.45 thf(fact_4848_mult__minus__right,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_right
% 5.17/5.45 thf(fact_4849_mult__minus__right,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus_right
% 5.17/5.45 thf(fact_4850_add__minus__cancel,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % add_minus_cancel
% 5.17/5.45 thf(fact_4851_add__minus__cancel,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % add_minus_cancel
% 5.17/5.45 thf(fact_4852_add__minus__cancel,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % add_minus_cancel
% 5.17/5.45 thf(fact_4853_add__minus__cancel,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % add_minus_cancel
% 5.17/5.45 thf(fact_4854_add__minus__cancel,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % add_minus_cancel
% 5.17/5.45 thf(fact_4855_minus__add__cancel,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_cancel
% 5.17/5.45 thf(fact_4856_minus__add__cancel,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_cancel
% 5.17/5.45 thf(fact_4857_minus__add__cancel,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_cancel
% 5.17/5.45 thf(fact_4858_minus__add__cancel,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_cancel
% 5.17/5.45 thf(fact_4859_minus__add__cancel,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.45 = B ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_cancel
% 5.17/5.45 thf(fact_4860_minus__add__distrib,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.17/5.45 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_distrib
% 5.17/5.45 thf(fact_4861_minus__add__distrib,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.17/5.45 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_distrib
% 5.17/5.45 thf(fact_4862_minus__add__distrib,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.17/5.45 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_distrib
% 5.17/5.45 thf(fact_4863_minus__add__distrib,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.45 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_distrib
% 5.17/5.45 thf(fact_4864_minus__add__distrib,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.45 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_add_distrib
% 5.17/5.45 thf(fact_4865_minus__diff__eq,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.17/5.45 = ( minus_minus_real @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_diff_eq
% 5.17/5.45 thf(fact_4866_minus__diff__eq,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.17/5.45 = ( minus_minus_int @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_diff_eq
% 5.17/5.45 thf(fact_4867_minus__diff__eq,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.17/5.45 = ( minus_minus_complex @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_diff_eq
% 5.17/5.45 thf(fact_4868_minus__diff__eq,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.17/5.45 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_diff_eq
% 5.17/5.45 thf(fact_4869_minus__diff__eq,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.17/5.45 = ( minus_minus_rat @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_diff_eq
% 5.17/5.45 thf(fact_4870_div__minus__minus,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.17/5.45 = ( divide_divide_int @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % div_minus_minus
% 5.17/5.45 thf(fact_4871_div__minus__minus,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % div_minus_minus
% 5.17/5.45 thf(fact_4872_abs__0,axiom,
% 5.17/5.45 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0
% 5.17/5.45 thf(fact_4873_abs__0,axiom,
% 5.17/5.45 ( ( abs_abs_complex @ zero_zero_complex )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0
% 5.17/5.45 thf(fact_4874_abs__0,axiom,
% 5.17/5.45 ( ( abs_abs_real @ zero_zero_real )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0
% 5.17/5.45 thf(fact_4875_abs__0,axiom,
% 5.17/5.45 ( ( abs_abs_rat @ zero_zero_rat )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0
% 5.17/5.45 thf(fact_4876_abs__0,axiom,
% 5.17/5.45 ( ( abs_abs_int @ zero_zero_int )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0
% 5.17/5.45 thf(fact_4877_abs__zero,axiom,
% 5.17/5.45 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % abs_zero
% 5.17/5.45 thf(fact_4878_abs__zero,axiom,
% 5.17/5.45 ( ( abs_abs_real @ zero_zero_real )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % abs_zero
% 5.17/5.45 thf(fact_4879_abs__zero,axiom,
% 5.17/5.45 ( ( abs_abs_rat @ zero_zero_rat )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % abs_zero
% 5.17/5.45 thf(fact_4880_abs__zero,axiom,
% 5.17/5.45 ( ( abs_abs_int @ zero_zero_int )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % abs_zero
% 5.17/5.45 thf(fact_4881_abs__eq__0,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ( abs_abs_Code_integer @ A )
% 5.17/5.45 = zero_z3403309356797280102nteger )
% 5.17/5.45 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_eq_0
% 5.17/5.45 thf(fact_4882_abs__eq__0,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ( abs_abs_real @ A )
% 5.17/5.45 = zero_zero_real )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_eq_0
% 5.17/5.45 thf(fact_4883_abs__eq__0,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ( abs_abs_rat @ A )
% 5.17/5.45 = zero_zero_rat )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_eq_0
% 5.17/5.45 thf(fact_4884_abs__eq__0,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ( abs_abs_int @ A )
% 5.17/5.45 = zero_zero_int )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_eq_0
% 5.17/5.45 thf(fact_4885_abs__0__eq,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( zero_z3403309356797280102nteger
% 5.17/5.45 = ( abs_abs_Code_integer @ A ) )
% 5.17/5.45 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0_eq
% 5.17/5.45 thf(fact_4886_abs__0__eq,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( zero_zero_real
% 5.17/5.45 = ( abs_abs_real @ A ) )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0_eq
% 5.17/5.45 thf(fact_4887_abs__0__eq,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( zero_zero_rat
% 5.17/5.45 = ( abs_abs_rat @ A ) )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0_eq
% 5.17/5.45 thf(fact_4888_abs__0__eq,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( zero_zero_int
% 5.17/5.45 = ( abs_abs_int @ A ) )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_0_eq
% 5.17/5.45 thf(fact_4889_minus__dvd__iff,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y4 )
% 5.17/5.45 = ( dvd_dvd_real @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_dvd_iff
% 5.17/5.45 thf(fact_4890_minus__dvd__iff,axiom,
% 5.17/5.45 ! [X: int,Y4: int] :
% 5.17/5.45 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y4 )
% 5.17/5.45 = ( dvd_dvd_int @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_dvd_iff
% 5.17/5.45 thf(fact_4891_minus__dvd__iff,axiom,
% 5.17/5.45 ! [X: complex,Y4: complex] :
% 5.17/5.45 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y4 )
% 5.17/5.45 = ( dvd_dvd_complex @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_dvd_iff
% 5.17/5.45 thf(fact_4892_minus__dvd__iff,axiom,
% 5.17/5.45 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.45 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y4 )
% 5.17/5.45 = ( dvd_dvd_Code_integer @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_dvd_iff
% 5.17/5.45 thf(fact_4893_minus__dvd__iff,axiom,
% 5.17/5.45 ! [X: rat,Y4: rat] :
% 5.17/5.45 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y4 )
% 5.17/5.45 = ( dvd_dvd_rat @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_dvd_iff
% 5.17/5.45 thf(fact_4894_dvd__minus__iff,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y4 ) )
% 5.17/5.45 = ( dvd_dvd_real @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_minus_iff
% 5.17/5.45 thf(fact_4895_dvd__minus__iff,axiom,
% 5.17/5.45 ! [X: int,Y4: int] :
% 5.17/5.45 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y4 ) )
% 5.17/5.45 = ( dvd_dvd_int @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_minus_iff
% 5.17/5.45 thf(fact_4896_dvd__minus__iff,axiom,
% 5.17/5.45 ! [X: complex,Y4: complex] :
% 5.17/5.45 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y4 ) )
% 5.17/5.45 = ( dvd_dvd_complex @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_minus_iff
% 5.17/5.45 thf(fact_4897_dvd__minus__iff,axiom,
% 5.17/5.45 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.45 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y4 ) )
% 5.17/5.45 = ( dvd_dvd_Code_integer @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_minus_iff
% 5.17/5.45 thf(fact_4898_dvd__minus__iff,axiom,
% 5.17/5.45 ! [X: rat,Y4: rat] :
% 5.17/5.45 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y4 ) )
% 5.17/5.45 = ( dvd_dvd_rat @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_minus_iff
% 5.17/5.45 thf(fact_4899_abs__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.17/5.45 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_numeral
% 5.17/5.45 thf(fact_4900_abs__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.17/5.45 = ( numeral_numeral_real @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_numeral
% 5.17/5.45 thf(fact_4901_abs__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.17/5.45 = ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_numeral
% 5.17/5.45 thf(fact_4902_abs__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.17/5.45 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_numeral
% 5.17/5.45 thf(fact_4903_abs__mult__self__eq,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.17/5.45 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_mult_self_eq
% 5.17/5.45 thf(fact_4904_abs__mult__self__eq,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.17/5.45 = ( times_times_real @ A @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_mult_self_eq
% 5.17/5.45 thf(fact_4905_abs__mult__self__eq,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.17/5.45 = ( times_times_rat @ A @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_mult_self_eq
% 5.17/5.45 thf(fact_4906_abs__mult__self__eq,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.17/5.45 = ( times_times_int @ A @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_mult_self_eq
% 5.17/5.45 thf(fact_4907_abs__add__abs,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.17/5.45 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_add_abs
% 5.17/5.45 thf(fact_4908_abs__add__abs,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.17/5.45 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_add_abs
% 5.17/5.45 thf(fact_4909_abs__add__abs,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.17/5.45 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_add_abs
% 5.17/5.45 thf(fact_4910_abs__add__abs,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.17/5.45 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_add_abs
% 5.17/5.45 thf(fact_4911_abs__1,axiom,
% 5.17/5.45 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.17/5.45 = one_one_Code_integer ) ).
% 5.17/5.45
% 5.17/5.45 % abs_1
% 5.17/5.45 thf(fact_4912_abs__1,axiom,
% 5.17/5.45 ( ( abs_abs_complex @ one_one_complex )
% 5.17/5.45 = one_one_complex ) ).
% 5.17/5.45
% 5.17/5.45 % abs_1
% 5.17/5.45 thf(fact_4913_abs__1,axiom,
% 5.17/5.45 ( ( abs_abs_real @ one_one_real )
% 5.17/5.45 = one_one_real ) ).
% 5.17/5.45
% 5.17/5.45 % abs_1
% 5.17/5.45 thf(fact_4914_abs__1,axiom,
% 5.17/5.45 ( ( abs_abs_rat @ one_one_rat )
% 5.17/5.45 = one_one_rat ) ).
% 5.17/5.45
% 5.17/5.45 % abs_1
% 5.17/5.45 thf(fact_4915_abs__1,axiom,
% 5.17/5.45 ( ( abs_abs_int @ one_one_int )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % abs_1
% 5.17/5.45 thf(fact_4916_abs__divide,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.45 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_divide
% 5.17/5.45 thf(fact_4917_abs__divide,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.45 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_divide
% 5.17/5.45 thf(fact_4918_abs__divide,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.45 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_divide
% 5.17/5.45 thf(fact_4919_abs__minus__cancel,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( abs_abs_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus_cancel
% 5.17/5.45 thf(fact_4920_abs__minus__cancel,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( abs_abs_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus_cancel
% 5.17/5.45 thf(fact_4921_abs__minus__cancel,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus_cancel
% 5.17/5.45 thf(fact_4922_abs__minus__cancel,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( abs_abs_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus_cancel
% 5.17/5.45 thf(fact_4923_abs__minus,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( abs_abs_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus
% 5.17/5.45 thf(fact_4924_abs__minus,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( abs_abs_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus
% 5.17/5.45 thf(fact_4925_abs__minus,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.45 = ( abs_abs_complex @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus
% 5.17/5.45 thf(fact_4926_abs__minus,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus
% 5.17/5.45 thf(fact_4927_abs__minus,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( abs_abs_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_minus
% 5.17/5.45 thf(fact_4928_mod__minus__minus,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mod_minus_minus
% 5.17/5.45 thf(fact_4929_mod__minus__minus,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mod_minus_minus
% 5.17/5.45 thf(fact_4930_dvd__abs__iff,axiom,
% 5.17/5.45 ! [M: real,K: real] :
% 5.17/5.45 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.17/5.45 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_abs_iff
% 5.17/5.45 thf(fact_4931_dvd__abs__iff,axiom,
% 5.17/5.45 ! [M: int,K: int] :
% 5.17/5.45 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.17/5.45 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_abs_iff
% 5.17/5.45 thf(fact_4932_dvd__abs__iff,axiom,
% 5.17/5.45 ! [M: code_integer,K: code_integer] :
% 5.17/5.45 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.17/5.45 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_abs_iff
% 5.17/5.45 thf(fact_4933_dvd__abs__iff,axiom,
% 5.17/5.45 ! [M: rat,K: rat] :
% 5.17/5.45 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.17/5.45 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % dvd_abs_iff
% 5.17/5.45 thf(fact_4934_abs__dvd__iff,axiom,
% 5.17/5.45 ! [M: real,K: real] :
% 5.17/5.45 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.17/5.45 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_dvd_iff
% 5.17/5.45 thf(fact_4935_abs__dvd__iff,axiom,
% 5.17/5.45 ! [M: int,K: int] :
% 5.17/5.45 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.17/5.45 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_dvd_iff
% 5.17/5.45 thf(fact_4936_abs__dvd__iff,axiom,
% 5.17/5.45 ! [M: code_integer,K: code_integer] :
% 5.17/5.45 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.17/5.45 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_dvd_iff
% 5.17/5.45 thf(fact_4937_abs__dvd__iff,axiom,
% 5.17/5.45 ! [M: rat,K: rat] :
% 5.17/5.45 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.17/5.45 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_dvd_iff
% 5.17/5.45 thf(fact_4938_abs__of__nat,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.17/5.45 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nat
% 5.17/5.45 thf(fact_4939_abs__of__nat,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.45 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nat
% 5.17/5.45 thf(fact_4940_abs__of__nat,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.45 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nat
% 5.17/5.45 thf(fact_4941_abs__of__nat,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.45 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nat
% 5.17/5.45 thf(fact_4942_abs__bool__eq,axiom,
% 5.17/5.45 ! [P: $o] :
% 5.17/5.45 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.17/5.45 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_bool_eq
% 5.17/5.45 thf(fact_4943_abs__bool__eq,axiom,
% 5.17/5.45 ! [P: $o] :
% 5.17/5.45 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.17/5.45 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_bool_eq
% 5.17/5.45 thf(fact_4944_abs__bool__eq,axiom,
% 5.17/5.45 ! [P: $o] :
% 5.17/5.45 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.45 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_bool_eq
% 5.17/5.45 thf(fact_4945_abs__bool__eq,axiom,
% 5.17/5.45 ! [P: $o] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.17/5.45 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_bool_eq
% 5.17/5.45 thf(fact_4946_tanh__0,axiom,
% 5.17/5.45 ( ( tanh_complex @ zero_zero_complex )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_0
% 5.17/5.45 thf(fact_4947_tanh__0,axiom,
% 5.17/5.45 ( ( tanh_real @ zero_zero_real )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_0
% 5.17/5.45 thf(fact_4948_tanh__real__zero__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ( tanh_real @ X )
% 5.17/5.45 = zero_zero_real )
% 5.17/5.45 = ( X = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_real_zero_iff
% 5.17/5.45 thf(fact_4949_tanh__real__le__iff,axiom,
% 5.17/5.45 ! [X: real,Y4: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y4 ) )
% 5.17/5.45 = ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_real_le_iff
% 5.17/5.45 thf(fact_4950_neg__less__eq__nonneg,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.17/5.45 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_eq_nonneg
% 5.17/5.45 thf(fact_4951_neg__less__eq__nonneg,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.17/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_eq_nonneg
% 5.17/5.45 thf(fact_4952_neg__less__eq__nonneg,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.17/5.45 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_eq_nonneg
% 5.17/5.45 thf(fact_4953_neg__less__eq__nonneg,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.17/5.45 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_eq_nonneg
% 5.17/5.45 thf(fact_4954_less__eq__neg__nonpos,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_eq_neg_nonpos
% 5.17/5.45 thf(fact_4955_less__eq__neg__nonpos,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_eq_neg_nonpos
% 5.17/5.45 thf(fact_4956_less__eq__neg__nonpos,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_eq_neg_nonpos
% 5.17/5.45 thf(fact_4957_less__eq__neg__nonpos,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_eq_neg_nonpos
% 5.17/5.45 thf(fact_4958_neg__le__0__iff__le,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.17/5.45 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_0_iff_le
% 5.17/5.45 thf(fact_4959_neg__le__0__iff__le,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.17/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_0_iff_le
% 5.17/5.45 thf(fact_4960_neg__le__0__iff__le,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.17/5.45 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_0_iff_le
% 5.17/5.45 thf(fact_4961_neg__le__0__iff__le,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.17/5.45 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_le_0_iff_le
% 5.17/5.45 thf(fact_4962_neg__0__le__iff__le,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_le_iff_le
% 5.17/5.45 thf(fact_4963_neg__0__le__iff__le,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_le_iff_le
% 5.17/5.45 thf(fact_4964_neg__0__le__iff__le,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_le_iff_le
% 5.17/5.45 thf(fact_4965_neg__0__le__iff__le,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_le_iff_le
% 5.17/5.45 thf(fact_4966_less__neg__neg,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_neg_neg
% 5.17/5.45 thf(fact_4967_less__neg__neg,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_neg_neg
% 5.17/5.45 thf(fact_4968_less__neg__neg,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_neg_neg
% 5.17/5.45 thf(fact_4969_less__neg__neg,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % less_neg_neg
% 5.17/5.45 thf(fact_4970_neg__less__pos,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.17/5.45 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_pos
% 5.17/5.45 thf(fact_4971_neg__less__pos,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.17/5.45 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_pos
% 5.17/5.45 thf(fact_4972_neg__less__pos,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.17/5.45 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_pos
% 5.17/5.45 thf(fact_4973_neg__less__pos,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.17/5.45 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_pos
% 5.17/5.45 thf(fact_4974_neg__0__less__iff__less,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_less_iff_less
% 5.17/5.45 thf(fact_4975_neg__0__less__iff__less,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_less_iff_less
% 5.17/5.45 thf(fact_4976_neg__0__less__iff__less,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_less_iff_less
% 5.17/5.45 thf(fact_4977_neg__0__less__iff__less,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_0_less_iff_less
% 5.17/5.45 thf(fact_4978_neg__less__0__iff__less,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.17/5.45 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_0_iff_less
% 5.17/5.45 thf(fact_4979_neg__less__0__iff__less,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.17/5.45 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_0_iff_less
% 5.17/5.45 thf(fact_4980_neg__less__0__iff__less,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.17/5.45 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_0_iff_less
% 5.17/5.45 thf(fact_4981_neg__less__0__iff__less,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.17/5.45 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_less_0_iff_less
% 5.17/5.45 thf(fact_4982_ab__left__minus,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % ab_left_minus
% 5.17/5.45 thf(fact_4983_ab__left__minus,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % ab_left_minus
% 5.17/5.45 thf(fact_4984_ab__left__minus,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % ab_left_minus
% 5.17/5.45 thf(fact_4985_ab__left__minus,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % ab_left_minus
% 5.17/5.45 thf(fact_4986_ab__left__minus,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % ab_left_minus
% 5.17/5.45 thf(fact_4987_add_Oright__inverse,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % add.right_inverse
% 5.17/5.45 thf(fact_4988_add_Oright__inverse,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % add.right_inverse
% 5.17/5.45 thf(fact_4989_add_Oright__inverse,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % add.right_inverse
% 5.17/5.45 thf(fact_4990_add_Oright__inverse,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % add.right_inverse
% 5.17/5.45 thf(fact_4991_add_Oright__inverse,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % add.right_inverse
% 5.17/5.45 thf(fact_4992_verit__minus__simplify_I3_J,axiom,
% 5.17/5.45 ! [B: real] :
% 5.17/5.45 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.17/5.45 = ( uminus_uminus_real @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(3)
% 5.17/5.45 thf(fact_4993_verit__minus__simplify_I3_J,axiom,
% 5.17/5.45 ! [B: int] :
% 5.17/5.45 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.17/5.45 = ( uminus_uminus_int @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(3)
% 5.17/5.45 thf(fact_4994_verit__minus__simplify_I3_J,axiom,
% 5.17/5.45 ! [B: complex] :
% 5.17/5.45 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(3)
% 5.17/5.45 thf(fact_4995_verit__minus__simplify_I3_J,axiom,
% 5.17/5.45 ! [B: code_integer] :
% 5.17/5.45 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(3)
% 5.17/5.45 thf(fact_4996_verit__minus__simplify_I3_J,axiom,
% 5.17/5.45 ! [B: rat] :
% 5.17/5.45 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.17/5.45 = ( uminus_uminus_rat @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % verit_minus_simplify(3)
% 5.17/5.45 thf(fact_4997_diff__0,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.17/5.45 = ( uminus_uminus_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_0
% 5.17/5.45 thf(fact_4998_diff__0,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.17/5.45 = ( uminus_uminus_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_0
% 5.17/5.45 thf(fact_4999_diff__0,axiom,
% 5.17/5.45 ! [A: complex] :
% 5.17/5.45 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_0
% 5.17/5.45 thf(fact_5000_diff__0,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_0
% 5.17/5.45 thf(fact_5001_diff__0,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.17/5.45 = ( uminus_uminus_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_0
% 5.17/5.45 thf(fact_5002_add__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5003_add__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5004_add__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5005_add__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5006_add__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5007_mult__minus1__right,axiom,
% 5.17/5.45 ! [Z: real] :
% 5.17/5.45 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = ( uminus_uminus_real @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1_right
% 5.17/5.45 thf(fact_5008_mult__minus1__right,axiom,
% 5.17/5.45 ! [Z: int] :
% 5.17/5.45 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = ( uminus_uminus_int @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1_right
% 5.17/5.45 thf(fact_5009_mult__minus1__right,axiom,
% 5.17/5.45 ! [Z: complex] :
% 5.17/5.45 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1_right
% 5.17/5.45 thf(fact_5010_mult__minus1__right,axiom,
% 5.17/5.45 ! [Z: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1_right
% 5.17/5.45 thf(fact_5011_mult__minus1__right,axiom,
% 5.17/5.45 ! [Z: rat] :
% 5.17/5.45 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = ( uminus_uminus_rat @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1_right
% 5.17/5.45 thf(fact_5012_mult__minus1,axiom,
% 5.17/5.45 ! [Z: real] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.17/5.45 = ( uminus_uminus_real @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1
% 5.17/5.45 thf(fact_5013_mult__minus1,axiom,
% 5.17/5.45 ! [Z: int] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.17/5.45 = ( uminus_uminus_int @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1
% 5.17/5.45 thf(fact_5014_mult__minus1,axiom,
% 5.17/5.45 ! [Z: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1
% 5.17/5.45 thf(fact_5015_mult__minus1,axiom,
% 5.17/5.45 ! [Z: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1
% 5.17/5.45 thf(fact_5016_mult__minus1,axiom,
% 5.17/5.45 ! [Z: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.17/5.45 = ( uminus_uminus_rat @ Z ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_minus1
% 5.17/5.45 thf(fact_5017_abs__le__zero__iff,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.17/5.45 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_zero_iff
% 5.17/5.45 thf(fact_5018_abs__le__zero__iff,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.17/5.45 = ( A = zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_zero_iff
% 5.17/5.45 thf(fact_5019_abs__le__zero__iff,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.17/5.45 = ( A = zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_zero_iff
% 5.17/5.45 thf(fact_5020_abs__le__zero__iff,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.17/5.45 = ( A = zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_zero_iff
% 5.17/5.45 thf(fact_5021_abs__le__self__iff,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.17/5.45 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_self_iff
% 5.17/5.45 thf(fact_5022_abs__le__self__iff,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.17/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_self_iff
% 5.17/5.45 thf(fact_5023_abs__le__self__iff,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.17/5.45 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_self_iff
% 5.17/5.45 thf(fact_5024_abs__le__self__iff,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.17/5.45 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_le_self_iff
% 5.17/5.45 thf(fact_5025_abs__of__nonneg,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.45 => ( ( abs_abs_Code_integer @ A )
% 5.17/5.45 = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonneg
% 5.17/5.45 thf(fact_5026_abs__of__nonneg,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.45 => ( ( abs_abs_rat @ A )
% 5.17/5.45 = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonneg
% 5.17/5.45 thf(fact_5027_abs__of__nonneg,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.45 => ( ( abs_abs_int @ A )
% 5.17/5.45 = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonneg
% 5.17/5.45 thf(fact_5028_abs__of__nonneg,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.45 => ( ( abs_abs_real @ A )
% 5.17/5.45 = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonneg
% 5.17/5.45 thf(fact_5029_diff__minus__eq__add,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.17/5.45 = ( plus_plus_real @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_minus_eq_add
% 5.17/5.45 thf(fact_5030_diff__minus__eq__add,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.45 = ( plus_plus_int @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_minus_eq_add
% 5.17/5.45 thf(fact_5031_diff__minus__eq__add,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.45 = ( plus_plus_complex @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_minus_eq_add
% 5.17/5.45 thf(fact_5032_diff__minus__eq__add,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.45 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_minus_eq_add
% 5.17/5.45 thf(fact_5033_diff__minus__eq__add,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.17/5.45 = ( plus_plus_rat @ A @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_minus_eq_add
% 5.17/5.45 thf(fact_5034_uminus__add__conv__diff,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.45 = ( minus_minus_real @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % uminus_add_conv_diff
% 5.17/5.45 thf(fact_5035_uminus__add__conv__diff,axiom,
% 5.17/5.45 ! [A: int,B: int] :
% 5.17/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.45 = ( minus_minus_int @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % uminus_add_conv_diff
% 5.17/5.45 thf(fact_5036_uminus__add__conv__diff,axiom,
% 5.17/5.45 ! [A: complex,B: complex] :
% 5.17/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.17/5.45 = ( minus_minus_complex @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % uminus_add_conv_diff
% 5.17/5.45 thf(fact_5037_uminus__add__conv__diff,axiom,
% 5.17/5.45 ! [A: code_integer,B: code_integer] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.45 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % uminus_add_conv_diff
% 5.17/5.45 thf(fact_5038_uminus__add__conv__diff,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.45 = ( minus_minus_rat @ B @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % uminus_add_conv_diff
% 5.17/5.45 thf(fact_5039_zero__less__abs__iff,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.17/5.45 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.17/5.45
% 5.17/5.45 % zero_less_abs_iff
% 5.17/5.45 thf(fact_5040_zero__less__abs__iff,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.17/5.45 = ( A != zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % zero_less_abs_iff
% 5.17/5.45 thf(fact_5041_zero__less__abs__iff,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.17/5.45 = ( A != zero_zero_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % zero_less_abs_iff
% 5.17/5.45 thf(fact_5042_zero__less__abs__iff,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.17/5.45 = ( A != zero_zero_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % zero_less_abs_iff
% 5.17/5.45 thf(fact_5043_div__minus1__right,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = ( uminus_uminus_int @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % div_minus1_right
% 5.17/5.45 thf(fact_5044_div__minus1__right,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.17/5.45
% 5.17/5.45 % div_minus1_right
% 5.17/5.45 thf(fact_5045_divide__minus1,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = ( uminus_uminus_real @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % divide_minus1
% 5.17/5.45 thf(fact_5046_divide__minus1,axiom,
% 5.17/5.45 ! [X: complex] :
% 5.17/5.45 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % divide_minus1
% 5.17/5.45 thf(fact_5047_divide__minus1,axiom,
% 5.17/5.45 ! [X: rat] :
% 5.17/5.45 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = ( uminus_uminus_rat @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % divide_minus1
% 5.17/5.45 thf(fact_5048_abs__neg__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_real @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_numeral
% 5.17/5.45 thf(fact_5049_abs__neg__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_numeral
% 5.17/5.45 thf(fact_5050_abs__neg__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_numeral
% 5.17/5.45 thf(fact_5051_abs__neg__numeral,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_numeral
% 5.17/5.45 thf(fact_5052_abs__neg__one,axiom,
% 5.17/5.45 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = one_one_real ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_one
% 5.17/5.45 thf(fact_5053_abs__neg__one,axiom,
% 5.17/5.45 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_one
% 5.17/5.45 thf(fact_5054_abs__neg__one,axiom,
% 5.17/5.45 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = one_one_Code_integer ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_one
% 5.17/5.45 thf(fact_5055_abs__neg__one,axiom,
% 5.17/5.45 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = one_one_rat ) ).
% 5.17/5.45
% 5.17/5.45 % abs_neg_one
% 5.17/5.45 thf(fact_5056_minus__mod__self1,axiom,
% 5.17/5.45 ! [B: int,A: int] :
% 5.17/5.45 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.17/5.45 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mod_self1
% 5.17/5.45 thf(fact_5057_minus__mod__self1,axiom,
% 5.17/5.45 ! [B: code_integer,A: code_integer] :
% 5.17/5.45 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.17/5.45 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.17/5.45
% 5.17/5.45 % minus_mod_self1
% 5.17/5.45 thf(fact_5058_negative__eq__positive,axiom,
% 5.17/5.45 ! [N: nat,M: nat] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.45 = ( semiri1314217659103216013at_int @ M ) )
% 5.17/5.45 = ( ( N = zero_zero_nat )
% 5.17/5.45 & ( M = zero_zero_nat ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % negative_eq_positive
% 5.17/5.45 thf(fact_5059_real__add__minus__iff,axiom,
% 5.17/5.45 ! [X: real,A: real] :
% 5.17/5.45 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.17/5.45 = zero_zero_real )
% 5.17/5.45 = ( X = A ) ) ).
% 5.17/5.45
% 5.17/5.45 % real_add_minus_iff
% 5.17/5.45 thf(fact_5060_signed__take__bit__of__minus__1,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_of_minus_1
% 5.17/5.45 thf(fact_5061_signed__take__bit__of__minus__1,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % signed_take_bit_of_minus_1
% 5.17/5.45 thf(fact_5062_negative__zle,axiom,
% 5.17/5.45 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % negative_zle
% 5.17/5.45 thf(fact_5063_tanh__real__neg__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.17/5.45 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_real_neg_iff
% 5.17/5.45 thf(fact_5064_tanh__real__pos__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.17/5.45 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_real_pos_iff
% 5.17/5.45 thf(fact_5065_tanh__real__nonpos__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.17/5.45 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_real_nonpos_iff
% 5.17/5.45 thf(fact_5066_tanh__real__nonneg__iff,axiom,
% 5.17/5.45 ! [X: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.17/5.45 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.45
% 5.17/5.45 % tanh_real_nonneg_iff
% 5.17/5.45 thf(fact_5067_dbl__simps_I1_J,axiom,
% 5.17/5.45 ! [K: num] :
% 5.17/5.45 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_simps(1)
% 5.17/5.45 thf(fact_5068_dbl__simps_I1_J,axiom,
% 5.17/5.45 ! [K: num] :
% 5.17/5.45 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_simps(1)
% 5.17/5.45 thf(fact_5069_dbl__simps_I1_J,axiom,
% 5.17/5.45 ! [K: num] :
% 5.17/5.45 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_simps(1)
% 5.17/5.45 thf(fact_5070_dbl__simps_I1_J,axiom,
% 5.17/5.45 ! [K: num] :
% 5.17/5.45 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_simps(1)
% 5.17/5.45 thf(fact_5071_dbl__simps_I1_J,axiom,
% 5.17/5.45 ! [K: num] :
% 5.17/5.45 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_simps(1)
% 5.17/5.45 thf(fact_5072_dbl__inc__simps_I4_J,axiom,
% 5.17/5.45 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_inc_simps(4)
% 5.17/5.45 thf(fact_5073_dbl__inc__simps_I4_J,axiom,
% 5.17/5.45 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_inc_simps(4)
% 5.17/5.45 thf(fact_5074_dbl__inc__simps_I4_J,axiom,
% 5.17/5.45 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_inc_simps(4)
% 5.17/5.45 thf(fact_5075_dbl__inc__simps_I4_J,axiom,
% 5.17/5.45 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_inc_simps(4)
% 5.17/5.45 thf(fact_5076_dbl__inc__simps_I4_J,axiom,
% 5.17/5.45 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.45
% 5.17/5.45 % dbl_inc_simps(4)
% 5.17/5.45 thf(fact_5077_add__neg__numeral__special_I8_J,axiom,
% 5.17/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(8)
% 5.17/5.45 thf(fact_5078_add__neg__numeral__special_I8_J,axiom,
% 5.17/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(8)
% 5.17/5.45 thf(fact_5079_add__neg__numeral__special_I8_J,axiom,
% 5.17/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(8)
% 5.17/5.45 thf(fact_5080_add__neg__numeral__special_I8_J,axiom,
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(8)
% 5.17/5.45 thf(fact_5081_add__neg__numeral__special_I8_J,axiom,
% 5.17/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(8)
% 5.17/5.45 thf(fact_5082_add__neg__numeral__special_I7_J,axiom,
% 5.17/5.45 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(7)
% 5.17/5.45 thf(fact_5083_add__neg__numeral__special_I7_J,axiom,
% 5.17/5.45 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(7)
% 5.17/5.45 thf(fact_5084_add__neg__numeral__special_I7_J,axiom,
% 5.17/5.45 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(7)
% 5.17/5.45 thf(fact_5085_add__neg__numeral__special_I7_J,axiom,
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(7)
% 5.17/5.45 thf(fact_5086_add__neg__numeral__special_I7_J,axiom,
% 5.17/5.45 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % add_neg_numeral_special(7)
% 5.17/5.45 thf(fact_5087_diff__numeral__special_I12_J,axiom,
% 5.17/5.45 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = zero_zero_real ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_special(12)
% 5.17/5.45 thf(fact_5088_diff__numeral__special_I12_J,axiom,
% 5.17/5.45 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_special(12)
% 5.17/5.45 thf(fact_5089_diff__numeral__special_I12_J,axiom,
% 5.17/5.45 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.45 = zero_zero_complex ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_special(12)
% 5.17/5.45 thf(fact_5090_diff__numeral__special_I12_J,axiom,
% 5.17/5.45 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_special(12)
% 5.17/5.45 thf(fact_5091_diff__numeral__special_I12_J,axiom,
% 5.17/5.45 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = zero_zero_rat ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_special(12)
% 5.17/5.45 thf(fact_5092_neg__one__eq__numeral__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_real @ one_one_real )
% 5.17/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_one_eq_numeral_iff
% 5.17/5.45 thf(fact_5093_neg__one__eq__numeral__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ one_one_int )
% 5.17/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_one_eq_numeral_iff
% 5.17/5.45 thf(fact_5094_neg__one__eq__numeral__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_one_eq_numeral_iff
% 5.17/5.45 thf(fact_5095_neg__one__eq__numeral__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_one_eq_numeral_iff
% 5.17/5.45 thf(fact_5096_neg__one__eq__numeral__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.17/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_one_eq_numeral_iff
% 5.17/5.45 thf(fact_5097_numeral__eq__neg__one__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.17/5.45 = ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % numeral_eq_neg_one_iff
% 5.17/5.45 thf(fact_5098_numeral__eq__neg__one__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.17/5.45 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % numeral_eq_neg_one_iff
% 5.17/5.45 thf(fact_5099_numeral__eq__neg__one__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % numeral_eq_neg_one_iff
% 5.17/5.45 thf(fact_5100_numeral__eq__neg__one__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % numeral_eq_neg_one_iff
% 5.17/5.45 thf(fact_5101_numeral__eq__neg__one__iff,axiom,
% 5.17/5.45 ! [N: num] :
% 5.17/5.45 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.17/5.45 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.45 = ( N = one ) ) ).
% 5.17/5.45
% 5.17/5.45 % numeral_eq_neg_one_iff
% 5.17/5.45 thf(fact_5102_divide__le__0__abs__iff,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.17/5.45 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.45 | ( B = zero_zero_rat ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % divide_le_0_abs_iff
% 5.17/5.45 thf(fact_5103_divide__le__0__abs__iff,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.17/5.45 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.45 | ( B = zero_zero_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % divide_le_0_abs_iff
% 5.17/5.45 thf(fact_5104_zero__le__divide__abs__iff,axiom,
% 5.17/5.45 ! [A: rat,B: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.17/5.45 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.45 | ( B = zero_zero_rat ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % zero_le_divide_abs_iff
% 5.17/5.45 thf(fact_5105_zero__le__divide__abs__iff,axiom,
% 5.17/5.45 ! [A: real,B: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.17/5.45 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.45 | ( B = zero_zero_real ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % zero_le_divide_abs_iff
% 5.17/5.45 thf(fact_5106_abs__of__nonpos,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.17/5.45 => ( ( abs_abs_Code_integer @ A )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonpos
% 5.17/5.45 thf(fact_5107_abs__of__nonpos,axiom,
% 5.17/5.45 ! [A: rat] :
% 5.17/5.45 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.17/5.45 => ( ( abs_abs_rat @ A )
% 5.17/5.45 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonpos
% 5.17/5.45 thf(fact_5108_abs__of__nonpos,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.17/5.45 => ( ( abs_abs_int @ A )
% 5.17/5.45 = ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonpos
% 5.17/5.45 thf(fact_5109_abs__of__nonpos,axiom,
% 5.17/5.45 ! [A: real] :
% 5.17/5.45 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.45 => ( ( abs_abs_real @ A )
% 5.17/5.45 = ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % abs_of_nonpos
% 5.17/5.45 thf(fact_5110_minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.17/5.45 = one_one_real ) ).
% 5.17/5.45
% 5.17/5.45 % minus_one_mult_self
% 5.17/5.45 thf(fact_5111_minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.17/5.45 = one_one_int ) ).
% 5.17/5.45
% 5.17/5.45 % minus_one_mult_self
% 5.17/5.45 thf(fact_5112_minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.17/5.45 = one_one_complex ) ).
% 5.17/5.45
% 5.17/5.45 % minus_one_mult_self
% 5.17/5.45 thf(fact_5113_minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.17/5.45 = one_one_Code_integer ) ).
% 5.17/5.45
% 5.17/5.45 % minus_one_mult_self
% 5.17/5.45 thf(fact_5114_minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat] :
% 5.17/5.45 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.17/5.45 = one_one_rat ) ).
% 5.17/5.45
% 5.17/5.45 % minus_one_mult_self
% 5.17/5.45 thf(fact_5115_left__minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat,A: real] :
% 5.17/5.45 ( ( 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 ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % left_minus_one_mult_self
% 5.17/5.45 thf(fact_5116_left__minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat,A: int] :
% 5.17/5.45 ( ( 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 ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % left_minus_one_mult_self
% 5.17/5.45 thf(fact_5117_left__minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat,A: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % left_minus_one_mult_self
% 5.17/5.45 thf(fact_5118_left__minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat,A: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % left_minus_one_mult_self
% 5.17/5.45 thf(fact_5119_left__minus__one__mult__self,axiom,
% 5.17/5.45 ! [N: nat,A: rat] :
% 5.17/5.45 ( ( 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 ) )
% 5.17/5.45 = A ) ).
% 5.17/5.45
% 5.17/5.45 % left_minus_one_mult_self
% 5.17/5.45 thf(fact_5120_mod__minus1__right,axiom,
% 5.17/5.45 ! [A: int] :
% 5.17/5.45 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.45 = zero_zero_int ) ).
% 5.17/5.45
% 5.17/5.45 % mod_minus1_right
% 5.17/5.45 thf(fact_5121_mod__minus1__right,axiom,
% 5.17/5.45 ! [A: code_integer] :
% 5.17/5.45 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.45 = zero_z3403309356797280102nteger ) ).
% 5.17/5.45
% 5.17/5.45 % mod_minus1_right
% 5.17/5.45 thf(fact_5122_norm__neg__numeral,axiom,
% 5.17/5.45 ! [W: num] :
% 5.17/5.45 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.45 = ( numeral_numeral_real @ W ) ) ).
% 5.17/5.45
% 5.17/5.45 % norm_neg_numeral
% 5.17/5.45 thf(fact_5123_norm__neg__numeral,axiom,
% 5.17/5.45 ! [W: num] :
% 5.17/5.45 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.45 = ( numeral_numeral_real @ W ) ) ).
% 5.17/5.45
% 5.17/5.45 % norm_neg_numeral
% 5.17/5.45 thf(fact_5124_semiring__norm_I168_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: real] :
% 5.17/5.45 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(168)
% 5.17/5.45 thf(fact_5125_semiring__norm_I168_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: int] :
% 5.17/5.45 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(168)
% 5.17/5.45 thf(fact_5126_semiring__norm_I168_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: complex] :
% 5.17/5.45 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(168)
% 5.17/5.45 thf(fact_5127_semiring__norm_I168_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: code_integer] :
% 5.17/5.45 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(168)
% 5.17/5.45 thf(fact_5128_semiring__norm_I168_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: rat] :
% 5.17/5.45 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(168)
% 5.17/5.45 thf(fact_5129_diff__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(3)
% 5.17/5.45 thf(fact_5130_diff__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(3)
% 5.17/5.45 thf(fact_5131_diff__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(3)
% 5.17/5.45 thf(fact_5132_diff__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(3)
% 5.17/5.45 thf(fact_5133_diff__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(3)
% 5.17/5.45 thf(fact_5134_diff__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(2)
% 5.17/5.45 thf(fact_5135_diff__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(2)
% 5.17/5.45 thf(fact_5136_diff__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.45 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(2)
% 5.17/5.45 thf(fact_5137_diff__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(2)
% 5.17/5.45 thf(fact_5138_diff__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % diff_numeral_simps(2)
% 5.17/5.45 thf(fact_5139_semiring__norm_I172_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: real] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(172)
% 5.17/5.45 thf(fact_5140_semiring__norm_I172_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: int] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(172)
% 5.17/5.45 thf(fact_5141_semiring__norm_I172_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(172)
% 5.17/5.45 thf(fact_5142_semiring__norm_I172_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(172)
% 5.17/5.45 thf(fact_5143_semiring__norm_I172_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(172)
% 5.17/5.45 thf(fact_5144_semiring__norm_I171_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: real] :
% 5.17/5.45 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(171)
% 5.17/5.45 thf(fact_5145_semiring__norm_I171_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: int] :
% 5.17/5.45 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(171)
% 5.17/5.45 thf(fact_5146_semiring__norm_I171_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(171)
% 5.17/5.45 thf(fact_5147_semiring__norm_I171_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(171)
% 5.17/5.45 thf(fact_5148_semiring__norm_I171_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y4 ) )
% 5.17/5.45 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(171)
% 5.17/5.45 thf(fact_5149_semiring__norm_I170_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: real] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y4 ) )
% 5.17/5.45 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(170)
% 5.17/5.45 thf(fact_5150_semiring__norm_I170_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: int] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y4 ) )
% 5.17/5.45 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(170)
% 5.17/5.45 thf(fact_5151_semiring__norm_I170_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: complex] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y4 ) )
% 5.17/5.45 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(170)
% 5.17/5.45 thf(fact_5152_semiring__norm_I170_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: code_integer] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y4 ) )
% 5.17/5.45 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(170)
% 5.17/5.45 thf(fact_5153_semiring__norm_I170_J,axiom,
% 5.17/5.45 ! [V: num,W: num,Y4: rat] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y4 ) )
% 5.17/5.45 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.17/5.45
% 5.17/5.45 % semiring_norm(170)
% 5.17/5.45 thf(fact_5154_mult__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5155_mult__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5156_mult__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5157_mult__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5158_mult__neg__numeral__simps_I3_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(3)
% 5.17/5.45 thf(fact_5159_mult__neg__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.45 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(2)
% 5.17/5.45 thf(fact_5160_mult__neg__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.45 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(2)
% 5.17/5.45 thf(fact_5161_mult__neg__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.45 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(2)
% 5.17/5.45 thf(fact_5162_mult__neg__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.17/5.45 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(2)
% 5.17/5.45 thf(fact_5163_mult__neg__numeral__simps_I2_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.45 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(2)
% 5.17/5.45 thf(fact_5164_mult__neg__numeral__simps_I1_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(1)
% 5.17/5.45 thf(fact_5165_mult__neg__numeral__simps_I1_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(1)
% 5.17/5.45 thf(fact_5166_mult__neg__numeral__simps_I1_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.45 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(1)
% 5.17/5.45 thf(fact_5167_mult__neg__numeral__simps_I1_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(1)
% 5.17/5.45 thf(fact_5168_mult__neg__numeral__simps_I1_J,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.17/5.45
% 5.17/5.45 % mult_neg_numeral_simps(1)
% 5.17/5.45 thf(fact_5169_negative__zless,axiom,
% 5.17/5.45 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % negative_zless
% 5.17/5.45 thf(fact_5170_neg__numeral__le__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.45 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_le_iff
% 5.17/5.45 thf(fact_5171_neg__numeral__le__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.45 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_le_iff
% 5.17/5.45 thf(fact_5172_neg__numeral__le__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_le_iff
% 5.17/5.45 thf(fact_5173_neg__numeral__le__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_le_iff
% 5.17/5.45 thf(fact_5174_neg__numeral__less__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.45 = ( ord_less_num @ N @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_less_iff
% 5.17/5.45 thf(fact_5175_neg__numeral__less__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.45 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.45 = ( ord_less_num @ N @ M ) ) ).
% 5.17/5.45
% 5.17/5.45 % neg_numeral_less_iff
% 5.17/5.45 thf(fact_5176_neg__numeral__less__iff,axiom,
% 5.17/5.45 ! [M: num,N: num] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.46 = ( ord_less_num @ N @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_iff
% 5.17/5.46 thf(fact_5177_neg__numeral__less__iff,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.46 = ( ord_less_num @ N @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_iff
% 5.17/5.46 thf(fact_5178_not__neg__one__le__neg__numeral__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_le_neg_numeral_iff
% 5.17/5.46 thf(fact_5179_not__neg__one__le__neg__numeral__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_le_neg_numeral_iff
% 5.17/5.46 thf(fact_5180_not__neg__one__le__neg__numeral__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_le_neg_numeral_iff
% 5.17/5.46 thf(fact_5181_not__neg__one__le__neg__numeral__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_le_neg_numeral_iff
% 5.17/5.46 thf(fact_5182_divide__le__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: rat,W: num,A: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.17/5.46 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_le_eq_numeral1(2)
% 5.17/5.46 thf(fact_5183_divide__le__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: real,W: num,A: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.17/5.46 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_le_eq_numeral1(2)
% 5.17/5.46 thf(fact_5184_le__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: rat,B: rat,W: num] :
% 5.17/5.46 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.17/5.46 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5185_le__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: real,B: real,W: num] :
% 5.17/5.46 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.17/5.46 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5186_divide__eq__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: real,W: num,A: real] :
% 5.17/5.46 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.46 = A )
% 5.17/5.46 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.46 != zero_zero_real )
% 5.17/5.46 => ( B
% 5.17/5.46 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.17/5.46 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.46 = zero_zero_real )
% 5.17/5.46 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_eq_eq_numeral1(2)
% 5.17/5.46 thf(fact_5187_divide__eq__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: complex,W: num,A: complex] :
% 5.17/5.46 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.46 = A )
% 5.17/5.46 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.46 != zero_zero_complex )
% 5.17/5.46 => ( B
% 5.17/5.46 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.17/5.46 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.46 = zero_zero_complex )
% 5.17/5.46 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_eq_eq_numeral1(2)
% 5.17/5.46 thf(fact_5188_divide__eq__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: rat,W: num,A: rat] :
% 5.17/5.46 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.46 = A )
% 5.17/5.46 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.46 != zero_zero_rat )
% 5.17/5.46 => ( B
% 5.17/5.46 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.17/5.46 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.46 = zero_zero_rat )
% 5.17/5.46 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_eq_eq_numeral1(2)
% 5.17/5.46 thf(fact_5189_eq__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: real,B: real,W: num] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.17/5.46 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.46 != zero_zero_real )
% 5.17/5.46 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.46 = B ) )
% 5.17/5.46 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.46 = zero_zero_real )
% 5.17/5.46 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5190_eq__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: complex,B: complex,W: num] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.17/5.46 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.46 != zero_zero_complex )
% 5.17/5.46 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.46 = B ) )
% 5.17/5.46 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.46 = zero_zero_complex )
% 5.17/5.46 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5191_eq__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: rat,B: rat,W: num] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.17/5.46 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.46 != zero_zero_rat )
% 5.17/5.46 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.46 = B ) )
% 5.17/5.46 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.46 = zero_zero_rat )
% 5.17/5.46 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5192_neg__numeral__less__neg__one__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_neg_one_iff
% 5.17/5.46 thf(fact_5193_neg__numeral__less__neg__one__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_neg_one_iff
% 5.17/5.46 thf(fact_5194_neg__numeral__less__neg__one__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_neg_one_iff
% 5.17/5.46 thf(fact_5195_neg__numeral__less__neg__one__iff,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.46 = ( M != one ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_neg_one_iff
% 5.17/5.46 thf(fact_5196_divide__less__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: real,W: num,A: real] :
% 5.17/5.46 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.17/5.46 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_less_eq_numeral1(2)
% 5.17/5.46 thf(fact_5197_divide__less__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [B: rat,W: num,A: rat] :
% 5.17/5.46 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.17/5.46 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_less_eq_numeral1(2)
% 5.17/5.46 thf(fact_5198_less__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: real,B: real,W: num] :
% 5.17/5.46 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.17/5.46 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5199_less__divide__eq__numeral1_I2_J,axiom,
% 5.17/5.46 ! [A: rat,B: rat,W: num] :
% 5.17/5.46 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.17/5.46 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_divide_eq_numeral1(2)
% 5.17/5.46 thf(fact_5200_power2__minus,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_minus
% 5.17/5.46 thf(fact_5201_power2__minus,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_minus
% 5.17/5.46 thf(fact_5202_power2__minus,axiom,
% 5.17/5.46 ! [A: complex] :
% 5.17/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_minus
% 5.17/5.46 thf(fact_5203_power2__minus,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_minus
% 5.17/5.46 thf(fact_5204_power2__minus,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_minus
% 5.17/5.46 thf(fact_5205_zero__less__power__abs__iff,axiom,
% 5.17/5.46 ! [A: code_integer,N: nat] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.17/5.46 = ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.46 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_less_power_abs_iff
% 5.17/5.46 thf(fact_5206_zero__less__power__abs__iff,axiom,
% 5.17/5.46 ! [A: real,N: nat] :
% 5.17/5.46 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.17/5.46 = ( ( A != zero_zero_real )
% 5.17/5.46 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_less_power_abs_iff
% 5.17/5.46 thf(fact_5207_zero__less__power__abs__iff,axiom,
% 5.17/5.46 ! [A: rat,N: nat] :
% 5.17/5.46 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.17/5.46 = ( ( A != zero_zero_rat )
% 5.17/5.46 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_less_power_abs_iff
% 5.17/5.46 thf(fact_5208_zero__less__power__abs__iff,axiom,
% 5.17/5.46 ! [A: int,N: nat] :
% 5.17/5.46 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.17/5.46 = ( ( A != zero_zero_int )
% 5.17/5.46 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_less_power_abs_iff
% 5.17/5.46 thf(fact_5209_abs__power2,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_power2
% 5.17/5.46 thf(fact_5210_abs__power2,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_power2
% 5.17/5.46 thf(fact_5211_abs__power2,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_power2
% 5.17/5.46 thf(fact_5212_abs__power2,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_power2
% 5.17/5.46 thf(fact_5213_power2__abs,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_abs
% 5.17/5.46 thf(fact_5214_power2__abs,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_abs
% 5.17/5.46 thf(fact_5215_power2__abs,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_abs
% 5.17/5.46 thf(fact_5216_power2__abs,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power2_abs
% 5.17/5.46 thf(fact_5217_add__neg__numeral__special_I9_J,axiom,
% 5.17/5.46 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.46 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_neg_numeral_special(9)
% 5.17/5.46 thf(fact_5218_add__neg__numeral__special_I9_J,axiom,
% 5.17/5.46 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_neg_numeral_special(9)
% 5.17/5.46 thf(fact_5219_add__neg__numeral__special_I9_J,axiom,
% 5.17/5.46 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_neg_numeral_special(9)
% 5.17/5.46 thf(fact_5220_add__neg__numeral__special_I9_J,axiom,
% 5.17/5.46 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_neg_numeral_special(9)
% 5.17/5.46 thf(fact_5221_add__neg__numeral__special_I9_J,axiom,
% 5.17/5.46 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.46 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_neg_numeral_special(9)
% 5.17/5.46 thf(fact_5222_diff__numeral__special_I11_J,axiom,
% 5.17/5.46 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.46 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(11)
% 5.17/5.46 thf(fact_5223_diff__numeral__special_I11_J,axiom,
% 5.17/5.46 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.46 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(11)
% 5.17/5.46 thf(fact_5224_diff__numeral__special_I11_J,axiom,
% 5.17/5.46 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.46 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(11)
% 5.17/5.46 thf(fact_5225_diff__numeral__special_I11_J,axiom,
% 5.17/5.46 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.46 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(11)
% 5.17/5.46 thf(fact_5226_diff__numeral__special_I11_J,axiom,
% 5.17/5.46 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.46 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(11)
% 5.17/5.46 thf(fact_5227_diff__numeral__special_I10_J,axiom,
% 5.17/5.46 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.17/5.46 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(10)
% 5.17/5.46 thf(fact_5228_diff__numeral__special_I10_J,axiom,
% 5.17/5.46 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.17/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(10)
% 5.17/5.46 thf(fact_5229_diff__numeral__special_I10_J,axiom,
% 5.17/5.46 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(10)
% 5.17/5.46 thf(fact_5230_diff__numeral__special_I10_J,axiom,
% 5.17/5.46 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(10)
% 5.17/5.46 thf(fact_5231_diff__numeral__special_I10_J,axiom,
% 5.17/5.46 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.17/5.46 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(10)
% 5.17/5.46 thf(fact_5232_minus__1__div__2__eq,axiom,
% 5.17/5.46 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_1_div_2_eq
% 5.17/5.46 thf(fact_5233_minus__1__div__2__eq,axiom,
% 5.17/5.46 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_1_div_2_eq
% 5.17/5.46 thf(fact_5234_minus__1__mod__2__eq,axiom,
% 5.17/5.46 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.46 = one_one_int ) ).
% 5.17/5.46
% 5.17/5.46 % minus_1_mod_2_eq
% 5.17/5.46 thf(fact_5235_minus__1__mod__2__eq,axiom,
% 5.17/5.46 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.46 = one_one_Code_integer ) ).
% 5.17/5.46
% 5.17/5.46 % minus_1_mod_2_eq
% 5.17/5.46 thf(fact_5236_bits__minus__1__mod__2__eq,axiom,
% 5.17/5.46 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.46 = one_one_int ) ).
% 5.17/5.46
% 5.17/5.46 % bits_minus_1_mod_2_eq
% 5.17/5.46 thf(fact_5237_bits__minus__1__mod__2__eq,axiom,
% 5.17/5.46 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.46 = one_one_Code_integer ) ).
% 5.17/5.46
% 5.17/5.46 % bits_minus_1_mod_2_eq
% 5.17/5.46 thf(fact_5238_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [A: real,N: nat] :
% 5.17/5.46 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Power.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5239_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [A: int,N: nat] :
% 5.17/5.46 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Power.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5240_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [A: complex,N: nat] :
% 5.17/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Power.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5241_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [A: code_integer,N: nat] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Power.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5242_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [A: rat,N: nat] :
% 5.17/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Power.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5243_power__minus__odd,axiom,
% 5.17/5.46 ! [N: nat,A: real] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.17/5.46 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_odd
% 5.17/5.46 thf(fact_5244_power__minus__odd,axiom,
% 5.17/5.46 ! [N: nat,A: int] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.17/5.46 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_odd
% 5.17/5.46 thf(fact_5245_power__minus__odd,axiom,
% 5.17/5.46 ! [N: nat,A: complex] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_odd
% 5.17/5.46 thf(fact_5246_power__minus__odd,axiom,
% 5.17/5.46 ! [N: nat,A: code_integer] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_odd
% 5.17/5.46 thf(fact_5247_power__minus__odd,axiom,
% 5.17/5.46 ! [N: nat,A: rat] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.17/5.46 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_odd
% 5.17/5.46 thf(fact_5248_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [N: nat,A: real] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.17/5.46 = ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Parity.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5249_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [N: nat,A: int] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.17/5.46 = ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Parity.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5250_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [N: nat,A: complex] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.17/5.46 = ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Parity.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5251_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [N: nat,A: code_integer] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.17/5.46 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Parity.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5252_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.17/5.46 ! [N: nat,A: rat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.17/5.46 = ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % Parity.ring_1_class.power_minus_even
% 5.17/5.46 thf(fact_5253_power__even__abs__numeral,axiom,
% 5.17/5.46 ! [W: num,A: code_integer] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_even_abs_numeral
% 5.17/5.46 thf(fact_5254_power__even__abs__numeral,axiom,
% 5.17/5.46 ! [W: num,A: rat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_even_abs_numeral
% 5.17/5.46 thf(fact_5255_power__even__abs__numeral,axiom,
% 5.17/5.46 ! [W: num,A: int] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_even_abs_numeral
% 5.17/5.46 thf(fact_5256_power__even__abs__numeral,axiom,
% 5.17/5.46 ! [W: num,A: real] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.17/5.46 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_even_abs_numeral
% 5.17/5.46 thf(fact_5257_diff__numeral__special_I3_J,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.46 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(3)
% 5.17/5.46 thf(fact_5258_diff__numeral__special_I3_J,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.46 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(3)
% 5.17/5.46 thf(fact_5259_diff__numeral__special_I3_J,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.46 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(3)
% 5.17/5.46 thf(fact_5260_diff__numeral__special_I3_J,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.46 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(3)
% 5.17/5.46 thf(fact_5261_diff__numeral__special_I3_J,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.46 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(3)
% 5.17/5.46 thf(fact_5262_diff__numeral__special_I4_J,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.17/5.46 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(4)
% 5.17/5.46 thf(fact_5263_diff__numeral__special_I4_J,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.17/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(4)
% 5.17/5.46 thf(fact_5264_diff__numeral__special_I4_J,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(4)
% 5.17/5.46 thf(fact_5265_diff__numeral__special_I4_J,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(4)
% 5.17/5.46 thf(fact_5266_diff__numeral__special_I4_J,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.17/5.46 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_numeral_special(4)
% 5.17/5.46 thf(fact_5267_dbl__simps_I4_J,axiom,
% 5.17/5.46 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.46 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dbl_simps(4)
% 5.17/5.46 thf(fact_5268_dbl__simps_I4_J,axiom,
% 5.17/5.46 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.46 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dbl_simps(4)
% 5.17/5.46 thf(fact_5269_dbl__simps_I4_J,axiom,
% 5.17/5.46 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dbl_simps(4)
% 5.17/5.46 thf(fact_5270_dbl__simps_I4_J,axiom,
% 5.17/5.46 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dbl_simps(4)
% 5.17/5.46 thf(fact_5271_dbl__simps_I4_J,axiom,
% 5.17/5.46 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.46 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dbl_simps(4)
% 5.17/5.46 thf(fact_5272_power__minus1__even,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = one_one_real ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus1_even
% 5.17/5.46 thf(fact_5273_power__minus1__even,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = one_one_int ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus1_even
% 5.17/5.46 thf(fact_5274_power__minus1__even,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = one_one_complex ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus1_even
% 5.17/5.46 thf(fact_5275_power__minus1__even,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = one_one_Code_integer ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus1_even
% 5.17/5.46 thf(fact_5276_power__minus1__even,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.46 = one_one_rat ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus1_even
% 5.17/5.46 thf(fact_5277_neg__one__odd__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.17/5.46 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_odd_power
% 5.17/5.46 thf(fact_5278_neg__one__odd__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_odd_power
% 5.17/5.46 thf(fact_5279_neg__one__odd__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_odd_power
% 5.17/5.46 thf(fact_5280_neg__one__odd__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_odd_power
% 5.17/5.46 thf(fact_5281_neg__one__odd__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.17/5.46 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_odd_power
% 5.17/5.46 thf(fact_5282_neg__one__even__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.17/5.46 = one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_even_power
% 5.17/5.46 thf(fact_5283_neg__one__even__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.17/5.46 = one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_even_power
% 5.17/5.46 thf(fact_5284_neg__one__even__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.17/5.46 = one_one_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_even_power
% 5.17/5.46 thf(fact_5285_neg__one__even__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.17/5.46 = one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_even_power
% 5.17/5.46 thf(fact_5286_neg__one__even__power,axiom,
% 5.17/5.46 ! [N: nat] :
% 5.17/5.46 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.46 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.17/5.46 = one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_even_power
% 5.17/5.46 thf(fact_5287_signed__take__bit__0,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % signed_take_bit_0
% 5.17/5.46 thf(fact_5288_signed__take__bit__0,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.17/5.46 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % signed_take_bit_0
% 5.17/5.46 thf(fact_5289_signed__take__bit__Suc__minus__bit0,axiom,
% 5.17/5.46 ! [N: nat,K: num] :
% 5.17/5.46 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.17/5.46 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % signed_take_bit_Suc_minus_bit0
% 5.17/5.46 thf(fact_5290_signed__take__bit__minus,axiom,
% 5.17/5.46 ! [N: nat,K: int] :
% 5.17/5.46 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.17/5.46 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % signed_take_bit_minus
% 5.17/5.46 thf(fact_5291_equation__minus__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % equation_minus_iff
% 5.17/5.46 thf(fact_5292_equation__minus__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % equation_minus_iff
% 5.17/5.46 thf(fact_5293_equation__minus__iff,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % equation_minus_iff
% 5.17/5.46 thf(fact_5294_equation__minus__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % equation_minus_iff
% 5.17/5.46 thf(fact_5295_equation__minus__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % equation_minus_iff
% 5.17/5.46 thf(fact_5296_minus__equation__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( uminus_uminus_real @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( uminus_uminus_real @ B )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_equation_iff
% 5.17/5.46 thf(fact_5297_minus__equation__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( uminus_uminus_int @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( uminus_uminus_int @ B )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_equation_iff
% 5.17/5.46 thf(fact_5298_minus__equation__iff,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( ( uminus1482373934393186551omplex @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( uminus1482373934393186551omplex @ B )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_equation_iff
% 5.17/5.46 thf(fact_5299_minus__equation__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( uminus1351360451143612070nteger @ B )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_equation_iff
% 5.17/5.46 thf(fact_5300_minus__equation__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( uminus_uminus_rat @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( uminus_uminus_rat @ B )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_equation_iff
% 5.17/5.46 thf(fact_5301_abs__eq__iff,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( ( abs_abs_real @ X )
% 5.17/5.46 = ( abs_abs_real @ Y4 ) )
% 5.17/5.46 = ( ( X = Y4 )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus_uminus_real @ Y4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff
% 5.17/5.46 thf(fact_5302_abs__eq__iff,axiom,
% 5.17/5.46 ! [X: int,Y4: int] :
% 5.17/5.46 ( ( ( abs_abs_int @ X )
% 5.17/5.46 = ( abs_abs_int @ Y4 ) )
% 5.17/5.46 = ( ( X = Y4 )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus_uminus_int @ Y4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff
% 5.17/5.46 thf(fact_5303_abs__eq__iff,axiom,
% 5.17/5.46 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.46 ( ( ( abs_abs_Code_integer @ X )
% 5.17/5.46 = ( abs_abs_Code_integer @ Y4 ) )
% 5.17/5.46 = ( ( X = Y4 )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus1351360451143612070nteger @ Y4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff
% 5.17/5.46 thf(fact_5304_abs__eq__iff,axiom,
% 5.17/5.46 ! [X: rat,Y4: rat] :
% 5.17/5.46 ( ( ( abs_abs_rat @ X )
% 5.17/5.46 = ( abs_abs_rat @ Y4 ) )
% 5.17/5.46 = ( ( X = Y4 )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus_uminus_rat @ Y4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff
% 5.17/5.46 thf(fact_5305_verit__negate__coefficient_I3_J,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( A = B )
% 5.17/5.46 => ( ( uminus_uminus_real @ A )
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(3)
% 5.17/5.46 thf(fact_5306_verit__negate__coefficient_I3_J,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( A = B )
% 5.17/5.46 => ( ( uminus_uminus_int @ A )
% 5.17/5.46 = ( uminus_uminus_int @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(3)
% 5.17/5.46 thf(fact_5307_verit__negate__coefficient_I3_J,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( A = B )
% 5.17/5.46 => ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(3)
% 5.17/5.46 thf(fact_5308_verit__negate__coefficient_I3_J,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( A = B )
% 5.17/5.46 => ( ( uminus_uminus_rat @ A )
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(3)
% 5.17/5.46 thf(fact_5309_abs__ge__minus__self,axiom,
% 5.17/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_minus_self
% 5.17/5.46 thf(fact_5310_abs__ge__minus__self,axiom,
% 5.17/5.46 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_minus_self
% 5.17/5.46 thf(fact_5311_abs__ge__minus__self,axiom,
% 5.17/5.46 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_minus_self
% 5.17/5.46 thf(fact_5312_abs__ge__minus__self,axiom,
% 5.17/5.46 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_minus_self
% 5.17/5.46 thf(fact_5313_abs__le__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.17/5.46 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.17/5.46 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_iff
% 5.17/5.46 thf(fact_5314_abs__le__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.17/5.46 = ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.46 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_iff
% 5.17/5.46 thf(fact_5315_abs__le__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.17/5.46 = ( ( ord_less_eq_int @ A @ B )
% 5.17/5.46 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_iff
% 5.17/5.46 thf(fact_5316_abs__le__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.17/5.46 = ( ( ord_less_eq_real @ A @ B )
% 5.17/5.46 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_iff
% 5.17/5.46 thf(fact_5317_abs__le__D2,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.17/5.46 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D2
% 5.17/5.46 thf(fact_5318_abs__le__D2,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D2
% 5.17/5.46 thf(fact_5319_abs__le__D2,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D2
% 5.17/5.46 thf(fact_5320_abs__le__D2,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D2
% 5.17/5.46 thf(fact_5321_abs__leI,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.17/5.46 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.46 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_leI
% 5.17/5.46 thf(fact_5322_abs__leI,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.46 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_leI
% 5.17/5.46 thf(fact_5323_abs__leI,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.46 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_leI
% 5.17/5.46 thf(fact_5324_abs__leI,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.46 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_leI
% 5.17/5.46 thf(fact_5325_abs__less__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.17/5.46 = ( ( ord_less_real @ A @ B )
% 5.17/5.46 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_less_iff
% 5.17/5.46 thf(fact_5326_abs__less__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.17/5.46 = ( ( ord_less_int @ A @ B )
% 5.17/5.46 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_less_iff
% 5.17/5.46 thf(fact_5327_abs__less__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.17/5.46 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.17/5.46 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_less_iff
% 5.17/5.46 thf(fact_5328_abs__less__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.17/5.46 = ( ( ord_less_rat @ A @ B )
% 5.17/5.46 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_less_iff
% 5.17/5.46 thf(fact_5329_eq__abs__iff_H,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( abs_abs_Code_integer @ B ) )
% 5.17/5.46 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.46 & ( ( B = A )
% 5.17/5.46 | ( B
% 5.17/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_abs_iff'
% 5.17/5.46 thf(fact_5330_eq__abs__iff_H,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( abs_abs_rat @ B ) )
% 5.17/5.46 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.46 & ( ( B = A )
% 5.17/5.46 | ( B
% 5.17/5.46 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_abs_iff'
% 5.17/5.46 thf(fact_5331_eq__abs__iff_H,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( abs_abs_int @ B ) )
% 5.17/5.46 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.46 & ( ( B = A )
% 5.17/5.46 | ( B
% 5.17/5.46 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_abs_iff'
% 5.17/5.46 thf(fact_5332_eq__abs__iff_H,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( abs_abs_real @ B ) )
% 5.17/5.46 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.46 & ( ( B = A )
% 5.17/5.46 | ( B
% 5.17/5.46 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_abs_iff'
% 5.17/5.46 thf(fact_5333_abs__eq__iff_H,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( abs_abs_Code_integer @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.46 & ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff'
% 5.17/5.46 thf(fact_5334_abs__eq__iff_H,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( abs_abs_rat @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.46 & ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff'
% 5.17/5.46 thf(fact_5335_abs__eq__iff_H,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( abs_abs_int @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.46 & ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff'
% 5.17/5.46 thf(fact_5336_abs__eq__iff_H,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( abs_abs_real @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.46 & ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_iff'
% 5.17/5.46 thf(fact_5337_abs__minus__le__zero,axiom,
% 5.17/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_le_zero
% 5.17/5.46 thf(fact_5338_abs__minus__le__zero,axiom,
% 5.17/5.46 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_le_zero
% 5.17/5.46 thf(fact_5339_abs__minus__le__zero,axiom,
% 5.17/5.46 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_le_zero
% 5.17/5.46 thf(fact_5340_abs__minus__le__zero,axiom,
% 5.17/5.46 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_le_zero
% 5.17/5.46 thf(fact_5341_abs__if__raw,axiom,
% 5.17/5.46 ( abs_abs_real
% 5.17/5.46 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if_raw
% 5.17/5.46 thf(fact_5342_abs__if__raw,axiom,
% 5.17/5.46 ( abs_abs_int
% 5.17/5.46 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if_raw
% 5.17/5.46 thf(fact_5343_abs__if__raw,axiom,
% 5.17/5.46 ( abs_abs_Code_integer
% 5.17/5.46 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if_raw
% 5.17/5.46 thf(fact_5344_abs__if__raw,axiom,
% 5.17/5.46 ( abs_abs_rat
% 5.17/5.46 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if_raw
% 5.17/5.46 thf(fact_5345_abs__of__neg,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.46 => ( ( abs_abs_real @ A )
% 5.17/5.46 = ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_neg
% 5.17/5.46 thf(fact_5346_abs__of__neg,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.46 => ( ( abs_abs_int @ A )
% 5.17/5.46 = ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_neg
% 5.17/5.46 thf(fact_5347_abs__of__neg,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.17/5.46 => ( ( abs_abs_Code_integer @ A )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_neg
% 5.17/5.46 thf(fact_5348_abs__of__neg,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.46 => ( ( abs_abs_rat @ A )
% 5.17/5.46 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_neg
% 5.17/5.46 thf(fact_5349_abs__if,axiom,
% 5.17/5.46 ( abs_abs_real
% 5.17/5.46 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if
% 5.17/5.46 thf(fact_5350_abs__if,axiom,
% 5.17/5.46 ( abs_abs_int
% 5.17/5.46 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if
% 5.17/5.46 thf(fact_5351_abs__if,axiom,
% 5.17/5.46 ( abs_abs_Code_integer
% 5.17/5.46 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if
% 5.17/5.46 thf(fact_5352_abs__if,axiom,
% 5.17/5.46 ( abs_abs_rat
% 5.17/5.46 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_if
% 5.17/5.46 thf(fact_5353_abs__real__def,axiom,
% 5.17/5.46 ( abs_abs_real
% 5.17/5.46 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_real_def
% 5.17/5.46 thf(fact_5354_abs__le__D1,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.17/5.46 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D1
% 5.17/5.46 thf(fact_5355_abs__le__D1,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D1
% 5.17/5.46 thf(fact_5356_abs__le__D1,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D1
% 5.17/5.46 thf(fact_5357_abs__le__D1,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.17/5.46 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_le_D1
% 5.17/5.46 thf(fact_5358_abs__ge__self,axiom,
% 5.17/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_self
% 5.17/5.46 thf(fact_5359_abs__ge__self,axiom,
% 5.17/5.46 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_self
% 5.17/5.46 thf(fact_5360_abs__ge__self,axiom,
% 5.17/5.46 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_self
% 5.17/5.46 thf(fact_5361_abs__ge__self,axiom,
% 5.17/5.46 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_self
% 5.17/5.46 thf(fact_5362_abs__eq__0__iff,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( ( abs_abs_Code_integer @ A )
% 5.17/5.46 = zero_z3403309356797280102nteger )
% 5.17/5.46 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_0_iff
% 5.17/5.46 thf(fact_5363_abs__eq__0__iff,axiom,
% 5.17/5.46 ! [A: complex] :
% 5.17/5.46 ( ( ( abs_abs_complex @ A )
% 5.17/5.46 = zero_zero_complex )
% 5.17/5.46 = ( A = zero_zero_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_0_iff
% 5.17/5.46 thf(fact_5364_abs__eq__0__iff,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( ( abs_abs_real @ A )
% 5.17/5.46 = zero_zero_real )
% 5.17/5.46 = ( A = zero_zero_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_0_iff
% 5.17/5.46 thf(fact_5365_abs__eq__0__iff,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( ( abs_abs_rat @ A )
% 5.17/5.46 = zero_zero_rat )
% 5.17/5.46 = ( A = zero_zero_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_0_iff
% 5.17/5.46 thf(fact_5366_abs__eq__0__iff,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( ( abs_abs_int @ A )
% 5.17/5.46 = zero_zero_int )
% 5.17/5.46 = ( A = zero_zero_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_0_iff
% 5.17/5.46 thf(fact_5367_abs__mult,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.17/5.46 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult
% 5.17/5.46 thf(fact_5368_abs__mult,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.17/5.46 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult
% 5.17/5.46 thf(fact_5369_abs__mult,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.46 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult
% 5.17/5.46 thf(fact_5370_abs__mult,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.17/5.46 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult
% 5.17/5.46 thf(fact_5371_abs__one,axiom,
% 5.17/5.46 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.17/5.46 = one_one_Code_integer ) ).
% 5.17/5.46
% 5.17/5.46 % abs_one
% 5.17/5.46 thf(fact_5372_abs__one,axiom,
% 5.17/5.46 ( ( abs_abs_real @ one_one_real )
% 5.17/5.46 = one_one_real ) ).
% 5.17/5.46
% 5.17/5.46 % abs_one
% 5.17/5.46 thf(fact_5373_abs__one,axiom,
% 5.17/5.46 ( ( abs_abs_rat @ one_one_rat )
% 5.17/5.46 = one_one_rat ) ).
% 5.17/5.46
% 5.17/5.46 % abs_one
% 5.17/5.46 thf(fact_5374_abs__one,axiom,
% 5.17/5.46 ( ( abs_abs_int @ one_one_int )
% 5.17/5.46 = one_one_int ) ).
% 5.17/5.46
% 5.17/5.46 % abs_one
% 5.17/5.46 thf(fact_5375_abs__minus__commute,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.17/5.46 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_commute
% 5.17/5.46 thf(fact_5376_abs__minus__commute,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.17/5.46 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_commute
% 5.17/5.46 thf(fact_5377_abs__minus__commute,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.17/5.46 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_commute
% 5.17/5.46 thf(fact_5378_abs__minus__commute,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.17/5.46 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_minus_commute
% 5.17/5.46 thf(fact_5379_dvd__if__abs__eq,axiom,
% 5.17/5.46 ! [L: real,K: real] :
% 5.17/5.46 ( ( ( abs_abs_real @ L )
% 5.17/5.46 = ( abs_abs_real @ K ) )
% 5.17/5.46 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_if_abs_eq
% 5.17/5.46 thf(fact_5380_dvd__if__abs__eq,axiom,
% 5.17/5.46 ! [L: int,K: int] :
% 5.17/5.46 ( ( ( abs_abs_int @ L )
% 5.17/5.46 = ( abs_abs_int @ K ) )
% 5.17/5.46 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_if_abs_eq
% 5.17/5.46 thf(fact_5381_dvd__if__abs__eq,axiom,
% 5.17/5.46 ! [L: code_integer,K: code_integer] :
% 5.17/5.46 ( ( ( abs_abs_Code_integer @ L )
% 5.17/5.46 = ( abs_abs_Code_integer @ K ) )
% 5.17/5.46 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_if_abs_eq
% 5.17/5.46 thf(fact_5382_dvd__if__abs__eq,axiom,
% 5.17/5.46 ! [L: rat,K: rat] :
% 5.17/5.46 ( ( ( abs_abs_rat @ L )
% 5.17/5.46 = ( abs_abs_rat @ K ) )
% 5.17/5.46 => ( dvd_dvd_rat @ L @ K ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_if_abs_eq
% 5.17/5.46 thf(fact_5383_le__minus__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_iff
% 5.17/5.46 thf(fact_5384_le__minus__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_iff
% 5.17/5.46 thf(fact_5385_le__minus__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_iff
% 5.17/5.46 thf(fact_5386_le__minus__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_iff
% 5.17/5.46 thf(fact_5387_minus__le__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.46 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_le_iff
% 5.17/5.46 thf(fact_5388_minus__le__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.46 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_le_iff
% 5.17/5.46 thf(fact_5389_minus__le__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_le_iff
% 5.17/5.46 thf(fact_5390_minus__le__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.46 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_le_iff
% 5.17/5.46 thf(fact_5391_le__imp__neg__le,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.17/5.46 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_imp_neg_le
% 5.17/5.46 thf(fact_5392_le__imp__neg__le,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.46 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_imp_neg_le
% 5.17/5.46 thf(fact_5393_le__imp__neg__le,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.46 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_imp_neg_le
% 5.17/5.46 thf(fact_5394_le__imp__neg__le,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.46 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_imp_neg_le
% 5.17/5.46 thf(fact_5395_less__minus__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_iff
% 5.17/5.46 thf(fact_5396_less__minus__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_iff
% 5.17/5.46 thf(fact_5397_less__minus__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_iff
% 5.17/5.46 thf(fact_5398_less__minus__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_iff
% 5.17/5.46 thf(fact_5399_minus__less__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.46 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_less_iff
% 5.17/5.46 thf(fact_5400_minus__less__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_less_iff
% 5.17/5.46 thf(fact_5401_minus__less__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.46 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_less_iff
% 5.17/5.46 thf(fact_5402_minus__less__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.46 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_less_iff
% 5.17/5.46 thf(fact_5403_verit__negate__coefficient_I2_J,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ord_less_real @ A @ B )
% 5.17/5.46 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(2)
% 5.17/5.46 thf(fact_5404_verit__negate__coefficient_I2_J,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ord_less_int @ A @ B )
% 5.17/5.46 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(2)
% 5.17/5.46 thf(fact_5405_verit__negate__coefficient_I2_J,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.17/5.46 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(2)
% 5.17/5.46 thf(fact_5406_verit__negate__coefficient_I2_J,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ord_less_rat @ A @ B )
% 5.17/5.46 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % verit_negate_coefficient(2)
% 5.17/5.46 thf(fact_5407_neg__numeral__neq__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.17/5.46 != ( numeral_numeral_real @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_neq_numeral
% 5.17/5.46 thf(fact_5408_neg__numeral__neq__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.17/5.46 != ( numeral_numeral_int @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_neq_numeral
% 5.17/5.46 thf(fact_5409_neg__numeral__neq__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.17/5.46 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_neq_numeral
% 5.17/5.46 thf(fact_5410_neg__numeral__neq__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.17/5.46 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_neq_numeral
% 5.17/5.46 thf(fact_5411_neg__numeral__neq__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.17/5.46 != ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_neq_numeral
% 5.17/5.46 thf(fact_5412_numeral__neq__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( numeral_numeral_real @ M )
% 5.17/5.46 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_numeral
% 5.17/5.46 thf(fact_5413_numeral__neq__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( numeral_numeral_int @ M )
% 5.17/5.46 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_numeral
% 5.17/5.46 thf(fact_5414_numeral__neq__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( numera6690914467698888265omplex @ M )
% 5.17/5.46 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_numeral
% 5.17/5.46 thf(fact_5415_numeral__neq__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( numera6620942414471956472nteger @ M )
% 5.17/5.46 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_numeral
% 5.17/5.46 thf(fact_5416_numeral__neq__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ( ( numeral_numeral_rat @ M )
% 5.17/5.46 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_numeral
% 5.17/5.46 thf(fact_5417_square__eq__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( times_times_real @ A @ A )
% 5.17/5.46 = ( times_times_real @ B @ B ) )
% 5.17/5.46 = ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_iff
% 5.17/5.46 thf(fact_5418_square__eq__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( times_times_int @ A @ A )
% 5.17/5.46 = ( times_times_int @ B @ B ) )
% 5.17/5.46 = ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_iff
% 5.17/5.46 thf(fact_5419_square__eq__iff,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( ( times_times_complex @ A @ A )
% 5.17/5.46 = ( times_times_complex @ B @ B ) )
% 5.17/5.46 = ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_iff
% 5.17/5.46 thf(fact_5420_square__eq__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.17/5.46 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.17/5.46 = ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_iff
% 5.17/5.46 thf(fact_5421_square__eq__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( times_times_rat @ A @ A )
% 5.17/5.46 = ( times_times_rat @ B @ B ) )
% 5.17/5.46 = ( ( A = B )
% 5.17/5.46 | ( A
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_iff
% 5.17/5.46 thf(fact_5422_minus__mult__commute,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.46 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_mult_commute
% 5.17/5.46 thf(fact_5423_minus__mult__commute,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_mult_commute
% 5.17/5.46 thf(fact_5424_minus__mult__commute,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.17/5.46 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_mult_commute
% 5.17/5.46 thf(fact_5425_minus__mult__commute,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.46 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_mult_commute
% 5.17/5.46 thf(fact_5426_minus__mult__commute,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.46 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_mult_commute
% 5.17/5.46 thf(fact_5427_group__cancel_Oneg1,axiom,
% 5.17/5.46 ! [A2: real,K: real,A: real] :
% 5.17/5.46 ( ( A2
% 5.17/5.46 = ( plus_plus_real @ K @ A ) )
% 5.17/5.46 => ( ( uminus_uminus_real @ A2 )
% 5.17/5.46 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.neg1
% 5.17/5.46 thf(fact_5428_group__cancel_Oneg1,axiom,
% 5.17/5.46 ! [A2: int,K: int,A: int] :
% 5.17/5.46 ( ( A2
% 5.17/5.46 = ( plus_plus_int @ K @ A ) )
% 5.17/5.46 => ( ( uminus_uminus_int @ A2 )
% 5.17/5.46 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.neg1
% 5.17/5.46 thf(fact_5429_group__cancel_Oneg1,axiom,
% 5.17/5.46 ! [A2: complex,K: complex,A: complex] :
% 5.17/5.46 ( ( A2
% 5.17/5.46 = ( plus_plus_complex @ K @ A ) )
% 5.17/5.46 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.17/5.46 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.neg1
% 5.17/5.46 thf(fact_5430_group__cancel_Oneg1,axiom,
% 5.17/5.46 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.17/5.46 ( ( A2
% 5.17/5.46 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.17/5.46 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.17/5.46 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.neg1
% 5.17/5.46 thf(fact_5431_group__cancel_Oneg1,axiom,
% 5.17/5.46 ! [A2: rat,K: rat,A: rat] :
% 5.17/5.46 ( ( A2
% 5.17/5.46 = ( plus_plus_rat @ K @ A ) )
% 5.17/5.46 => ( ( uminus_uminus_rat @ A2 )
% 5.17/5.46 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.neg1
% 5.17/5.46 thf(fact_5432_add_Oinverse__distrib__swap,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.17/5.46 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_distrib_swap
% 5.17/5.46 thf(fact_5433_add_Oinverse__distrib__swap,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.17/5.46 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_distrib_swap
% 5.17/5.46 thf(fact_5434_add_Oinverse__distrib__swap,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.17/5.46 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_distrib_swap
% 5.17/5.46 thf(fact_5435_add_Oinverse__distrib__swap,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.46 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_distrib_swap
% 5.17/5.46 thf(fact_5436_add_Oinverse__distrib__swap,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.46 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_distrib_swap
% 5.17/5.46 thf(fact_5437_is__num__normalize_I8_J,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.17/5.46 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % is_num_normalize(8)
% 5.17/5.46 thf(fact_5438_is__num__normalize_I8_J,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.17/5.46 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % is_num_normalize(8)
% 5.17/5.46 thf(fact_5439_is__num__normalize_I8_J,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.17/5.46 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % is_num_normalize(8)
% 5.17/5.46 thf(fact_5440_is__num__normalize_I8_J,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.46 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % is_num_normalize(8)
% 5.17/5.46 thf(fact_5441_is__num__normalize_I8_J,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.46 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % is_num_normalize(8)
% 5.17/5.46 thf(fact_5442_one__neq__neg__one,axiom,
% 5.17/5.46 ( one_one_real
% 5.17/5.46 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_one
% 5.17/5.46 thf(fact_5443_one__neq__neg__one,axiom,
% 5.17/5.46 ( one_one_int
% 5.17/5.46 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_one
% 5.17/5.46 thf(fact_5444_one__neq__neg__one,axiom,
% 5.17/5.46 ( one_one_complex
% 5.17/5.46 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_one
% 5.17/5.46 thf(fact_5445_one__neq__neg__one,axiom,
% 5.17/5.46 ( one_one_Code_integer
% 5.17/5.46 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_one
% 5.17/5.46 thf(fact_5446_one__neq__neg__one,axiom,
% 5.17/5.46 ( one_one_rat
% 5.17/5.46 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_one
% 5.17/5.46 thf(fact_5447_minus__diff__commute,axiom,
% 5.17/5.46 ! [B: real,A: real] :
% 5.17/5.46 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.17/5.46 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_commute
% 5.17/5.46 thf(fact_5448_minus__diff__commute,axiom,
% 5.17/5.46 ! [B: int,A: int] :
% 5.17/5.46 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.17/5.46 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_commute
% 5.17/5.46 thf(fact_5449_minus__diff__commute,axiom,
% 5.17/5.46 ! [B: complex,A: complex] :
% 5.17/5.46 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.17/5.46 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_commute
% 5.17/5.46 thf(fact_5450_minus__diff__commute,axiom,
% 5.17/5.46 ! [B: code_integer,A: code_integer] :
% 5.17/5.46 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.17/5.46 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_commute
% 5.17/5.46 thf(fact_5451_minus__diff__commute,axiom,
% 5.17/5.46 ! [B: rat,A: rat] :
% 5.17/5.46 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.17/5.46 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_commute
% 5.17/5.46 thf(fact_5452_minus__diff__minus,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_minus
% 5.17/5.46 thf(fact_5453_minus__diff__minus,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_minus
% 5.17/5.46 thf(fact_5454_minus__diff__minus,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_minus
% 5.17/5.46 thf(fact_5455_minus__diff__minus,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_minus
% 5.17/5.46 thf(fact_5456_minus__diff__minus,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_diff_minus
% 5.17/5.46 thf(fact_5457_div__minus__right,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % div_minus_right
% 5.17/5.46 thf(fact_5458_div__minus__right,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % div_minus_right
% 5.17/5.46 thf(fact_5459_minus__divide__right,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.46 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_right
% 5.17/5.46 thf(fact_5460_minus__divide__right,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.46 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_right
% 5.17/5.46 thf(fact_5461_minus__divide__right,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.46 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_right
% 5.17/5.46 thf(fact_5462_minus__divide__divide,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( divide_divide_real @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_divide
% 5.17/5.46 thf(fact_5463_minus__divide__divide,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.46 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_divide
% 5.17/5.46 thf(fact_5464_minus__divide__divide,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( divide_divide_rat @ A @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_divide
% 5.17/5.46 thf(fact_5465_minus__divide__left,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.46 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_left
% 5.17/5.46 thf(fact_5466_minus__divide__left,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.46 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_left
% 5.17/5.46 thf(fact_5467_minus__divide__left,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.46 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_left
% 5.17/5.46 thf(fact_5468_mod__minus__eq,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.17/5.46 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mod_minus_eq
% 5.17/5.46 thf(fact_5469_mod__minus__eq,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.17/5.46 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mod_minus_eq
% 5.17/5.46 thf(fact_5470_mod__minus__cong,axiom,
% 5.17/5.46 ! [A: int,B: int,A6: int] :
% 5.17/5.46 ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.46 = ( modulo_modulo_int @ A6 @ B ) )
% 5.17/5.46 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = ( modulo_modulo_int @ ( uminus_uminus_int @ A6 ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % mod_minus_cong
% 5.17/5.46 thf(fact_5471_mod__minus__cong,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer,A6: code_integer] :
% 5.17/5.46 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.17/5.46 = ( modulo364778990260209775nteger @ A6 @ B ) )
% 5.17/5.46 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.46 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A6 ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % mod_minus_cong
% 5.17/5.46 thf(fact_5472_mod__minus__right,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % mod_minus_right
% 5.17/5.46 thf(fact_5473_mod__minus__right,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % mod_minus_right
% 5.17/5.46 thf(fact_5474_uminus__int__code_I1_J,axiom,
% 5.17/5.46 ( ( uminus_uminus_int @ zero_zero_int )
% 5.17/5.46 = zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_int_code(1)
% 5.17/5.46 thf(fact_5475_int__cases2,axiom,
% 5.17/5.46 ! [Z: int] :
% 5.17/5.46 ( ! [N2: nat] :
% 5.17/5.46 ( Z
% 5.17/5.46 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.17/5.46 => ~ ! [N2: nat] :
% 5.17/5.46 ( Z
% 5.17/5.46 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % int_cases2
% 5.17/5.46 thf(fact_5476_uminus__dvd__conv_I1_J,axiom,
% 5.17/5.46 ( dvd_dvd_int
% 5.17/5.46 = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_dvd_conv(1)
% 5.17/5.46 thf(fact_5477_uminus__dvd__conv_I2_J,axiom,
% 5.17/5.46 ( dvd_dvd_int
% 5.17/5.46 = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_dvd_conv(2)
% 5.17/5.46 thf(fact_5478_abs__ge__zero,axiom,
% 5.17/5.46 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_zero
% 5.17/5.46 thf(fact_5479_abs__ge__zero,axiom,
% 5.17/5.46 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_zero
% 5.17/5.46 thf(fact_5480_abs__ge__zero,axiom,
% 5.17/5.46 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_zero
% 5.17/5.46 thf(fact_5481_abs__ge__zero,axiom,
% 5.17/5.46 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_ge_zero
% 5.17/5.46 thf(fact_5482_abs__of__pos,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.46 => ( ( abs_abs_Code_integer @ A )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_pos
% 5.17/5.46 thf(fact_5483_abs__of__pos,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.46 => ( ( abs_abs_real @ A )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_pos
% 5.17/5.46 thf(fact_5484_abs__of__pos,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.46 => ( ( abs_abs_rat @ A )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_pos
% 5.17/5.46 thf(fact_5485_abs__of__pos,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.46 => ( ( abs_abs_int @ A )
% 5.17/5.46 = A ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_of_pos
% 5.17/5.46 thf(fact_5486_abs__not__less__zero,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.17/5.46
% 5.17/5.46 % abs_not_less_zero
% 5.17/5.46 thf(fact_5487_abs__not__less__zero,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.17/5.46
% 5.17/5.46 % abs_not_less_zero
% 5.17/5.46 thf(fact_5488_abs__not__less__zero,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.17/5.46
% 5.17/5.46 % abs_not_less_zero
% 5.17/5.46 thf(fact_5489_abs__not__less__zero,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % abs_not_less_zero
% 5.17/5.46 thf(fact_5490_abs__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq
% 5.17/5.46 thf(fact_5491_abs__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq
% 5.17/5.46 thf(fact_5492_abs__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq
% 5.17/5.46 thf(fact_5493_abs__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq
% 5.17/5.46 thf(fact_5494_abs__mult__less,axiom,
% 5.17/5.46 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.17/5.46 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.17/5.46 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_less
% 5.17/5.46 thf(fact_5495_abs__mult__less,axiom,
% 5.17/5.46 ! [A: real,C: real,B: real,D: real] :
% 5.17/5.46 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.17/5.46 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.17/5.46 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_less
% 5.17/5.46 thf(fact_5496_abs__mult__less,axiom,
% 5.17/5.46 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.17/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.17/5.46 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.17/5.46 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_less
% 5.17/5.46 thf(fact_5497_abs__mult__less,axiom,
% 5.17/5.46 ! [A: int,C: int,B: int,D: int] :
% 5.17/5.46 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.17/5.46 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.17/5.46 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_less
% 5.17/5.46 thf(fact_5498_abs__triangle__ineq2,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2
% 5.17/5.46 thf(fact_5499_abs__triangle__ineq2,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2
% 5.17/5.46 thf(fact_5500_abs__triangle__ineq2,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2
% 5.17/5.46 thf(fact_5501_abs__triangle__ineq2,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2
% 5.17/5.46 thf(fact_5502_abs__triangle__ineq3,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq3
% 5.17/5.46 thf(fact_5503_abs__triangle__ineq3,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq3
% 5.17/5.46 thf(fact_5504_abs__triangle__ineq3,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq3
% 5.17/5.46 thf(fact_5505_abs__triangle__ineq3,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq3
% 5.17/5.46 thf(fact_5506_abs__triangle__ineq2__sym,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2_sym
% 5.17/5.46 thf(fact_5507_abs__triangle__ineq2__sym,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2_sym
% 5.17/5.46 thf(fact_5508_abs__triangle__ineq2__sym,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2_sym
% 5.17/5.46 thf(fact_5509_abs__triangle__ineq2__sym,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq2_sym
% 5.17/5.46 thf(fact_5510_nonzero__abs__divide,axiom,
% 5.17/5.46 ! [B: real,A: real] :
% 5.17/5.46 ( ( B != zero_zero_real )
% 5.17/5.46 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.46 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_abs_divide
% 5.17/5.46 thf(fact_5511_nonzero__abs__divide,axiom,
% 5.17/5.46 ! [B: rat,A: rat] :
% 5.17/5.46 ( ( B != zero_zero_rat )
% 5.17/5.46 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.46 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_abs_divide
% 5.17/5.46 thf(fact_5512_neg__numeral__le__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_numeral
% 5.17/5.46 thf(fact_5513_neg__numeral__le__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_numeral
% 5.17/5.46 thf(fact_5514_neg__numeral__le__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_numeral
% 5.17/5.46 thf(fact_5515_neg__numeral__le__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_numeral
% 5.17/5.46 thf(fact_5516_not__numeral__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_numeral
% 5.17/5.46 thf(fact_5517_not__numeral__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_numeral
% 5.17/5.46 thf(fact_5518_not__numeral__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_numeral
% 5.17/5.46 thf(fact_5519_not__numeral__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_numeral
% 5.17/5.46 thf(fact_5520_zero__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( zero_zero_real
% 5.17/5.46 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_numeral
% 5.17/5.46 thf(fact_5521_zero__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( zero_zero_int
% 5.17/5.46 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_numeral
% 5.17/5.46 thf(fact_5522_zero__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( zero_zero_complex
% 5.17/5.46 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_numeral
% 5.17/5.46 thf(fact_5523_zero__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( zero_z3403309356797280102nteger
% 5.17/5.46 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_numeral
% 5.17/5.46 thf(fact_5524_zero__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( zero_zero_rat
% 5.17/5.46 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_numeral
% 5.17/5.46 thf(fact_5525_not__numeral__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_numeral
% 5.17/5.46 thf(fact_5526_not__numeral__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_numeral
% 5.17/5.46 thf(fact_5527_not__numeral__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_numeral
% 5.17/5.46 thf(fact_5528_not__numeral__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] :
% 5.17/5.46 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_numeral
% 5.17/5.46 thf(fact_5529_neg__numeral__less__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_numeral
% 5.17/5.46 thf(fact_5530_neg__numeral__less__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_numeral
% 5.17/5.46 thf(fact_5531_neg__numeral__less__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_numeral
% 5.17/5.46 thf(fact_5532_neg__numeral__less__numeral,axiom,
% 5.17/5.46 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_numeral
% 5.17/5.46 thf(fact_5533_le__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(2)
% 5.17/5.46 thf(fact_5534_le__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(2)
% 5.17/5.46 thf(fact_5535_le__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(2)
% 5.17/5.46 thf(fact_5536_le__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(2)
% 5.17/5.46 thf(fact_5537_le__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(4)
% 5.17/5.46 thf(fact_5538_le__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(4)
% 5.17/5.46 thf(fact_5539_le__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(4)
% 5.17/5.46 thf(fact_5540_le__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(4)
% 5.17/5.46 thf(fact_5541_neg__eq__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( uminus_uminus_real @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( plus_plus_real @ A @ B )
% 5.17/5.46 = zero_zero_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_eq_iff_add_eq_0
% 5.17/5.46 thf(fact_5542_neg__eq__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( uminus_uminus_int @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( plus_plus_int @ A @ B )
% 5.17/5.46 = zero_zero_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_eq_iff_add_eq_0
% 5.17/5.46 thf(fact_5543_neg__eq__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( ( uminus1482373934393186551omplex @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( plus_plus_complex @ A @ B )
% 5.17/5.46 = zero_zero_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_eq_iff_add_eq_0
% 5.17/5.46 thf(fact_5544_neg__eq__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.17/5.46 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_eq_iff_add_eq_0
% 5.17/5.46 thf(fact_5545_neg__eq__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( uminus_uminus_rat @ A )
% 5.17/5.46 = B )
% 5.17/5.46 = ( ( plus_plus_rat @ A @ B )
% 5.17/5.46 = zero_zero_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_eq_iff_add_eq_0
% 5.17/5.46 thf(fact_5546_eq__neg__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( ( plus_plus_real @ A @ B )
% 5.17/5.46 = zero_zero_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_neg_iff_add_eq_0
% 5.17/5.46 thf(fact_5547_eq__neg__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( ( plus_plus_int @ A @ B )
% 5.17/5.46 = zero_zero_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_neg_iff_add_eq_0
% 5.17/5.46 thf(fact_5548_eq__neg__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.46 = ( ( plus_plus_complex @ A @ B )
% 5.17/5.46 = zero_zero_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_neg_iff_add_eq_0
% 5.17/5.46 thf(fact_5549_eq__neg__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.17/5.46 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_neg_iff_add_eq_0
% 5.17/5.46 thf(fact_5550_eq__neg__iff__add__eq__0,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( ( plus_plus_rat @ A @ B )
% 5.17/5.46 = zero_zero_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_neg_iff_add_eq_0
% 5.17/5.46 thf(fact_5551_add_Oinverse__unique,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( plus_plus_real @ A @ B )
% 5.17/5.46 = zero_zero_real )
% 5.17/5.46 => ( ( uminus_uminus_real @ A )
% 5.17/5.46 = B ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_unique
% 5.17/5.46 thf(fact_5552_add_Oinverse__unique,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( plus_plus_int @ A @ B )
% 5.17/5.46 = zero_zero_int )
% 5.17/5.46 => ( ( uminus_uminus_int @ A )
% 5.17/5.46 = B ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_unique
% 5.17/5.46 thf(fact_5553_add_Oinverse__unique,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( ( plus_plus_complex @ A @ B )
% 5.17/5.46 = zero_zero_complex )
% 5.17/5.46 => ( ( uminus1482373934393186551omplex @ A )
% 5.17/5.46 = B ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_unique
% 5.17/5.46 thf(fact_5554_add_Oinverse__unique,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.17/5.46 = zero_z3403309356797280102nteger )
% 5.17/5.46 => ( ( uminus1351360451143612070nteger @ A )
% 5.17/5.46 = B ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_unique
% 5.17/5.46 thf(fact_5555_add_Oinverse__unique,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( plus_plus_rat @ A @ B )
% 5.17/5.46 = zero_zero_rat )
% 5.17/5.46 => ( ( uminus_uminus_rat @ A )
% 5.17/5.46 = B ) ) ).
% 5.17/5.46
% 5.17/5.46 % add.inverse_unique
% 5.17/5.46 thf(fact_5556_ab__group__add__class_Oab__left__minus,axiom,
% 5.17/5.46 ! [A: real] :
% 5.17/5.46 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.17/5.46 = zero_zero_real ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_left_minus
% 5.17/5.46 thf(fact_5557_ab__group__add__class_Oab__left__minus,axiom,
% 5.17/5.46 ! [A: int] :
% 5.17/5.46 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.17/5.46 = zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_left_minus
% 5.17/5.46 thf(fact_5558_ab__group__add__class_Oab__left__minus,axiom,
% 5.17/5.46 ! [A: complex] :
% 5.17/5.46 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.17/5.46 = zero_zero_complex ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_left_minus
% 5.17/5.46 thf(fact_5559_ab__group__add__class_Oab__left__minus,axiom,
% 5.17/5.46 ! [A: code_integer] :
% 5.17/5.46 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.17/5.46 = zero_z3403309356797280102nteger ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_left_minus
% 5.17/5.46 thf(fact_5560_ab__group__add__class_Oab__left__minus,axiom,
% 5.17/5.46 ! [A: rat] :
% 5.17/5.46 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.17/5.46 = zero_zero_rat ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_left_minus
% 5.17/5.46 thf(fact_5561_add__eq__0__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( plus_plus_real @ A @ B )
% 5.17/5.46 = zero_zero_real )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_eq_0_iff
% 5.17/5.46 thf(fact_5562_add__eq__0__iff,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( plus_plus_int @ A @ B )
% 5.17/5.46 = zero_zero_int )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus_uminus_int @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_eq_0_iff
% 5.17/5.46 thf(fact_5563_add__eq__0__iff,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( ( plus_plus_complex @ A @ B )
% 5.17/5.46 = zero_zero_complex )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_eq_0_iff
% 5.17/5.46 thf(fact_5564_add__eq__0__iff,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.17/5.46 = zero_z3403309356797280102nteger )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_eq_0_iff
% 5.17/5.46 thf(fact_5565_add__eq__0__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( plus_plus_rat @ A @ B )
% 5.17/5.46 = zero_zero_rat )
% 5.17/5.46 = ( B
% 5.17/5.46 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % add_eq_0_iff
% 5.17/5.46 thf(fact_5566_zero__neq__neg__one,axiom,
% 5.17/5.46 ( zero_zero_real
% 5.17/5.46 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_one
% 5.17/5.46 thf(fact_5567_zero__neq__neg__one,axiom,
% 5.17/5.46 ( zero_zero_int
% 5.17/5.46 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_one
% 5.17/5.46 thf(fact_5568_zero__neq__neg__one,axiom,
% 5.17/5.46 ( zero_zero_complex
% 5.17/5.46 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_one
% 5.17/5.46 thf(fact_5569_zero__neq__neg__one,axiom,
% 5.17/5.46 ( zero_z3403309356797280102nteger
% 5.17/5.46 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_one
% 5.17/5.46 thf(fact_5570_zero__neq__neg__one,axiom,
% 5.17/5.46 ( zero_zero_rat
% 5.17/5.46 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_neq_neg_one
% 5.17/5.46 thf(fact_5571_less__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(4)
% 5.17/5.46 thf(fact_5572_less__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(4)
% 5.17/5.46 thf(fact_5573_less__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(4)
% 5.17/5.46 thf(fact_5574_less__minus__one__simps_I4_J,axiom,
% 5.17/5.46 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(4)
% 5.17/5.46 thf(fact_5575_less__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(2)
% 5.17/5.46 thf(fact_5576_less__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(2)
% 5.17/5.46 thf(fact_5577_less__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(2)
% 5.17/5.46 thf(fact_5578_less__minus__one__simps_I2_J,axiom,
% 5.17/5.46 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(2)
% 5.17/5.46 thf(fact_5579_numeral__times__minus__swap,axiom,
% 5.17/5.46 ! [W: num,X: real] :
% 5.17/5.46 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.17/5.46 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_times_minus_swap
% 5.17/5.46 thf(fact_5580_numeral__times__minus__swap,axiom,
% 5.17/5.46 ! [W: num,X: int] :
% 5.17/5.46 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.17/5.46 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_times_minus_swap
% 5.17/5.46 thf(fact_5581_numeral__times__minus__swap,axiom,
% 5.17/5.46 ! [W: num,X: complex] :
% 5.17/5.46 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.17/5.46 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_times_minus_swap
% 5.17/5.46 thf(fact_5582_numeral__times__minus__swap,axiom,
% 5.17/5.46 ! [W: num,X: code_integer] :
% 5.17/5.46 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.17/5.46 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_times_minus_swap
% 5.17/5.46 thf(fact_5583_numeral__times__minus__swap,axiom,
% 5.17/5.46 ! [W: num,X: rat] :
% 5.17/5.46 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 5.17/5.46 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_times_minus_swap
% 5.17/5.46 thf(fact_5584_nonzero__minus__divide__right,axiom,
% 5.17/5.46 ! [B: real,A: real] :
% 5.17/5.46 ( ( B != zero_zero_real )
% 5.17/5.46 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.46 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_minus_divide_right
% 5.17/5.46 thf(fact_5585_nonzero__minus__divide__right,axiom,
% 5.17/5.46 ! [B: complex,A: complex] :
% 5.17/5.46 ( ( B != zero_zero_complex )
% 5.17/5.46 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.46 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_minus_divide_right
% 5.17/5.46 thf(fact_5586_nonzero__minus__divide__right,axiom,
% 5.17/5.46 ! [B: rat,A: rat] :
% 5.17/5.46 ( ( B != zero_zero_rat )
% 5.17/5.46 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.46 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_minus_divide_right
% 5.17/5.46 thf(fact_5587_nonzero__minus__divide__divide,axiom,
% 5.17/5.46 ! [B: real,A: real] :
% 5.17/5.46 ( ( B != zero_zero_real )
% 5.17/5.46 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_minus_divide_divide
% 5.17/5.46 thf(fact_5588_nonzero__minus__divide__divide,axiom,
% 5.17/5.46 ! [B: complex,A: complex] :
% 5.17/5.46 ( ( B != zero_zero_complex )
% 5.17/5.46 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.46 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_minus_divide_divide
% 5.17/5.46 thf(fact_5589_nonzero__minus__divide__divide,axiom,
% 5.17/5.46 ! [B: rat,A: rat] :
% 5.17/5.46 ( ( B != zero_zero_rat )
% 5.17/5.46 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_minus_divide_divide
% 5.17/5.46 thf(fact_5590_one__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( one_one_real
% 5.17/5.46 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_numeral
% 5.17/5.46 thf(fact_5591_one__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( one_one_int
% 5.17/5.46 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_numeral
% 5.17/5.46 thf(fact_5592_one__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( one_one_complex
% 5.17/5.46 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_numeral
% 5.17/5.46 thf(fact_5593_one__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( one_one_Code_integer
% 5.17/5.46 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_numeral
% 5.17/5.46 thf(fact_5594_one__neq__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( one_one_rat
% 5.17/5.46 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % one_neq_neg_numeral
% 5.17/5.46 thf(fact_5595_numeral__neq__neg__one,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( numeral_numeral_real @ N )
% 5.17/5.46 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_one
% 5.17/5.46 thf(fact_5596_numeral__neq__neg__one,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( numeral_numeral_int @ N )
% 5.17/5.46 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_one
% 5.17/5.46 thf(fact_5597_numeral__neq__neg__one,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( numera6690914467698888265omplex @ N )
% 5.17/5.46 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_one
% 5.17/5.46 thf(fact_5598_numeral__neq__neg__one,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( numera6620942414471956472nteger @ N )
% 5.17/5.46 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_one
% 5.17/5.46 thf(fact_5599_numeral__neq__neg__one,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ( ( numeral_numeral_rat @ N )
% 5.17/5.46 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % numeral_neq_neg_one
% 5.17/5.46 thf(fact_5600_square__eq__1__iff,axiom,
% 5.17/5.46 ! [X: real] :
% 5.17/5.46 ( ( ( times_times_real @ X @ X )
% 5.17/5.46 = one_one_real )
% 5.17/5.46 = ( ( X = one_one_real )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_1_iff
% 5.17/5.46 thf(fact_5601_square__eq__1__iff,axiom,
% 5.17/5.46 ! [X: int] :
% 5.17/5.46 ( ( ( times_times_int @ X @ X )
% 5.17/5.46 = one_one_int )
% 5.17/5.46 = ( ( X = one_one_int )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_1_iff
% 5.17/5.46 thf(fact_5602_square__eq__1__iff,axiom,
% 5.17/5.46 ! [X: complex] :
% 5.17/5.46 ( ( ( times_times_complex @ X @ X )
% 5.17/5.46 = one_one_complex )
% 5.17/5.46 = ( ( X = one_one_complex )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_1_iff
% 5.17/5.46 thf(fact_5603_square__eq__1__iff,axiom,
% 5.17/5.46 ! [X: code_integer] :
% 5.17/5.46 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.17/5.46 = one_one_Code_integer )
% 5.17/5.46 = ( ( X = one_one_Code_integer )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_1_iff
% 5.17/5.46 thf(fact_5604_square__eq__1__iff,axiom,
% 5.17/5.46 ! [X: rat] :
% 5.17/5.46 ( ( ( times_times_rat @ X @ X )
% 5.17/5.46 = one_one_rat )
% 5.17/5.46 = ( ( X = one_one_rat )
% 5.17/5.46 | ( X
% 5.17/5.46 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % square_eq_1_iff
% 5.17/5.46 thf(fact_5605_group__cancel_Osub2,axiom,
% 5.17/5.46 ! [B4: real,K: real,B: real,A: real] :
% 5.17/5.46 ( ( B4
% 5.17/5.46 = ( plus_plus_real @ K @ B ) )
% 5.17/5.46 => ( ( minus_minus_real @ A @ B4 )
% 5.17/5.46 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.sub2
% 5.17/5.46 thf(fact_5606_group__cancel_Osub2,axiom,
% 5.17/5.46 ! [B4: int,K: int,B: int,A: int] :
% 5.17/5.46 ( ( B4
% 5.17/5.46 = ( plus_plus_int @ K @ B ) )
% 5.17/5.46 => ( ( minus_minus_int @ A @ B4 )
% 5.17/5.46 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.sub2
% 5.17/5.46 thf(fact_5607_group__cancel_Osub2,axiom,
% 5.17/5.46 ! [B4: complex,K: complex,B: complex,A: complex] :
% 5.17/5.46 ( ( B4
% 5.17/5.46 = ( plus_plus_complex @ K @ B ) )
% 5.17/5.46 => ( ( minus_minus_complex @ A @ B4 )
% 5.17/5.46 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.sub2
% 5.17/5.46 thf(fact_5608_group__cancel_Osub2,axiom,
% 5.17/5.46 ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.17/5.46 ( ( B4
% 5.17/5.46 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.17/5.46 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 5.17/5.46 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.sub2
% 5.17/5.46 thf(fact_5609_group__cancel_Osub2,axiom,
% 5.17/5.46 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.17/5.46 ( ( B4
% 5.17/5.46 = ( plus_plus_rat @ K @ B ) )
% 5.17/5.46 => ( ( minus_minus_rat @ A @ B4 )
% 5.17/5.46 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % group_cancel.sub2
% 5.17/5.46 thf(fact_5610_diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_real
% 5.17/5.46 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_conv_add_uminus
% 5.17/5.46 thf(fact_5611_diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_int
% 5.17/5.46 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_conv_add_uminus
% 5.17/5.46 thf(fact_5612_diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_complex
% 5.17/5.46 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_conv_add_uminus
% 5.17/5.46 thf(fact_5613_diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_8373710615458151222nteger
% 5.17/5.46 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_conv_add_uminus
% 5.17/5.46 thf(fact_5614_diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_rat
% 5.17/5.46 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % diff_conv_add_uminus
% 5.17/5.46 thf(fact_5615_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_real
% 5.17/5.46 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.17/5.46 thf(fact_5616_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_int
% 5.17/5.46 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.17/5.46 thf(fact_5617_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_complex
% 5.17/5.46 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.17/5.46 thf(fact_5618_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_8373710615458151222nteger
% 5.17/5.46 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.17/5.46 thf(fact_5619_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.17/5.46 ( minus_minus_rat
% 5.17/5.46 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.17/5.46 thf(fact_5620_dvd__div__neg,axiom,
% 5.17/5.46 ! [B: real,A: real] :
% 5.17/5.46 ( ( dvd_dvd_real @ B @ A )
% 5.17/5.46 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.17/5.46 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_div_neg
% 5.17/5.46 thf(fact_5621_dvd__div__neg,axiom,
% 5.17/5.46 ! [B: int,A: int] :
% 5.17/5.46 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.46 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_div_neg
% 5.17/5.46 thf(fact_5622_dvd__div__neg,axiom,
% 5.17/5.46 ! [B: complex,A: complex] :
% 5.17/5.46 ( ( dvd_dvd_complex @ B @ A )
% 5.17/5.46 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_div_neg
% 5.17/5.46 thf(fact_5623_dvd__div__neg,axiom,
% 5.17/5.46 ! [B: code_integer,A: code_integer] :
% 5.17/5.46 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.46 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_div_neg
% 5.17/5.46 thf(fact_5624_dvd__div__neg,axiom,
% 5.17/5.46 ! [B: rat,A: rat] :
% 5.17/5.46 ( ( dvd_dvd_rat @ B @ A )
% 5.17/5.46 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.17/5.46 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_div_neg
% 5.17/5.46 thf(fact_5625_dvd__neg__div,axiom,
% 5.17/5.46 ! [B: real,A: real] :
% 5.17/5.46 ( ( dvd_dvd_real @ B @ A )
% 5.17/5.46 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.17/5.46 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_neg_div
% 5.17/5.46 thf(fact_5626_dvd__neg__div,axiom,
% 5.17/5.46 ! [B: int,A: int] :
% 5.17/5.46 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.46 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_neg_div
% 5.17/5.46 thf(fact_5627_dvd__neg__div,axiom,
% 5.17/5.46 ! [B: complex,A: complex] :
% 5.17/5.46 ( ( dvd_dvd_complex @ B @ A )
% 5.17/5.46 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_neg_div
% 5.17/5.46 thf(fact_5628_dvd__neg__div,axiom,
% 5.17/5.46 ! [B: code_integer,A: code_integer] :
% 5.17/5.46 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.17/5.46 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_neg_div
% 5.17/5.46 thf(fact_5629_dvd__neg__div,axiom,
% 5.17/5.46 ! [B: rat,A: rat] :
% 5.17/5.46 ( ( dvd_dvd_rat @ B @ A )
% 5.17/5.46 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.17/5.46 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % dvd_neg_div
% 5.17/5.46 thf(fact_5630_real__minus__mult__self__le,axiom,
% 5.17/5.46 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.17/5.46
% 5.17/5.46 % real_minus_mult_self_le
% 5.17/5.46 thf(fact_5631_int__of__nat__induct,axiom,
% 5.17/5.46 ! [P: int > $o,Z: int] :
% 5.17/5.46 ( ! [N2: nat] : ( P @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.17/5.46 => ( ! [N2: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 5.17/5.46 => ( P @ Z ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % int_of_nat_induct
% 5.17/5.46 thf(fact_5632_int__cases,axiom,
% 5.17/5.46 ! [Z: int] :
% 5.17/5.46 ( ! [N2: nat] :
% 5.17/5.46 ( Z
% 5.17/5.46 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.17/5.46 => ~ ! [N2: nat] :
% 5.17/5.46 ( Z
% 5.17/5.46 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % int_cases
% 5.17/5.46 thf(fact_5633_zmult__eq__1__iff,axiom,
% 5.17/5.46 ! [M: int,N: int] :
% 5.17/5.46 ( ( ( times_times_int @ M @ N )
% 5.17/5.46 = one_one_int )
% 5.17/5.46 = ( ( ( M = one_one_int )
% 5.17/5.46 & ( N = one_one_int ) )
% 5.17/5.46 | ( ( M
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.46 & ( N
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zmult_eq_1_iff
% 5.17/5.46 thf(fact_5634_pos__zmult__eq__1__iff__lemma,axiom,
% 5.17/5.46 ! [M: int,N: int] :
% 5.17/5.46 ( ( ( times_times_int @ M @ N )
% 5.17/5.46 = one_one_int )
% 5.17/5.46 => ( ( M = one_one_int )
% 5.17/5.46 | ( M
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % pos_zmult_eq_1_iff_lemma
% 5.17/5.46 thf(fact_5635_minus__int__code_I2_J,axiom,
% 5.17/5.46 ! [L: int] :
% 5.17/5.46 ( ( minus_minus_int @ zero_zero_int @ L )
% 5.17/5.46 = ( uminus_uminus_int @ L ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_int_code(2)
% 5.17/5.46 thf(fact_5636_not__int__zless__negative,axiom,
% 5.17/5.46 ! [N: nat,M: nat] :
% 5.17/5.46 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_int_zless_negative
% 5.17/5.46 thf(fact_5637_zmod__zminus1__not__zero,axiom,
% 5.17/5.46 ! [K: int,L: int] :
% 5.17/5.46 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.17/5.46 != zero_zero_int )
% 5.17/5.46 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.46 != zero_zero_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % zmod_zminus1_not_zero
% 5.17/5.46 thf(fact_5638_zmod__zminus2__not__zero,axiom,
% 5.17/5.46 ! [K: int,L: int] :
% 5.17/5.46 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.17/5.46 != zero_zero_int )
% 5.17/5.46 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.46 != zero_zero_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % zmod_zminus2_not_zero
% 5.17/5.46 thf(fact_5639_minus__real__def,axiom,
% 5.17/5.46 ( minus_minus_real
% 5.17/5.46 = ( ^ [X3: real,Y6: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y6 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_real_def
% 5.17/5.46 thf(fact_5640_dense__eq0__I,axiom,
% 5.17/5.46 ! [X: rat] :
% 5.17/5.46 ( ! [E: rat] :
% 5.17/5.46 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.17/5.46 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E ) )
% 5.17/5.46 => ( X = zero_zero_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % dense_eq0_I
% 5.17/5.46 thf(fact_5641_dense__eq0__I,axiom,
% 5.17/5.46 ! [X: real] :
% 5.17/5.46 ( ! [E: real] :
% 5.17/5.46 ( ( ord_less_real @ zero_zero_real @ E )
% 5.17/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E ) )
% 5.17/5.46 => ( X = zero_zero_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % dense_eq0_I
% 5.17/5.46 thf(fact_5642_abs__mult__pos,axiom,
% 5.17/5.46 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.17/5.46 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y4 ) @ X )
% 5.17/5.46 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y4 @ X ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_pos
% 5.17/5.46 thf(fact_5643_abs__mult__pos,axiom,
% 5.17/5.46 ! [X: rat,Y4: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.46 => ( ( times_times_rat @ ( abs_abs_rat @ Y4 ) @ X )
% 5.17/5.46 = ( abs_abs_rat @ ( times_times_rat @ Y4 @ X ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_pos
% 5.17/5.46 thf(fact_5644_abs__mult__pos,axiom,
% 5.17/5.46 ! [X: int,Y4: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.46 => ( ( times_times_int @ ( abs_abs_int @ Y4 ) @ X )
% 5.17/5.46 = ( abs_abs_int @ ( times_times_int @ Y4 @ X ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_pos
% 5.17/5.46 thf(fact_5645_abs__mult__pos,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.46 => ( ( times_times_real @ ( abs_abs_real @ Y4 ) @ X )
% 5.17/5.46 = ( abs_abs_real @ ( times_times_real @ Y4 @ X ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_mult_pos
% 5.17/5.46 thf(fact_5646_abs__eq__mult,axiom,
% 5.17/5.46 ! [A: code_integer,B: code_integer] :
% 5.17/5.46 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.46 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.17/5.46 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.17/5.46 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.17/5.46 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.17/5.46 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_mult
% 5.17/5.46 thf(fact_5647_abs__eq__mult,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.46 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.17/5.46 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.46 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.17/5.46 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.46 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_mult
% 5.17/5.46 thf(fact_5648_abs__eq__mult,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.17/5.46 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.17/5.46 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.46 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.17/5.46 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.17/5.46 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_mult
% 5.17/5.46 thf(fact_5649_abs__eq__mult,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.46 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.17/5.46 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.46 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.17/5.46 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.17/5.46 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_eq_mult
% 5.17/5.46 thf(fact_5650_zero__le__power__abs,axiom,
% 5.17/5.46 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_le_power_abs
% 5.17/5.46 thf(fact_5651_zero__le__power__abs,axiom,
% 5.17/5.46 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_le_power_abs
% 5.17/5.46 thf(fact_5652_zero__le__power__abs,axiom,
% 5.17/5.46 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_le_power_abs
% 5.17/5.46 thf(fact_5653_zero__le__power__abs,axiom,
% 5.17/5.46 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.17/5.46
% 5.17/5.46 % zero_le_power_abs
% 5.17/5.46 thf(fact_5654_abs__div__pos,axiom,
% 5.17/5.46 ! [Y4: real,X: real] :
% 5.17/5.46 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.46 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y4 )
% 5.17/5.46 = ( abs_abs_real @ ( divide_divide_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_div_pos
% 5.17/5.46 thf(fact_5655_abs__div__pos,axiom,
% 5.17/5.46 ! [Y4: rat,X: rat] :
% 5.17/5.46 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.17/5.46 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y4 )
% 5.17/5.46 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y4 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_div_pos
% 5.17/5.46 thf(fact_5656_abs__diff__le__iff,axiom,
% 5.17/5.46 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.17/5.46 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_le_iff
% 5.17/5.46 thf(fact_5657_abs__diff__le__iff,axiom,
% 5.17/5.46 ! [X: rat,A: rat,R2: rat] :
% 5.17/5.46 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_le_iff
% 5.17/5.46 thf(fact_5658_abs__diff__le__iff,axiom,
% 5.17/5.46 ! [X: int,A: int,R2: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_le_iff
% 5.17/5.46 thf(fact_5659_abs__diff__le__iff,axiom,
% 5.17/5.46 ! [X: real,A: real,R2: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_le_iff
% 5.17/5.46 thf(fact_5660_abs__triangle__ineq4,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq4
% 5.17/5.46 thf(fact_5661_abs__triangle__ineq4,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq4
% 5.17/5.46 thf(fact_5662_abs__triangle__ineq4,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq4
% 5.17/5.46 thf(fact_5663_abs__triangle__ineq4,axiom,
% 5.17/5.46 ! [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 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_triangle_ineq4
% 5.17/5.46 thf(fact_5664_abs__diff__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_triangle_ineq
% 5.17/5.46 thf(fact_5665_abs__diff__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_triangle_ineq
% 5.17/5.46 thf(fact_5666_abs__diff__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_triangle_ineq
% 5.17/5.46 thf(fact_5667_abs__diff__triangle__ineq,axiom,
% 5.17/5.46 ! [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 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_triangle_ineq
% 5.17/5.46 thf(fact_5668_abs__diff__less__iff,axiom,
% 5.17/5.46 ! [X: code_integer,A: code_integer,R2: code_integer] :
% 5.17/5.46 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_less_iff
% 5.17/5.46 thf(fact_5669_abs__diff__less__iff,axiom,
% 5.17/5.46 ! [X: real,A: real,R2: real] :
% 5.17/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_less_iff
% 5.17/5.46 thf(fact_5670_abs__diff__less__iff,axiom,
% 5.17/5.46 ! [X: rat,A: rat,R2: rat] :
% 5.17/5.46 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_less_iff
% 5.17/5.46 thf(fact_5671_abs__diff__less__iff,axiom,
% 5.17/5.46 ! [X: int,A: int,R2: int] :
% 5.17/5.46 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R2 )
% 5.17/5.46 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X )
% 5.17/5.46 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_diff_less_iff
% 5.17/5.46 thf(fact_5672_neg__numeral__le__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_zero
% 5.17/5.46 thf(fact_5673_neg__numeral__le__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_zero
% 5.17/5.46 thf(fact_5674_neg__numeral__le__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_zero
% 5.17/5.46 thf(fact_5675_neg__numeral__le__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_zero
% 5.17/5.46 thf(fact_5676_not__zero__le__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_le_neg_numeral
% 5.17/5.46 thf(fact_5677_not__zero__le__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_le_neg_numeral
% 5.17/5.46 thf(fact_5678_not__zero__le__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_le_neg_numeral
% 5.17/5.46 thf(fact_5679_not__zero__le__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_le_neg_numeral
% 5.17/5.46 thf(fact_5680_neg__numeral__less__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_zero
% 5.17/5.46 thf(fact_5681_neg__numeral__less__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_zero
% 5.17/5.46 thf(fact_5682_neg__numeral__less__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_zero
% 5.17/5.46 thf(fact_5683_neg__numeral__less__zero,axiom,
% 5.17/5.46 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_zero
% 5.17/5.46 thf(fact_5684_not__zero__less__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_less_neg_numeral
% 5.17/5.46 thf(fact_5685_not__zero__less__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_less_neg_numeral
% 5.17/5.46 thf(fact_5686_not__zero__less__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_less_neg_numeral
% 5.17/5.46 thf(fact_5687_not__zero__less__neg__numeral,axiom,
% 5.17/5.46 ! [N: num] :
% 5.17/5.46 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_zero_less_neg_numeral
% 5.17/5.46 thf(fact_5688_le__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(1)
% 5.17/5.46 thf(fact_5689_le__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(1)
% 5.17/5.46 thf(fact_5690_le__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(1)
% 5.17/5.46 thf(fact_5691_le__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(1)
% 5.17/5.46 thf(fact_5692_le__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(3)
% 5.17/5.46 thf(fact_5693_le__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(3)
% 5.17/5.46 thf(fact_5694_le__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(3)
% 5.17/5.46 thf(fact_5695_le__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % le_minus_one_simps(3)
% 5.17/5.46 thf(fact_5696_less__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(3)
% 5.17/5.46 thf(fact_5697_less__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(3)
% 5.17/5.46 thf(fact_5698_less__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(3)
% 5.17/5.46 thf(fact_5699_less__minus__one__simps_I3_J,axiom,
% 5.17/5.46 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(3)
% 5.17/5.46 thf(fact_5700_less__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(1)
% 5.17/5.46 thf(fact_5701_less__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(1)
% 5.17/5.46 thf(fact_5702_less__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(1)
% 5.17/5.46 thf(fact_5703_less__minus__one__simps_I1_J,axiom,
% 5.17/5.46 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.17/5.46
% 5.17/5.46 % less_minus_one_simps(1)
% 5.17/5.46 thf(fact_5704_neg__numeral__le__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_one
% 5.17/5.46 thf(fact_5705_neg__numeral__le__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_one
% 5.17/5.46 thf(fact_5706_neg__numeral__le__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_one
% 5.17/5.46 thf(fact_5707_neg__numeral__le__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_one
% 5.17/5.46 thf(fact_5708_neg__one__le__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_le_numeral
% 5.17/5.46 thf(fact_5709_neg__one__le__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_le_numeral
% 5.17/5.46 thf(fact_5710_neg__one__le__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_le_numeral
% 5.17/5.46 thf(fact_5711_neg__one__le__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_le_numeral
% 5.17/5.46 thf(fact_5712_neg__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_neg_one
% 5.17/5.46 thf(fact_5713_neg__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_neg_one
% 5.17/5.46 thf(fact_5714_neg__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_neg_one
% 5.17/5.46 thf(fact_5715_neg__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_le_neg_one
% 5.17/5.46 thf(fact_5716_not__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_one
% 5.17/5.46 thf(fact_5717_not__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_one
% 5.17/5.46 thf(fact_5718_not__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_one
% 5.17/5.46 thf(fact_5719_not__numeral__le__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_le_neg_one
% 5.17/5.46 thf(fact_5720_not__one__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_le_neg_numeral
% 5.17/5.46 thf(fact_5721_not__one__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_le_neg_numeral
% 5.17/5.46 thf(fact_5722_not__one__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_le_neg_numeral
% 5.17/5.46 thf(fact_5723_not__one__le__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_le_neg_numeral
% 5.17/5.46 thf(fact_5724_neg__numeral__less__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_one
% 5.17/5.46 thf(fact_5725_neg__numeral__less__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_one
% 5.17/5.46 thf(fact_5726_neg__numeral__less__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_one
% 5.17/5.46 thf(fact_5727_neg__numeral__less__one,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.17/5.46
% 5.17/5.46 % neg_numeral_less_one
% 5.17/5.46 thf(fact_5728_neg__one__less__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_less_numeral
% 5.17/5.46 thf(fact_5729_neg__one__less__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_less_numeral
% 5.17/5.46 thf(fact_5730_neg__one__less__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_less_numeral
% 5.17/5.46 thf(fact_5731_neg__one__less__numeral,axiom,
% 5.17/5.46 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.17/5.46
% 5.17/5.46 % neg_one_less_numeral
% 5.17/5.46 thf(fact_5732_not__numeral__less__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_one
% 5.17/5.46 thf(fact_5733_not__numeral__less__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_one
% 5.17/5.46 thf(fact_5734_not__numeral__less__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_one
% 5.17/5.46 thf(fact_5735_not__numeral__less__neg__one,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_numeral_less_neg_one
% 5.17/5.46 thf(fact_5736_not__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_less_neg_numeral
% 5.17/5.46 thf(fact_5737_not__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_less_neg_numeral
% 5.17/5.46 thf(fact_5738_not__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_less_neg_numeral
% 5.17/5.46 thf(fact_5739_not__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_one_less_neg_numeral
% 5.17/5.46 thf(fact_5740_not__neg__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_less_neg_numeral
% 5.17/5.46 thf(fact_5741_not__neg__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_less_neg_numeral
% 5.17/5.46 thf(fact_5742_not__neg__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_less_neg_numeral
% 5.17/5.46 thf(fact_5743_not__neg__one__less__neg__numeral,axiom,
% 5.17/5.46 ! [M: num] :
% 5.17/5.46 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % not_neg_one_less_neg_numeral
% 5.17/5.46 thf(fact_5744_eq__minus__divide__eq,axiom,
% 5.17/5.46 ! [A: real,B: real,C: real] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.46 = ( ( ( C != zero_zero_real )
% 5.17/5.46 => ( ( times_times_real @ A @ C )
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) )
% 5.17/5.46 & ( ( C = zero_zero_real )
% 5.17/5.46 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_minus_divide_eq
% 5.17/5.46 thf(fact_5745_eq__minus__divide__eq,axiom,
% 5.17/5.46 ! [A: complex,B: complex,C: complex] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.17/5.46 = ( ( ( C != zero_zero_complex )
% 5.17/5.46 => ( ( times_times_complex @ A @ C )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.17/5.46 & ( ( C = zero_zero_complex )
% 5.17/5.46 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_minus_divide_eq
% 5.17/5.46 thf(fact_5746_eq__minus__divide__eq,axiom,
% 5.17/5.46 ! [A: rat,B: rat,C: rat] :
% 5.17/5.46 ( ( A
% 5.17/5.46 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.46 = ( ( ( C != zero_zero_rat )
% 5.17/5.46 => ( ( times_times_rat @ A @ C )
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) )
% 5.17/5.46 & ( ( C = zero_zero_rat )
% 5.17/5.46 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % eq_minus_divide_eq
% 5.17/5.46 thf(fact_5747_minus__divide__eq__eq,axiom,
% 5.17/5.46 ! [B: real,C: real,A: real] :
% 5.17/5.46 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.17/5.46 = A )
% 5.17/5.46 = ( ( ( C != zero_zero_real )
% 5.17/5.46 => ( ( uminus_uminus_real @ B )
% 5.17/5.46 = ( times_times_real @ A @ C ) ) )
% 5.17/5.46 & ( ( C = zero_zero_real )
% 5.17/5.46 => ( A = zero_zero_real ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_eq_eq
% 5.17/5.46 thf(fact_5748_minus__divide__eq__eq,axiom,
% 5.17/5.46 ! [B: complex,C: complex,A: complex] :
% 5.17/5.46 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.46 = A )
% 5.17/5.46 = ( ( ( C != zero_zero_complex )
% 5.17/5.46 => ( ( uminus1482373934393186551omplex @ B )
% 5.17/5.46 = ( times_times_complex @ A @ C ) ) )
% 5.17/5.46 & ( ( C = zero_zero_complex )
% 5.17/5.46 => ( A = zero_zero_complex ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_eq_eq
% 5.17/5.46 thf(fact_5749_minus__divide__eq__eq,axiom,
% 5.17/5.46 ! [B: rat,C: rat,A: rat] :
% 5.17/5.46 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.46 = A )
% 5.17/5.46 = ( ( ( C != zero_zero_rat )
% 5.17/5.46 => ( ( uminus_uminus_rat @ B )
% 5.17/5.46 = ( times_times_rat @ A @ C ) ) )
% 5.17/5.46 & ( ( C = zero_zero_rat )
% 5.17/5.46 => ( A = zero_zero_rat ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % minus_divide_eq_eq
% 5.17/5.46 thf(fact_5750_nonzero__neg__divide__eq__eq,axiom,
% 5.17/5.46 ! [B: real,A: real,C: real] :
% 5.17/5.46 ( ( B != zero_zero_real )
% 5.17/5.46 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.46 = C )
% 5.17/5.46 = ( ( uminus_uminus_real @ A )
% 5.17/5.46 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_neg_divide_eq_eq
% 5.17/5.46 thf(fact_5751_nonzero__neg__divide__eq__eq,axiom,
% 5.17/5.46 ! [B: complex,A: complex,C: complex] :
% 5.17/5.46 ( ( B != zero_zero_complex )
% 5.17/5.46 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.46 = C )
% 5.17/5.46 = ( ( uminus1482373934393186551omplex @ A )
% 5.17/5.46 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_neg_divide_eq_eq
% 5.17/5.46 thf(fact_5752_nonzero__neg__divide__eq__eq,axiom,
% 5.17/5.46 ! [B: rat,A: rat,C: rat] :
% 5.17/5.46 ( ( B != zero_zero_rat )
% 5.17/5.46 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.46 = C )
% 5.17/5.46 = ( ( uminus_uminus_rat @ A )
% 5.17/5.46 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_neg_divide_eq_eq
% 5.17/5.46 thf(fact_5753_nonzero__neg__divide__eq__eq2,axiom,
% 5.17/5.46 ! [B: real,C: real,A: real] :
% 5.17/5.46 ( ( B != zero_zero_real )
% 5.17/5.46 => ( ( C
% 5.17/5.46 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.17/5.46 = ( ( times_times_real @ C @ B )
% 5.17/5.46 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_neg_divide_eq_eq2
% 5.17/5.46 thf(fact_5754_nonzero__neg__divide__eq__eq2,axiom,
% 5.17/5.46 ! [B: complex,C: complex,A: complex] :
% 5.17/5.46 ( ( B != zero_zero_complex )
% 5.17/5.46 => ( ( C
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.46 = ( ( times_times_complex @ C @ B )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_neg_divide_eq_eq2
% 5.17/5.46 thf(fact_5755_nonzero__neg__divide__eq__eq2,axiom,
% 5.17/5.46 ! [B: rat,C: rat,A: rat] :
% 5.17/5.46 ( ( B != zero_zero_rat )
% 5.17/5.46 => ( ( C
% 5.17/5.46 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.17/5.46 = ( ( times_times_rat @ C @ B )
% 5.17/5.46 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonzero_neg_divide_eq_eq2
% 5.17/5.46 thf(fact_5756_mult__1s__ring__1_I2_J,axiom,
% 5.17/5.46 ! [B: real] :
% 5.17/5.46 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(2)
% 5.17/5.46 thf(fact_5757_mult__1s__ring__1_I2_J,axiom,
% 5.17/5.46 ! [B: int] :
% 5.17/5.46 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.17/5.46 = ( uminus_uminus_int @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(2)
% 5.17/5.46 thf(fact_5758_mult__1s__ring__1_I2_J,axiom,
% 5.17/5.46 ! [B: complex] :
% 5.17/5.46 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(2)
% 5.17/5.46 thf(fact_5759_mult__1s__ring__1_I2_J,axiom,
% 5.17/5.46 ! [B: code_integer] :
% 5.17/5.46 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(2)
% 5.17/5.46 thf(fact_5760_mult__1s__ring__1_I2_J,axiom,
% 5.17/5.46 ! [B: rat] :
% 5.17/5.46 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(2)
% 5.17/5.46 thf(fact_5761_mult__1s__ring__1_I1_J,axiom,
% 5.17/5.46 ! [B: real] :
% 5.17/5.46 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(1)
% 5.17/5.46 thf(fact_5762_mult__1s__ring__1_I1_J,axiom,
% 5.17/5.46 ! [B: int] :
% 5.17/5.46 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.17/5.46 = ( uminus_uminus_int @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(1)
% 5.17/5.46 thf(fact_5763_mult__1s__ring__1_I1_J,axiom,
% 5.17/5.46 ! [B: complex] :
% 5.17/5.46 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(1)
% 5.17/5.46 thf(fact_5764_mult__1s__ring__1_I1_J,axiom,
% 5.17/5.46 ! [B: code_integer] :
% 5.17/5.46 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(1)
% 5.17/5.46 thf(fact_5765_mult__1s__ring__1_I1_J,axiom,
% 5.17/5.46 ! [B: rat] :
% 5.17/5.46 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) ).
% 5.17/5.46
% 5.17/5.46 % mult_1s_ring_1(1)
% 5.17/5.46 thf(fact_5766_divide__eq__minus__1__iff,axiom,
% 5.17/5.46 ! [A: real,B: real] :
% 5.17/5.46 ( ( ( divide_divide_real @ A @ B )
% 5.17/5.46 = ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.46 = ( ( B != zero_zero_real )
% 5.17/5.46 & ( A
% 5.17/5.46 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_eq_minus_1_iff
% 5.17/5.46 thf(fact_5767_divide__eq__minus__1__iff,axiom,
% 5.17/5.46 ! [A: complex,B: complex] :
% 5.17/5.46 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.46 = ( ( B != zero_zero_complex )
% 5.17/5.46 & ( A
% 5.17/5.46 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_eq_minus_1_iff
% 5.17/5.46 thf(fact_5768_divide__eq__minus__1__iff,axiom,
% 5.17/5.46 ! [A: rat,B: rat] :
% 5.17/5.46 ( ( ( divide_divide_rat @ A @ B )
% 5.17/5.46 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.46 = ( ( B != zero_zero_rat )
% 5.17/5.46 & ( A
% 5.17/5.46 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % divide_eq_minus_1_iff
% 5.17/5.46 thf(fact_5769_uminus__numeral__One,axiom,
% 5.17/5.46 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.17/5.46 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_numeral_One
% 5.17/5.46 thf(fact_5770_uminus__numeral__One,axiom,
% 5.17/5.46 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.17/5.46 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_numeral_One
% 5.17/5.46 thf(fact_5771_uminus__numeral__One,axiom,
% 5.17/5.46 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_numeral_One
% 5.17/5.46 thf(fact_5772_uminus__numeral__One,axiom,
% 5.17/5.46 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_numeral_One
% 5.17/5.46 thf(fact_5773_uminus__numeral__One,axiom,
% 5.17/5.46 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.17/5.46 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.46
% 5.17/5.46 % uminus_numeral_One
% 5.17/5.46 thf(fact_5774_power__minus,axiom,
% 5.17/5.46 ! [A: real,N: nat] :
% 5.17/5.46 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.17/5.46 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus
% 5.17/5.46 thf(fact_5775_power__minus,axiom,
% 5.17/5.46 ! [A: int,N: nat] :
% 5.17/5.46 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.17/5.46 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus
% 5.17/5.46 thf(fact_5776_power__minus,axiom,
% 5.17/5.46 ! [A: complex,N: nat] :
% 5.17/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.17/5.46 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus
% 5.17/5.46 thf(fact_5777_power__minus,axiom,
% 5.17/5.46 ! [A: code_integer,N: nat] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.17/5.46 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus
% 5.17/5.46 thf(fact_5778_power__minus,axiom,
% 5.17/5.46 ! [A: rat,N: nat] :
% 5.17/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.17/5.46 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus
% 5.17/5.46 thf(fact_5779_power__minus__Bit0,axiom,
% 5.17/5.46 ! [X: real,K: num] :
% 5.17/5.46 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.46 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit0
% 5.17/5.46 thf(fact_5780_power__minus__Bit0,axiom,
% 5.17/5.46 ! [X: int,K: num] :
% 5.17/5.46 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.46 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit0
% 5.17/5.46 thf(fact_5781_power__minus__Bit0,axiom,
% 5.17/5.46 ! [X: complex,K: num] :
% 5.17/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.46 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit0
% 5.17/5.46 thf(fact_5782_power__minus__Bit0,axiom,
% 5.17/5.46 ! [X: code_integer,K: num] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.46 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit0
% 5.17/5.46 thf(fact_5783_power__minus__Bit0,axiom,
% 5.17/5.46 ! [X: rat,K: num] :
% 5.17/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.46 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit0
% 5.17/5.46 thf(fact_5784_lemma__interval__lt,axiom,
% 5.17/5.46 ! [A: real,X: real,B: real] :
% 5.17/5.46 ( ( ord_less_real @ A @ X )
% 5.17/5.46 => ( ( ord_less_real @ X @ B )
% 5.17/5.46 => ? [D2: real] :
% 5.17/5.46 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.46 & ! [Y3: real] :
% 5.17/5.46 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 5.17/5.46 => ( ( ord_less_real @ A @ Y3 )
% 5.17/5.46 & ( ord_less_real @ Y3 @ B ) ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % lemma_interval_lt
% 5.17/5.46 thf(fact_5785_norm__uminus__minus,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y4 ) )
% 5.17/5.46 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y4 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % norm_uminus_minus
% 5.17/5.46 thf(fact_5786_norm__uminus__minus,axiom,
% 5.17/5.46 ! [X: complex,Y4: complex] :
% 5.17/5.46 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y4 ) )
% 5.17/5.46 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y4 ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % norm_uminus_minus
% 5.17/5.46 thf(fact_5787_power__minus__Bit1,axiom,
% 5.17/5.46 ! [X: real,K: num] :
% 5.17/5.46 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.46 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit1
% 5.17/5.46 thf(fact_5788_power__minus__Bit1,axiom,
% 5.17/5.46 ! [X: int,K: num] :
% 5.17/5.46 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.46 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit1
% 5.17/5.46 thf(fact_5789_power__minus__Bit1,axiom,
% 5.17/5.46 ! [X: complex,K: num] :
% 5.17/5.46 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.46 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit1
% 5.17/5.46 thf(fact_5790_power__minus__Bit1,axiom,
% 5.17/5.46 ! [X: code_integer,K: num] :
% 5.17/5.46 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.46 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit1
% 5.17/5.46 thf(fact_5791_power__minus__Bit1,axiom,
% 5.17/5.46 ! [X: rat,K: num] :
% 5.17/5.46 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.46 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % power_minus_Bit1
% 5.17/5.46 thf(fact_5792_sin__bound__lemma,axiom,
% 5.17/5.46 ! [X: real,Y4: real,U: real,V: real] :
% 5.17/5.46 ( ( X = Y4 )
% 5.17/5.46 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.17/5.46 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y4 ) ) @ V ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % sin_bound_lemma
% 5.17/5.46 thf(fact_5793_int__cases4,axiom,
% 5.17/5.46 ! [M: int] :
% 5.17/5.46 ( ! [N2: nat] :
% 5.17/5.46 ( M
% 5.17/5.46 != ( semiri1314217659103216013at_int @ N2 ) )
% 5.17/5.46 => ~ ! [N2: nat] :
% 5.17/5.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.46 => ( M
% 5.17/5.46 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % int_cases4
% 5.17/5.46 thf(fact_5794_real__0__less__add__iff,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.46 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y4 ) ) ).
% 5.17/5.46
% 5.17/5.46 % real_0_less_add_iff
% 5.17/5.46 thf(fact_5795_real__add__less__0__iff,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( ord_less_real @ ( plus_plus_real @ X @ Y4 ) @ zero_zero_real )
% 5.17/5.46 = ( ord_less_real @ Y4 @ ( uminus_uminus_real @ X ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % real_add_less_0_iff
% 5.17/5.46 thf(fact_5796_real__add__le__0__iff,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y4 ) @ zero_zero_real )
% 5.17/5.46 = ( ord_less_eq_real @ Y4 @ ( uminus_uminus_real @ X ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % real_add_le_0_iff
% 5.17/5.46 thf(fact_5797_real__0__le__add__iff,axiom,
% 5.17/5.46 ! [X: real,Y4: real] :
% 5.17/5.46 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.46 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y4 ) ) ).
% 5.17/5.46
% 5.17/5.46 % real_0_le_add_iff
% 5.17/5.46 thf(fact_5798_int__zle__neg,axiom,
% 5.17/5.46 ! [N: nat,M: nat] :
% 5.17/5.46 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.17/5.46 = ( ( N = zero_zero_nat )
% 5.17/5.46 & ( M = zero_zero_nat ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % int_zle_neg
% 5.17/5.46 thf(fact_5799_nonpos__int__cases,axiom,
% 5.17/5.46 ! [K: int] :
% 5.17/5.46 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.17/5.46 => ~ ! [N2: nat] :
% 5.17/5.46 ( K
% 5.17/5.46 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % nonpos_int_cases
% 5.17/5.46 thf(fact_5800_negative__zle__0,axiom,
% 5.17/5.46 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.17/5.46
% 5.17/5.46 % negative_zle_0
% 5.17/5.46 thf(fact_5801_zmod__zminus1__eq__if,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.46 = zero_zero_int )
% 5.17/5.46 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = zero_zero_int ) )
% 5.17/5.46 & ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.46 != zero_zero_int )
% 5.17/5.46 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.46 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zmod_zminus1_eq_if
% 5.17/5.46 thf(fact_5802_zmod__zminus2__eq__if,axiom,
% 5.17/5.46 ! [A: int,B: int] :
% 5.17/5.46 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.46 = zero_zero_int )
% 5.17/5.46 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = zero_zero_int ) )
% 5.17/5.46 & ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.46 != zero_zero_int )
% 5.17/5.46 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.46 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % zmod_zminus2_eq_if
% 5.17/5.46 thf(fact_5803_abs__add__one__gt__zero,axiom,
% 5.17/5.46 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_add_one_gt_zero
% 5.17/5.46 thf(fact_5804_abs__add__one__gt__zero,axiom,
% 5.17/5.46 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_add_one_gt_zero
% 5.17/5.46 thf(fact_5805_abs__add__one__gt__zero,axiom,
% 5.17/5.46 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_add_one_gt_zero
% 5.17/5.46 thf(fact_5806_abs__add__one__gt__zero,axiom,
% 5.17/5.46 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % abs_add_one_gt_zero
% 5.17/5.46 thf(fact_5807_less__minus__divide__eq,axiom,
% 5.17/5.46 ! [A: real,B: real,C: real] :
% 5.17/5.46 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.46 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.17/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.46 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.17/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.46 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_divide_eq
% 5.17/5.46 thf(fact_5808_less__minus__divide__eq,axiom,
% 5.17/5.46 ! [A: rat,B: rat,C: rat] :
% 5.17/5.46 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.46 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.46 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.17/5.46 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.46 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.46 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.46 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.46 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.46
% 5.17/5.46 % less_minus_divide_eq
% 5.17/5.46 thf(fact_5809_minus__divide__less__eq,axiom,
% 5.17/5.46 ! [B: real,C: real,A: real] :
% 5.17/5.46 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.17/5.46 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.46 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.17/5.46 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.46 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.46 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.17/5.46 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_less_eq
% 5.17/5.47 thf(fact_5810_minus__divide__less__eq,axiom,
% 5.17/5.47 ! [B: rat,C: rat,A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_less_eq
% 5.17/5.47 thf(fact_5811_neg__less__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: real,A: real,B: real] :
% 5.17/5.47 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_less_minus_divide_eq
% 5.17/5.47 thf(fact_5812_neg__less__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_less_minus_divide_eq
% 5.17/5.47 thf(fact_5813_neg__minus__divide__less__eq,axiom,
% 5.17/5.47 ! [C: real,B: real,A: real] :
% 5.17/5.47 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_minus_divide_less_eq
% 5.17/5.47 thf(fact_5814_neg__minus__divide__less__eq,axiom,
% 5.17/5.47 ! [C: rat,B: rat,A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_minus_divide_less_eq
% 5.17/5.47 thf(fact_5815_pos__less__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: real,A: real,B: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_less_minus_divide_eq
% 5.17/5.47 thf(fact_5816_pos__less__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_less_minus_divide_eq
% 5.17/5.47 thf(fact_5817_pos__minus__divide__less__eq,axiom,
% 5.17/5.47 ! [C: real,B: real,A: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_minus_divide_less_eq
% 5.17/5.47 thf(fact_5818_pos__minus__divide__less__eq,axiom,
% 5.17/5.47 ! [C: rat,B: rat,A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_minus_divide_less_eq
% 5.17/5.47 thf(fact_5819_divide__eq__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: real,C: real,W: num] :
% 5.17/5.47 ( ( ( divide_divide_real @ B @ C )
% 5.17/5.47 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.47 = ( ( ( C != zero_zero_real )
% 5.17/5.47 => ( B
% 5.17/5.47 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ( C = zero_zero_real )
% 5.17/5.47 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.47 = zero_zero_real ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_eq_eq_numeral(2)
% 5.17/5.47 thf(fact_5820_divide__eq__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: complex,C: complex,W: num] :
% 5.17/5.47 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.47 = ( ( ( C != zero_zero_complex )
% 5.17/5.47 => ( B
% 5.17/5.47 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ( C = zero_zero_complex )
% 5.17/5.47 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.47 = zero_zero_complex ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_eq_eq_numeral(2)
% 5.17/5.47 thf(fact_5821_divide__eq__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: rat,C: rat,W: num] :
% 5.17/5.47 ( ( ( divide_divide_rat @ B @ C )
% 5.17/5.47 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.47 = ( ( ( C != zero_zero_rat )
% 5.17/5.47 => ( B
% 5.17/5.47 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ( C = zero_zero_rat )
% 5.17/5.47 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.47 = zero_zero_rat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_eq_eq_numeral(2)
% 5.17/5.47 thf(fact_5822_eq__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: real,C: real] :
% 5.17/5.47 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.47 = ( divide_divide_real @ B @ C ) )
% 5.17/5.47 = ( ( ( C != zero_zero_real )
% 5.17/5.47 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.17/5.47 = B ) )
% 5.17/5.47 & ( ( C = zero_zero_real )
% 5.17/5.47 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.47 = zero_zero_real ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % eq_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5823_eq__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: complex,C: complex] :
% 5.17/5.47 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.47 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.17/5.47 = ( ( ( C != zero_zero_complex )
% 5.17/5.47 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.17/5.47 = B ) )
% 5.17/5.47 & ( ( C = zero_zero_complex )
% 5.17/5.47 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.47 = zero_zero_complex ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % eq_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5824_eq__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: rat,C: rat] :
% 5.17/5.47 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.47 = ( divide_divide_rat @ B @ C ) )
% 5.17/5.47 = ( ( ( C != zero_zero_rat )
% 5.17/5.47 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.17/5.47 = B ) )
% 5.17/5.47 & ( ( C = zero_zero_rat )
% 5.17/5.47 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.47 = zero_zero_rat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % eq_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5825_add__divide__eq__if__simps_I3_J,axiom,
% 5.17/5.47 ! [Z: real,A: real,B: real] :
% 5.17/5.47 ( ( ( Z = zero_zero_real )
% 5.17/5.47 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.17/5.47 = B ) )
% 5.17/5.47 & ( ( Z != zero_zero_real )
% 5.17/5.47 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.17/5.47 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(3)
% 5.17/5.47 thf(fact_5826_add__divide__eq__if__simps_I3_J,axiom,
% 5.17/5.47 ! [Z: complex,A: complex,B: complex] :
% 5.17/5.47 ( ( ( Z = zero_zero_complex )
% 5.17/5.47 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.17/5.47 = B ) )
% 5.17/5.47 & ( ( Z != zero_zero_complex )
% 5.17/5.47 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(3)
% 5.17/5.47 thf(fact_5827_add__divide__eq__if__simps_I3_J,axiom,
% 5.17/5.47 ! [Z: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ( Z = zero_zero_rat )
% 5.17/5.47 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.17/5.47 = B ) )
% 5.17/5.47 & ( ( Z != zero_zero_rat )
% 5.17/5.47 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.17/5.47 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(3)
% 5.17/5.47 thf(fact_5828_minus__divide__add__eq__iff,axiom,
% 5.17/5.47 ! [Z: real,X: real,Y4: real] :
% 5.17/5.47 ( ( Z != zero_zero_real )
% 5.17/5.47 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y4 )
% 5.17/5.47 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_add_eq_iff
% 5.17/5.47 thf(fact_5829_minus__divide__add__eq__iff,axiom,
% 5.17/5.47 ! [Z: complex,X: complex,Y4: complex] :
% 5.17/5.47 ( ( Z != zero_zero_complex )
% 5.17/5.47 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y4 )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_add_eq_iff
% 5.17/5.47 thf(fact_5830_minus__divide__add__eq__iff,axiom,
% 5.17/5.47 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.47 ( ( Z != zero_zero_rat )
% 5.17/5.47 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y4 )
% 5.17/5.47 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_add_eq_iff
% 5.17/5.47 thf(fact_5831_add__divide__eq__if__simps_I6_J,axiom,
% 5.17/5.47 ! [Z: real,A: real,B: real] :
% 5.17/5.47 ( ( ( Z = zero_zero_real )
% 5.17/5.47 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.17/5.47 = ( uminus_uminus_real @ B ) ) )
% 5.17/5.47 & ( ( Z != zero_zero_real )
% 5.17/5.47 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.17/5.47 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(6)
% 5.17/5.47 thf(fact_5832_add__divide__eq__if__simps_I6_J,axiom,
% 5.17/5.47 ! [Z: complex,A: complex,B: complex] :
% 5.17/5.47 ( ( ( Z = zero_zero_complex )
% 5.17/5.47 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.17/5.47 & ( ( Z != zero_zero_complex )
% 5.17/5.47 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(6)
% 5.17/5.47 thf(fact_5833_add__divide__eq__if__simps_I6_J,axiom,
% 5.17/5.47 ! [Z: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ( Z = zero_zero_rat )
% 5.17/5.47 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.17/5.47 = ( uminus_uminus_rat @ B ) ) )
% 5.17/5.47 & ( ( Z != zero_zero_rat )
% 5.17/5.47 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.17/5.47 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(6)
% 5.17/5.47 thf(fact_5834_add__divide__eq__if__simps_I5_J,axiom,
% 5.17/5.47 ! [Z: real,A: real,B: real] :
% 5.17/5.47 ( ( ( Z = zero_zero_real )
% 5.17/5.47 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.17/5.47 = ( uminus_uminus_real @ B ) ) )
% 5.17/5.47 & ( ( Z != zero_zero_real )
% 5.17/5.47 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.17/5.47 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(5)
% 5.17/5.47 thf(fact_5835_add__divide__eq__if__simps_I5_J,axiom,
% 5.17/5.47 ! [Z: complex,A: complex,B: complex] :
% 5.17/5.47 ( ( ( Z = zero_zero_complex )
% 5.17/5.47 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.17/5.47 & ( ( Z != zero_zero_complex )
% 5.17/5.47 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(5)
% 5.17/5.47 thf(fact_5836_add__divide__eq__if__simps_I5_J,axiom,
% 5.17/5.47 ! [Z: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ( Z = zero_zero_rat )
% 5.17/5.47 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.17/5.47 = ( uminus_uminus_rat @ B ) ) )
% 5.17/5.47 & ( ( Z != zero_zero_rat )
% 5.17/5.47 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.17/5.47 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % add_divide_eq_if_simps(5)
% 5.17/5.47 thf(fact_5837_minus__divide__diff__eq__iff,axiom,
% 5.17/5.47 ! [Z: real,X: real,Y4: real] :
% 5.17/5.47 ( ( Z != zero_zero_real )
% 5.17/5.47 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y4 )
% 5.17/5.47 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_diff_eq_iff
% 5.17/5.47 thf(fact_5838_minus__divide__diff__eq__iff,axiom,
% 5.17/5.47 ! [Z: complex,X: complex,Y4: complex] :
% 5.17/5.47 ( ( Z != zero_zero_complex )
% 5.17/5.47 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y4 )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_diff_eq_iff
% 5.17/5.47 thf(fact_5839_minus__divide__diff__eq__iff,axiom,
% 5.17/5.47 ! [Z: rat,X: rat,Y4: rat] :
% 5.17/5.47 ( ( Z != zero_zero_rat )
% 5.17/5.47 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y4 )
% 5.17/5.47 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_diff_eq_iff
% 5.17/5.47 thf(fact_5840_even__minus,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.17/5.47 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_minus
% 5.17/5.47 thf(fact_5841_even__minus,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.47 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_minus
% 5.17/5.47 thf(fact_5842_lemma__interval,axiom,
% 5.17/5.47 ! [A: real,X: real,B: real] :
% 5.17/5.47 ( ( ord_less_real @ A @ X )
% 5.17/5.47 => ( ( ord_less_real @ X @ B )
% 5.17/5.47 => ? [D2: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.47 & ! [Y3: real] :
% 5.17/5.47 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D2 )
% 5.17/5.47 => ( ( ord_less_eq_real @ A @ Y3 )
% 5.17/5.47 & ( ord_less_eq_real @ Y3 @ B ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % lemma_interval
% 5.17/5.47 thf(fact_5843_power2__eq__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 | ( X
% 5.17/5.47 = ( uminus_uminus_real @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_iff
% 5.17/5.47 thf(fact_5844_power2__eq__iff,axiom,
% 5.17/5.47 ! [X: int,Y4: int] :
% 5.17/5.47 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 | ( X
% 5.17/5.47 = ( uminus_uminus_int @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_iff
% 5.17/5.47 thf(fact_5845_power2__eq__iff,axiom,
% 5.17/5.47 ! [X: complex,Y4: complex] :
% 5.17/5.47 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 | ( X
% 5.17/5.47 = ( uminus1482373934393186551omplex @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_iff
% 5.17/5.47 thf(fact_5846_power2__eq__iff,axiom,
% 5.17/5.47 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.47 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 | ( X
% 5.17/5.47 = ( uminus1351360451143612070nteger @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_iff
% 5.17/5.47 thf(fact_5847_power2__eq__iff,axiom,
% 5.17/5.47 ! [X: rat,Y4: rat] :
% 5.17/5.47 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 | ( X
% 5.17/5.47 = ( uminus_uminus_rat @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_iff
% 5.17/5.47 thf(fact_5848_norm__triangle__ineq3,axiom,
% 5.17/5.47 ! [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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % norm_triangle_ineq3
% 5.17/5.47 thf(fact_5849_norm__triangle__ineq3,axiom,
% 5.17/5.47 ! [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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % norm_triangle_ineq3
% 5.17/5.47 thf(fact_5850_int__cases3,axiom,
% 5.17/5.47 ! [K: int] :
% 5.17/5.47 ( ( K != zero_zero_int )
% 5.17/5.47 => ( ! [N2: nat] :
% 5.17/5.47 ( ( K
% 5.17/5.47 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.17/5.47 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.17/5.47 => ~ ! [N2: nat] :
% 5.17/5.47 ( ( K
% 5.17/5.47 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.17/5.47 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % int_cases3
% 5.17/5.47 thf(fact_5851_pochhammer__eq__0__iff,axiom,
% 5.17/5.47 ! [A: complex,N: nat] :
% 5.17/5.47 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.17/5.47 = zero_zero_complex )
% 5.17/5.47 = ( ? [K3: nat] :
% 5.17/5.47 ( ( ord_less_nat @ K3 @ N )
% 5.17/5.47 & ( A
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_eq_0_iff
% 5.17/5.47 thf(fact_5852_pochhammer__eq__0__iff,axiom,
% 5.17/5.47 ! [A: real,N: nat] :
% 5.17/5.47 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( ? [K3: nat] :
% 5.17/5.47 ( ( ord_less_nat @ K3 @ N )
% 5.17/5.47 & ( A
% 5.17/5.47 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_eq_0_iff
% 5.17/5.47 thf(fact_5853_pochhammer__eq__0__iff,axiom,
% 5.17/5.47 ! [A: rat,N: nat] :
% 5.17/5.47 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.17/5.47 = zero_zero_rat )
% 5.17/5.47 = ( ? [K3: nat] :
% 5.17/5.47 ( ( ord_less_nat @ K3 @ N )
% 5.17/5.47 & ( A
% 5.17/5.47 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_eq_0_iff
% 5.17/5.47 thf(fact_5854_pochhammer__of__nat__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.17/5.47 = zero_z3403309356797280102nteger )
% 5.17/5.47 = ( ord_less_nat @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_iff
% 5.17/5.47 thf(fact_5855_pochhammer__of__nat__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.17/5.47 = zero_zero_complex )
% 5.17/5.47 = ( ord_less_nat @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_iff
% 5.17/5.47 thf(fact_5856_pochhammer__of__nat__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( ord_less_nat @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_iff
% 5.17/5.47 thf(fact_5857_pochhammer__of__nat__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.17/5.47 = zero_zero_rat )
% 5.17/5.47 = ( ord_less_nat @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_iff
% 5.17/5.47 thf(fact_5858_pochhammer__of__nat__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 = ( ord_less_nat @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_iff
% 5.17/5.47 thf(fact_5859_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ord_less_nat @ N @ K )
% 5.17/5.47 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.17/5.47 = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma
% 5.17/5.47 thf(fact_5860_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ord_less_nat @ N @ K )
% 5.17/5.47 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.17/5.47 = zero_zero_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma
% 5.17/5.47 thf(fact_5861_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ord_less_nat @ N @ K )
% 5.17/5.47 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.17/5.47 = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma
% 5.17/5.47 thf(fact_5862_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ord_less_nat @ N @ K )
% 5.17/5.47 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.17/5.47 = zero_zero_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma
% 5.17/5.47 thf(fact_5863_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.17/5.47 ! [N: nat,K: nat] :
% 5.17/5.47 ( ( ord_less_nat @ N @ K )
% 5.17/5.47 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.17/5.47 = zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma
% 5.17/5.47 thf(fact_5864_ln__add__one__self__le__self2,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.47 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % ln_add_one_self_le_self2
% 5.17/5.47 thf(fact_5865_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.17/5.47 != zero_z3403309356797280102nteger ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma'
% 5.17/5.47 thf(fact_5866_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.17/5.47 != zero_zero_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma'
% 5.17/5.47 thf(fact_5867_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.17/5.47 != zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma'
% 5.17/5.47 thf(fact_5868_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.17/5.47 != zero_zero_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma'
% 5.17/5.47 thf(fact_5869_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.17/5.47 != zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_of_nat_eq_0_lemma'
% 5.17/5.47 thf(fact_5870_not__zle__0__negative,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % not_zle_0_negative
% 5.17/5.47 thf(fact_5871_negD,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( ord_less_int @ X @ zero_zero_int )
% 5.17/5.47 => ? [N2: nat] :
% 5.17/5.47 ( X
% 5.17/5.47 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % negD
% 5.17/5.47 thf(fact_5872_negative__zless__0,axiom,
% 5.17/5.47 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % negative_zless_0
% 5.17/5.47 thf(fact_5873_verit__less__mono__div__int2,axiom,
% 5.17/5.47 ! [A2: int,B4: int,N: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ A2 @ B4 )
% 5.17/5.47 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.17/5.47 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % verit_less_mono_div_int2
% 5.17/5.47 thf(fact_5874_div__eq__minus1,axiom,
% 5.17/5.47 ! [B: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.47 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % div_eq_minus1
% 5.17/5.47 thf(fact_5875_abs__le__square__iff,axiom,
% 5.17/5.47 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.47 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y4 ) )
% 5.17/5.47 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_le_square_iff
% 5.17/5.47 thf(fact_5876_abs__le__square__iff,axiom,
% 5.17/5.47 ! [X: rat,Y4: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_le_square_iff
% 5.17/5.47 thf(fact_5877_abs__le__square__iff,axiom,
% 5.17/5.47 ! [X: int,Y4: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_le_square_iff
% 5.17/5.47 thf(fact_5878_abs__le__square__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_le_square_iff
% 5.17/5.47 thf(fact_5879_abs__square__eq__1,axiom,
% 5.17/5.47 ! [X: code_integer] :
% 5.17/5.47 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_Code_integer )
% 5.17/5.47 = ( ( abs_abs_Code_integer @ X )
% 5.17/5.47 = one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_eq_1
% 5.17/5.47 thf(fact_5880_abs__square__eq__1,axiom,
% 5.17/5.47 ! [X: rat] :
% 5.17/5.47 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_rat )
% 5.17/5.47 = ( ( abs_abs_rat @ X )
% 5.17/5.47 = one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_eq_1
% 5.17/5.47 thf(fact_5881_abs__square__eq__1,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_int )
% 5.17/5.47 = ( ( abs_abs_int @ X )
% 5.17/5.47 = one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_eq_1
% 5.17/5.47 thf(fact_5882_abs__square__eq__1,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_real )
% 5.17/5.47 = ( ( abs_abs_real @ X )
% 5.17/5.47 = one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_eq_1
% 5.17/5.47 thf(fact_5883_power__even__abs,axiom,
% 5.17/5.47 ! [N: nat,A: code_integer] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.17/5.47 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_even_abs
% 5.17/5.47 thf(fact_5884_power__even__abs,axiom,
% 5.17/5.47 ! [N: nat,A: rat] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.17/5.47 = ( power_power_rat @ A @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_even_abs
% 5.17/5.47 thf(fact_5885_power__even__abs,axiom,
% 5.17/5.47 ! [N: nat,A: int] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.17/5.47 = ( power_power_int @ A @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_even_abs
% 5.17/5.47 thf(fact_5886_power__even__abs,axiom,
% 5.17/5.47 ! [N: nat,A: real] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.17/5.47 = ( power_power_real @ A @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_even_abs
% 5.17/5.47 thf(fact_5887_le__minus__divide__eq,axiom,
% 5.17/5.47 ! [A: rat,B: rat,C: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_minus_divide_eq
% 5.17/5.47 thf(fact_5888_le__minus__divide__eq,axiom,
% 5.17/5.47 ! [A: real,B: real,C: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.47 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_minus_divide_eq
% 5.17/5.47 thf(fact_5889_minus__divide__le__eq,axiom,
% 5.17/5.47 ! [B: rat,C: rat,A: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_le_eq
% 5.17/5.47 thf(fact_5890_minus__divide__le__eq,axiom,
% 5.17/5.47 ! [B: real,C: real,A: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.17/5.47 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_divide_le_eq
% 5.17/5.47 thf(fact_5891_neg__le__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_le_minus_divide_eq
% 5.17/5.47 thf(fact_5892_neg__le__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: real,A: real,B: real] :
% 5.17/5.47 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_le_minus_divide_eq
% 5.17/5.47 thf(fact_5893_neg__minus__divide__le__eq,axiom,
% 5.17/5.47 ! [C: rat,B: rat,A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_minus_divide_le_eq
% 5.17/5.47 thf(fact_5894_neg__minus__divide__le__eq,axiom,
% 5.17/5.47 ! [C: real,B: real,A: real] :
% 5.17/5.47 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_minus_divide_le_eq
% 5.17/5.47 thf(fact_5895_pos__le__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: rat,A: rat,B: rat] :
% 5.17/5.47 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_le_minus_divide_eq
% 5.17/5.47 thf(fact_5896_pos__le__minus__divide__eq,axiom,
% 5.17/5.47 ! [C: real,A: real,B: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.17/5.47 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_le_minus_divide_eq
% 5.17/5.47 thf(fact_5897_pos__minus__divide__le__eq,axiom,
% 5.17/5.47 ! [C: rat,B: rat,A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_minus_divide_le_eq
% 5.17/5.47 thf(fact_5898_pos__minus__divide__le__eq,axiom,
% 5.17/5.47 ! [C: real,B: real,A: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.17/5.47 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pos_minus_divide_le_eq
% 5.17/5.47 thf(fact_5899_divide__less__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: real,C: real,W: num] :
% 5.17/5.47 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.47 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_less_eq_numeral(2)
% 5.17/5.47 thf(fact_5900_divide__less__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: rat,C: rat,W: num] :
% 5.17/5.47 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_less_eq_numeral(2)
% 5.17/5.47 thf(fact_5901_less__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: real,C: real] :
% 5.17/5.47 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.17/5.47 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % less_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5902_less__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: rat,C: rat] :
% 5.17/5.47 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % less_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5903_power2__eq__1__iff,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_real )
% 5.17/5.47 = ( ( A = one_one_real )
% 5.17/5.47 | ( A
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_1_iff
% 5.17/5.47 thf(fact_5904_power2__eq__1__iff,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_int )
% 5.17/5.47 = ( ( A = one_one_int )
% 5.17/5.47 | ( A
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_1_iff
% 5.17/5.47 thf(fact_5905_power2__eq__1__iff,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_complex )
% 5.17/5.47 = ( ( A = one_one_complex )
% 5.17/5.47 | ( A
% 5.17/5.47 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_1_iff
% 5.17/5.47 thf(fact_5906_power2__eq__1__iff,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_Code_integer )
% 5.17/5.47 = ( ( A = one_one_Code_integer )
% 5.17/5.47 | ( A
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_1_iff
% 5.17/5.47 thf(fact_5907_power2__eq__1__iff,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = one_one_rat )
% 5.17/5.47 = ( ( A = one_one_rat )
% 5.17/5.47 | ( A
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_eq_1_iff
% 5.17/5.47 thf(fact_5908_uminus__power__if,axiom,
% 5.17/5.47 ! [N: nat,A: real] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.17/5.47 = ( power_power_real @ A @ N ) ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.17/5.47 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % uminus_power_if
% 5.17/5.47 thf(fact_5909_uminus__power__if,axiom,
% 5.17/5.47 ! [N: nat,A: int] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.17/5.47 = ( power_power_int @ A @ N ) ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.17/5.47 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % uminus_power_if
% 5.17/5.47 thf(fact_5910_uminus__power__if,axiom,
% 5.17/5.47 ! [N: nat,A: complex] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.17/5.47 = ( power_power_complex @ A @ N ) ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % uminus_power_if
% 5.17/5.47 thf(fact_5911_uminus__power__if,axiom,
% 5.17/5.47 ! [N: nat,A: code_integer] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.17/5.47 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % uminus_power_if
% 5.17/5.47 thf(fact_5912_uminus__power__if,axiom,
% 5.17/5.47 ! [N: nat,A: rat] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.17/5.47 = ( power_power_rat @ A @ N ) ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.17/5.47 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % uminus_power_if
% 5.17/5.47 thf(fact_5913_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.17/5.47 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_one_power_add_eq_neg_one_power_diff
% 5.17/5.47 thf(fact_5914_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.17/5.47 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_one_power_add_eq_neg_one_power_diff
% 5.17/5.47 thf(fact_5915_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.17/5.47 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_one_power_add_eq_neg_one_power_diff
% 5.17/5.47 thf(fact_5916_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.17/5.47 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_one_power_add_eq_neg_one_power_diff
% 5.17/5.47 thf(fact_5917_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.17/5.47 ! [K: nat,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.47 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.17/5.47 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_one_power_add_eq_neg_one_power_diff
% 5.17/5.47 thf(fact_5918_realpow__square__minus__le,axiom,
% 5.17/5.47 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % realpow_square_minus_le
% 5.17/5.47 thf(fact_5919_neg__int__cases,axiom,
% 5.17/5.47 ! [K: int] :
% 5.17/5.47 ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.47 => ~ ! [N2: nat] :
% 5.17/5.47 ( ( K
% 5.17/5.47 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.17/5.47 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % neg_int_cases
% 5.17/5.47 thf(fact_5920_ln__one__minus__pos__upper__bound,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ln_one_minus_pos_upper_bound
% 5.17/5.47 thf(fact_5921_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.17/5.47 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_int_less_eq_self_iff
% 5.17/5.47 thf(fact_5922_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.17/5.47 ! [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 ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_int_greater_eq_minus_exp
% 5.17/5.47 thf(fact_5923_signed__take__bit__int__greater__self__iff,axiom,
% 5.17/5.47 ! [K: int,N: nat] :
% 5.17/5.47 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.17/5.47 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_int_greater_self_iff
% 5.17/5.47 thf(fact_5924_minus__mod__int__eq,axiom,
% 5.17/5.47 ! [L: int,K: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.17/5.47 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.17/5.47 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_mod_int_eq
% 5.17/5.47 thf(fact_5925_zmod__minus1,axiom,
% 5.17/5.47 ! [B: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.47 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.17/5.47 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zmod_minus1
% 5.17/5.47 thf(fact_5926_zdiv__zminus2__eq__if,axiom,
% 5.17/5.47 ! [B: int,A: int] :
% 5.17/5.47 ( ( B != zero_zero_int )
% 5.17/5.47 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.47 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.17/5.47 & ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.47 != zero_zero_int )
% 5.17/5.47 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.17/5.47 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zdiv_zminus2_eq_if
% 5.17/5.47 thf(fact_5927_zdiv__zminus1__eq__if,axiom,
% 5.17/5.47 ! [B: int,A: int] :
% 5.17/5.47 ( ( B != zero_zero_int )
% 5.17/5.47 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.47 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.17/5.47 & ( ( ( modulo_modulo_int @ A @ B )
% 5.17/5.47 != zero_zero_int )
% 5.17/5.47 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.17/5.47 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zdiv_zminus1_eq_if
% 5.17/5.47 thf(fact_5928_power2__le__iff__abs__le,axiom,
% 5.17/5.47 ! [Y4: code_integer,X: code_integer] :
% 5.17/5.47 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y4 )
% 5.17/5.47 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_le_iff_abs_le
% 5.17/5.47 thf(fact_5929_power2__le__iff__abs__le,axiom,
% 5.17/5.47 ! [Y4: rat,X: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.17/5.47 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_le_iff_abs_le
% 5.17/5.47 thf(fact_5930_power2__le__iff__abs__le,axiom,
% 5.17/5.47 ! [Y4: int,X: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.47 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_le_iff_abs_le
% 5.17/5.47 thf(fact_5931_power2__le__iff__abs__le,axiom,
% 5.17/5.47 ! [Y4: real,X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.47 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power2_le_iff_abs_le
% 5.17/5.47 thf(fact_5932_abs__square__le__1,axiom,
% 5.17/5.47 ! [X: code_integer] :
% 5.17/5.47 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.17/5.47 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_le_1
% 5.17/5.47 thf(fact_5933_abs__square__le__1,axiom,
% 5.17/5.47 ! [X: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.17/5.47 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_le_1
% 5.17/5.47 thf(fact_5934_abs__square__le__1,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.17/5.47 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_le_1
% 5.17/5.47 thf(fact_5935_abs__square__le__1,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.17/5.47 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_le_1
% 5.17/5.47 thf(fact_5936_abs__square__less__1,axiom,
% 5.17/5.47 ! [X: code_integer] :
% 5.17/5.47 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.17/5.47 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_less_1
% 5.17/5.47 thf(fact_5937_abs__square__less__1,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.17/5.47 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_less_1
% 5.17/5.47 thf(fact_5938_abs__square__less__1,axiom,
% 5.17/5.47 ! [X: rat] :
% 5.17/5.47 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.17/5.47 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_less_1
% 5.17/5.47 thf(fact_5939_abs__square__less__1,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.17/5.47 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_square_less_1
% 5.17/5.47 thf(fact_5940_power__mono__even,axiom,
% 5.17/5.47 ! [N: nat,A: code_integer,B: code_integer] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.17/5.47 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_mono_even
% 5.17/5.47 thf(fact_5941_power__mono__even,axiom,
% 5.17/5.47 ! [N: nat,A: rat,B: rat] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.17/5.47 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_mono_even
% 5.17/5.47 thf(fact_5942_power__mono__even,axiom,
% 5.17/5.47 ! [N: nat,A: int,B: int] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.17/5.47 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_mono_even
% 5.17/5.47 thf(fact_5943_power__mono__even,axiom,
% 5.17/5.47 ! [N: nat,A: real,B: real] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.17/5.47 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_mono_even
% 5.17/5.47 thf(fact_5944_divide__le__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: rat,C: rat,W: num] :
% 5.17/5.47 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_le_eq_numeral(2)
% 5.17/5.47 thf(fact_5945_divide__le__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [B: real,C: real,W: num] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.47 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_le_eq_numeral(2)
% 5.17/5.47 thf(fact_5946_le__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: rat,C: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.17/5.47 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.17/5.47 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5947_le__divide__eq__numeral_I2_J,axiom,
% 5.17/5.47 ! [W: num,B: real,C: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.17/5.47 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.47 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.17/5.47 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_divide_eq_numeral(2)
% 5.17/5.47 thf(fact_5948_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.47 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.17/5.47 thf(fact_5949_square__le__1,axiom,
% 5.17/5.47 ! [X: code_integer] :
% 5.17/5.47 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.17/5.47 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.17/5.47 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % square_le_1
% 5.17/5.47 thf(fact_5950_square__le__1,axiom,
% 5.17/5.47 ! [X: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.17/5.47 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.17/5.47 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % square_le_1
% 5.17/5.47 thf(fact_5951_square__le__1,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.17/5.47 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.17/5.47 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % square_le_1
% 5.17/5.47 thf(fact_5952_square__le__1,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.47 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % square_le_1
% 5.17/5.47 thf(fact_5953_minus__power__mult__self,axiom,
% 5.17/5.47 ! [A: real,N: nat] :
% 5.17/5.47 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.17/5.47 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_power_mult_self
% 5.17/5.47 thf(fact_5954_minus__power__mult__self,axiom,
% 5.17/5.47 ! [A: int,N: nat] :
% 5.17/5.47 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.17/5.47 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_power_mult_self
% 5.17/5.47 thf(fact_5955_minus__power__mult__self,axiom,
% 5.17/5.47 ! [A: complex,N: nat] :
% 5.17/5.47 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.17/5.47 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_power_mult_self
% 5.17/5.47 thf(fact_5956_minus__power__mult__self,axiom,
% 5.17/5.47 ! [A: code_integer,N: nat] :
% 5.17/5.47 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.17/5.47 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_power_mult_self
% 5.17/5.47 thf(fact_5957_minus__power__mult__self,axiom,
% 5.17/5.47 ! [A: rat,N: nat] :
% 5.17/5.47 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.17/5.47 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_power_mult_self
% 5.17/5.47 thf(fact_5958_minus__one__power__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.17/5.47 = one_one_real ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_one_power_iff
% 5.17/5.47 thf(fact_5959_minus__one__power__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.17/5.47 = one_one_int ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_one_power_iff
% 5.17/5.47 thf(fact_5960_minus__one__power__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.17/5.47 = one_one_complex ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_one_power_iff
% 5.17/5.47 thf(fact_5961_minus__one__power__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.17/5.47 = one_one_Code_integer ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_one_power_iff
% 5.17/5.47 thf(fact_5962_minus__one__power__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.17/5.47 = one_one_rat ) )
% 5.17/5.47 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.47 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_one_power_iff
% 5.17/5.47 thf(fact_5963_pochhammer__absorb__comp,axiom,
% 5.17/5.47 ! [R2: code_integer,K: nat] :
% 5.17/5.47 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.17/5.47 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_absorb_comp
% 5.17/5.47 thf(fact_5964_pochhammer__absorb__comp,axiom,
% 5.17/5.47 ! [R2: complex,K: nat] :
% 5.17/5.47 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.17/5.47 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_absorb_comp
% 5.17/5.47 thf(fact_5965_pochhammer__absorb__comp,axiom,
% 5.17/5.47 ! [R2: real,K: nat] :
% 5.17/5.47 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.17/5.47 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_absorb_comp
% 5.17/5.47 thf(fact_5966_pochhammer__absorb__comp,axiom,
% 5.17/5.47 ! [R2: rat,K: nat] :
% 5.17/5.47 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.17/5.47 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_absorb_comp
% 5.17/5.47 thf(fact_5967_pochhammer__absorb__comp,axiom,
% 5.17/5.47 ! [R2: int,K: nat] :
% 5.17/5.47 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.17/5.47 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_absorb_comp
% 5.17/5.47 thf(fact_5968_pochhammer__same,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.17/5.47 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_same
% 5.17/5.47 thf(fact_5969_pochhammer__same,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.17/5.47 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_same
% 5.17/5.47 thf(fact_5970_pochhammer__same,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.17/5.47 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_same
% 5.17/5.47 thf(fact_5971_pochhammer__same,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.17/5.47 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_same
% 5.17/5.47 thf(fact_5972_pochhammer__same,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.17/5.47 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_same
% 5.17/5.47 thf(fact_5973_signed__take__bit__int__eq__self__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.17/5.47 = K )
% 5.17/5.47 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.17/5.47 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_int_eq_self_iff
% 5.17/5.47 thf(fact_5974_signed__take__bit__int__eq__self,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.17/5.47 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.47 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.17/5.47 = K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_int_eq_self
% 5.17/5.47 thf(fact_5975_Bernoulli__inequality,axiom,
% 5.17/5.47 ! [X: real,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.47 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Bernoulli_inequality
% 5.17/5.47 thf(fact_5976_minus__1__div__exp__eq__int,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % minus_1_div_exp_eq_int
% 5.17/5.47 thf(fact_5977_div__pos__neg__trivial,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.47 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.17/5.47 => ( ( divide_divide_int @ K @ L )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % div_pos_neg_trivial
% 5.17/5.47 thf(fact_5978_power__minus1__odd,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_minus1_odd
% 5.17/5.47 thf(fact_5979_power__minus1__odd,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_minus1_odd
% 5.17/5.47 thf(fact_5980_power__minus1__odd,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_minus1_odd
% 5.17/5.47 thf(fact_5981_power__minus1__odd,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_minus1_odd
% 5.17/5.47 thf(fact_5982_power__minus1__odd,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_minus1_odd
% 5.17/5.47 thf(fact_5983_pochhammer__minus,axiom,
% 5.17/5.47 ! [B: code_integer,K: nat] :
% 5.17/5.47 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.17/5.47 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus
% 5.17/5.47 thf(fact_5984_pochhammer__minus,axiom,
% 5.17/5.47 ! [B: complex,K: nat] :
% 5.17/5.47 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.17/5.47 = ( 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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus
% 5.17/5.47 thf(fact_5985_pochhammer__minus,axiom,
% 5.17/5.47 ! [B: real,K: nat] :
% 5.17/5.47 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.17/5.47 = ( 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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus
% 5.17/5.47 thf(fact_5986_pochhammer__minus,axiom,
% 5.17/5.47 ! [B: rat,K: nat] :
% 5.17/5.47 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.17/5.47 = ( 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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus
% 5.17/5.47 thf(fact_5987_pochhammer__minus,axiom,
% 5.17/5.47 ! [B: int,K: nat] :
% 5.17/5.47 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.17/5.47 = ( 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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus
% 5.17/5.47 thf(fact_5988_pochhammer__minus_H,axiom,
% 5.17/5.47 ! [B: code_integer,K: nat] :
% 5.17/5.47 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.17/5.47 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus'
% 5.17/5.47 thf(fact_5989_pochhammer__minus_H,axiom,
% 5.17/5.47 ! [B: complex,K: nat] :
% 5.17/5.47 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.17/5.47 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus'
% 5.17/5.47 thf(fact_5990_pochhammer__minus_H,axiom,
% 5.17/5.47 ! [B: real,K: nat] :
% 5.17/5.47 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.17/5.47 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus'
% 5.17/5.47 thf(fact_5991_pochhammer__minus_H,axiom,
% 5.17/5.47 ! [B: rat,K: nat] :
% 5.17/5.47 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.17/5.47 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus'
% 5.17/5.47 thf(fact_5992_pochhammer__minus_H,axiom,
% 5.17/5.47 ! [B: int,K: nat] :
% 5.17/5.47 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.17/5.47 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pochhammer_minus'
% 5.17/5.47 thf(fact_5993_int__bit__induct,axiom,
% 5.17/5.47 ! [P: int > $o,K: int] :
% 5.17/5.47 ( ( P @ zero_zero_int )
% 5.17/5.47 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 => ( ! [K2: int] :
% 5.17/5.47 ( ( P @ K2 )
% 5.17/5.47 => ( ( K2 != zero_zero_int )
% 5.17/5.47 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.47 => ( ! [K2: int] :
% 5.17/5.47 ( ( P @ K2 )
% 5.17/5.47 => ( ( K2
% 5.17/5.47 != ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.17/5.47 => ( P @ K ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % int_bit_induct
% 5.17/5.47 thf(fact_5994_signed__take__bit__int__greater__eq,axiom,
% 5.17/5.47 ! [K: int,N: nat] :
% 5.17/5.47 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.47 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_int_greater_eq
% 5.17/5.47 thf(fact_5995_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.17/5.47 thf(fact_5996_fact__code,axiom,
% 5.17/5.47 ( semiri773545260158071498ct_rat
% 5.17/5.47 = ( ^ [N4: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_code
% 5.17/5.47 thf(fact_5997_fact__code,axiom,
% 5.17/5.47 ( semiri1406184849735516958ct_int
% 5.17/5.47 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_code
% 5.17/5.47 thf(fact_5998_fact__code,axiom,
% 5.17/5.47 ( semiri1408675320244567234ct_nat
% 5.17/5.47 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_code
% 5.17/5.47 thf(fact_5999_fact__code,axiom,
% 5.17/5.47 ( semiri2265585572941072030t_real
% 5.17/5.47 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_code
% 5.17/5.47 thf(fact_6000_fact__code,axiom,
% 5.17/5.47 ( semiri5044797733671781792omplex
% 5.17/5.47 = ( ^ [N4: nat] : ( semiri8010041392384452111omplex @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_code
% 5.17/5.47 thf(fact_6001_abs__sqrt__wlog,axiom,
% 5.17/5.47 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.17/5.47 ( ! [X4: code_integer] :
% 5.17/5.47 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.17/5.47 => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.47 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sqrt_wlog
% 5.17/5.47 thf(fact_6002_abs__sqrt__wlog,axiom,
% 5.17/5.47 ! [P: rat > rat > $o,X: rat] :
% 5.17/5.47 ( ! [X4: rat] :
% 5.17/5.47 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.17/5.47 => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.47 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sqrt_wlog
% 5.17/5.47 thf(fact_6003_abs__sqrt__wlog,axiom,
% 5.17/5.47 ! [P: int > int > $o,X: int] :
% 5.17/5.47 ( ! [X4: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.17/5.47 => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.47 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sqrt_wlog
% 5.17/5.47 thf(fact_6004_abs__sqrt__wlog,axiom,
% 5.17/5.47 ! [P: real > real > $o,X: real] :
% 5.17/5.47 ( ! [X4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.17/5.47 => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.47 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sqrt_wlog
% 5.17/5.47 thf(fact_6005_sin__coeff__def,axiom,
% 5.17/5.47 ( sin_coeff
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sin_coeff_def
% 5.17/5.47 thf(fact_6006_cos__coeff__def,axiom,
% 5.17/5.47 ( cos_coeff
% 5.17/5.47 = ( ^ [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 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % cos_coeff_def
% 5.17/5.47 thf(fact_6007_compl__le__compl__iff,axiom,
% 5.17/5.47 ! [X: set_int,Y4: set_int] :
% 5.17/5.47 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_set_int @ Y4 @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % compl_le_compl_iff
% 5.17/5.47 thf(fact_6008_listsum__bound,axiom,
% 5.17/5.47 ! [Xs: list_complex,F: complex > real,Y4: real] :
% 5.17/5.47 ( ! [X4: complex] :
% 5.17/5.47 ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.47 => ( ord_less_eq_real @ Y4 @ ( foldr_real_real @ plus_plus_real @ ( map_complex_real @ F @ Xs ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % listsum_bound
% 5.17/5.47 thf(fact_6009_listsum__bound,axiom,
% 5.17/5.47 ! [Xs: list_set_nat,F: set_nat > real,Y4: real] :
% 5.17/5.47 ( ! [X4: set_nat] :
% 5.17/5.47 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.47 => ( ord_less_eq_real @ Y4 @ ( foldr_real_real @ plus_plus_real @ ( map_set_nat_real @ F @ Xs ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % listsum_bound
% 5.17/5.47 thf(fact_6010_listsum__bound,axiom,
% 5.17/5.47 ! [Xs: list_VEBT_VEBT,F: vEBT_VEBT > real,Y4: real] :
% 5.17/5.47 ( ! [X4: vEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.47 => ( ord_less_eq_real @ Y4 @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ F @ Xs ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % listsum_bound
% 5.17/5.47 thf(fact_6011_listsum__bound,axiom,
% 5.17/5.47 ! [Xs: list_nat,F: nat > real,Y4: real] :
% 5.17/5.47 ( ! [X4: nat] :
% 5.17/5.47 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.47 => ( ord_less_eq_real @ Y4 @ ( foldr_real_real @ plus_plus_real @ ( map_nat_real @ F @ Xs ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % listsum_bound
% 5.17/5.47 thf(fact_6012_listsum__bound,axiom,
% 5.17/5.47 ! [Xs: list_real,F: real > real,Y4: real] :
% 5.17/5.47 ( ! [X4: real] :
% 5.17/5.47 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.47 => ( ord_less_eq_real @ Y4 @ ( foldr_real_real @ plus_plus_real @ ( map_real_real @ F @ Xs ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % listsum_bound
% 5.17/5.47 thf(fact_6013_listsum__bound,axiom,
% 5.17/5.47 ! [Xs: list_int,F: int > real,Y4: real] :
% 5.17/5.47 ( ! [X4: int] :
% 5.17/5.47 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.47 => ( ord_less_eq_real @ Y4 @ ( foldr_real_real @ plus_plus_real @ ( map_int_real @ F @ Xs ) @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % listsum_bound
% 5.17/5.47 thf(fact_6014_signed__take__bit__numeral__minus__bit1,axiom,
% 5.17/5.47 ! [L: num,K: num] :
% 5.17/5.47 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.17/5.47 = ( 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 ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_numeral_minus_bit1
% 5.17/5.47 thf(fact_6015_dbl__dec__simps_I4_J,axiom,
% 5.17/5.47 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.47 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(4)
% 5.17/5.47 thf(fact_6016_dbl__dec__simps_I4_J,axiom,
% 5.17/5.47 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(4)
% 5.17/5.47 thf(fact_6017_dbl__dec__simps_I4_J,axiom,
% 5.17/5.47 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(4)
% 5.17/5.47 thf(fact_6018_dbl__dec__simps_I4_J,axiom,
% 5.17/5.47 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(4)
% 5.17/5.47 thf(fact_6019_dbl__dec__simps_I4_J,axiom,
% 5.17/5.47 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.47 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(4)
% 5.17/5.47 thf(fact_6020_ComplI,axiom,
% 5.17/5.47 ! [C: complex,A2: set_complex] :
% 5.17/5.47 ( ~ ( member_complex @ C @ A2 )
% 5.17/5.47 => ( member_complex @ C @ ( uminus8566677241136511917omplex @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplI
% 5.17/5.47 thf(fact_6021_ComplI,axiom,
% 5.17/5.47 ! [C: real,A2: set_real] :
% 5.17/5.47 ( ~ ( member_real @ C @ A2 )
% 5.17/5.47 => ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplI
% 5.17/5.47 thf(fact_6022_ComplI,axiom,
% 5.17/5.47 ! [C: set_nat,A2: set_set_nat] :
% 5.17/5.47 ( ~ ( member_set_nat @ C @ A2 )
% 5.17/5.47 => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplI
% 5.17/5.47 thf(fact_6023_ComplI,axiom,
% 5.17/5.47 ! [C: nat,A2: set_nat] :
% 5.17/5.47 ( ~ ( member_nat @ C @ A2 )
% 5.17/5.47 => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplI
% 5.17/5.47 thf(fact_6024_ComplI,axiom,
% 5.17/5.47 ! [C: int,A2: set_int] :
% 5.17/5.47 ( ~ ( member_int @ C @ A2 )
% 5.17/5.47 => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplI
% 5.17/5.47 thf(fact_6025_Compl__iff,axiom,
% 5.17/5.47 ! [C: complex,A2: set_complex] :
% 5.17/5.47 ( ( member_complex @ C @ ( uminus8566677241136511917omplex @ A2 ) )
% 5.17/5.47 = ( ~ ( member_complex @ C @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Compl_iff
% 5.17/5.47 thf(fact_6026_Compl__iff,axiom,
% 5.17/5.47 ! [C: real,A2: set_real] :
% 5.17/5.47 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 5.17/5.47 = ( ~ ( member_real @ C @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Compl_iff
% 5.17/5.47 thf(fact_6027_Compl__iff,axiom,
% 5.17/5.47 ! [C: set_nat,A2: set_set_nat] :
% 5.17/5.47 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 5.17/5.47 = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Compl_iff
% 5.17/5.47 thf(fact_6028_Compl__iff,axiom,
% 5.17/5.47 ! [C: nat,A2: set_nat] :
% 5.17/5.47 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.17/5.47 = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Compl_iff
% 5.17/5.47 thf(fact_6029_Compl__iff,axiom,
% 5.17/5.47 ! [C: int,A2: set_int] :
% 5.17/5.47 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.17/5.47 = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Compl_iff
% 5.17/5.47 thf(fact_6030_zdvd1__eq,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ X @ one_one_int )
% 5.17/5.47 = ( ( abs_abs_int @ X )
% 5.17/5.47 = one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % zdvd1_eq
% 5.17/5.47 thf(fact_6031_dbl__dec__simps_I3_J,axiom,
% 5.17/5.47 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.17/5.47 = one_one_complex ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(3)
% 5.17/5.47 thf(fact_6032_dbl__dec__simps_I3_J,axiom,
% 5.17/5.47 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.17/5.47 = one_one_real ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(3)
% 5.17/5.47 thf(fact_6033_dbl__dec__simps_I3_J,axiom,
% 5.17/5.47 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.17/5.47 = one_one_rat ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(3)
% 5.17/5.47 thf(fact_6034_dbl__dec__simps_I3_J,axiom,
% 5.17/5.47 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(3)
% 5.17/5.47 thf(fact_6035_zabs__less__one__iff,axiom,
% 5.17/5.47 ! [Z: int] :
% 5.17/5.47 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.17/5.47 = ( Z = zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % zabs_less_one_iff
% 5.17/5.47 thf(fact_6036_in__set__replicate,axiom,
% 5.17/5.47 ! [X: complex,N: nat,Y4: complex] :
% 5.17/5.47 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y4 ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % in_set_replicate
% 5.17/5.47 thf(fact_6037_in__set__replicate,axiom,
% 5.17/5.47 ! [X: set_nat,N: nat,Y4: set_nat] :
% 5.17/5.47 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y4 ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % in_set_replicate
% 5.17/5.47 thf(fact_6038_in__set__replicate,axiom,
% 5.17/5.47 ! [X: nat,N: nat,Y4: nat] :
% 5.17/5.47 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y4 ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % in_set_replicate
% 5.17/5.47 thf(fact_6039_in__set__replicate,axiom,
% 5.17/5.47 ! [X: int,N: nat,Y4: int] :
% 5.17/5.47 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y4 ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % in_set_replicate
% 5.17/5.47 thf(fact_6040_in__set__replicate,axiom,
% 5.17/5.47 ! [X: real,N: nat,Y4: real] :
% 5.17/5.47 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y4 ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % in_set_replicate
% 5.17/5.47 thf(fact_6041_in__set__replicate,axiom,
% 5.17/5.47 ! [X: vEBT_VEBT,N: nat,Y4: vEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y4 ) ) )
% 5.17/5.47 = ( ( X = Y4 )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % in_set_replicate
% 5.17/5.47 thf(fact_6042_Bex__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: nat,P: nat > $o] :
% 5.17/5.47 ( ( ? [X3: nat] :
% 5.17/5.47 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.17/5.47 & ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Bex_set_replicate
% 5.17/5.47 thf(fact_6043_Bex__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: int,P: int > $o] :
% 5.17/5.47 ( ( ? [X3: int] :
% 5.17/5.47 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.17/5.47 & ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Bex_set_replicate
% 5.17/5.47 thf(fact_6044_Bex__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: real,P: real > $o] :
% 5.17/5.47 ( ( ? [X3: real] :
% 5.17/5.47 ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ A ) ) )
% 5.17/5.47 & ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Bex_set_replicate
% 5.17/5.47 thf(fact_6045_Bex__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.17/5.47 ( ( ? [X3: vEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.17/5.47 & ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 & ( N != zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Bex_set_replicate
% 5.17/5.47 thf(fact_6046_Ball__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: nat,P: nat > $o] :
% 5.17/5.47 ( ( ! [X3: nat] :
% 5.17/5.47 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.17/5.47 => ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Ball_set_replicate
% 5.17/5.47 thf(fact_6047_Ball__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: int,P: int > $o] :
% 5.17/5.47 ( ( ! [X3: int] :
% 5.17/5.47 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.17/5.47 => ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Ball_set_replicate
% 5.17/5.47 thf(fact_6048_Ball__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: real,P: real > $o] :
% 5.17/5.47 ( ( ! [X3: real] :
% 5.17/5.47 ( ( member_real @ X3 @ ( set_real2 @ ( replicate_real @ N @ A ) ) )
% 5.17/5.47 => ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Ball_set_replicate
% 5.17/5.47 thf(fact_6049_Ball__set__replicate,axiom,
% 5.17/5.47 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.17/5.47 ( ( ! [X3: vEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.17/5.47 => ( P @ X3 ) ) )
% 5.17/5.47 = ( ( P @ A )
% 5.17/5.47 | ( N = zero_zero_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Ball_set_replicate
% 5.17/5.47 thf(fact_6050_pred__numeral__simps_I1_J,axiom,
% 5.17/5.47 ( ( pred_numeral @ one )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % pred_numeral_simps(1)
% 5.17/5.47 thf(fact_6051_eq__numeral__Suc,axiom,
% 5.17/5.47 ! [K: num,N: nat] :
% 5.17/5.47 ( ( ( numeral_numeral_nat @ K )
% 5.17/5.47 = ( suc @ N ) )
% 5.17/5.47 = ( ( pred_numeral @ K )
% 5.17/5.47 = N ) ) ).
% 5.17/5.47
% 5.17/5.47 % eq_numeral_Suc
% 5.17/5.47 thf(fact_6052_Suc__eq__numeral,axiom,
% 5.17/5.47 ! [N: nat,K: num] :
% 5.17/5.47 ( ( ( suc @ N )
% 5.17/5.47 = ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( N
% 5.17/5.47 = ( pred_numeral @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Suc_eq_numeral
% 5.17/5.47 thf(fact_6053_sin__coeff__0,axiom,
% 5.17/5.47 ( ( sin_coeff @ zero_zero_nat )
% 5.17/5.47 = zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % sin_coeff_0
% 5.17/5.47 thf(fact_6054_cos__coeff__0,axiom,
% 5.17/5.47 ( ( cos_coeff @ zero_zero_nat )
% 5.17/5.47 = one_one_real ) ).
% 5.17/5.47
% 5.17/5.47 % cos_coeff_0
% 5.17/5.47 thf(fact_6055_pred__numeral__simps_I3_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.17/5.47 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pred_numeral_simps(3)
% 5.17/5.47 thf(fact_6056_less__numeral__Suc,axiom,
% 5.17/5.47 ! [K: num,N: nat] :
% 5.17/5.47 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.17/5.47 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % less_numeral_Suc
% 5.17/5.47 thf(fact_6057_less__Suc__numeral,axiom,
% 5.17/5.47 ! [N: nat,K: num] :
% 5.17/5.47 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % less_Suc_numeral
% 5.17/5.47 thf(fact_6058_le__numeral__Suc,axiom,
% 5.17/5.47 ! [K: num,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.17/5.47 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_numeral_Suc
% 5.17/5.47 thf(fact_6059_le__Suc__numeral,axiom,
% 5.17/5.47 ! [N: nat,K: num] :
% 5.17/5.47 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_Suc_numeral
% 5.17/5.47 thf(fact_6060_diff__numeral__Suc,axiom,
% 5.17/5.47 ! [K: num,N: nat] :
% 5.17/5.47 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.17/5.47 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % diff_numeral_Suc
% 5.17/5.47 thf(fact_6061_diff__Suc__numeral,axiom,
% 5.17/5.47 ! [N: nat,K: num] :
% 5.17/5.47 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % diff_Suc_numeral
% 5.17/5.47 thf(fact_6062_dbl__dec__simps_I2_J,axiom,
% 5.17/5.47 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(2)
% 5.17/5.47 thf(fact_6063_dbl__dec__simps_I2_J,axiom,
% 5.17/5.47 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(2)
% 5.17/5.47 thf(fact_6064_dbl__dec__simps_I2_J,axiom,
% 5.17/5.47 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(2)
% 5.17/5.47 thf(fact_6065_dbl__dec__simps_I2_J,axiom,
% 5.17/5.47 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(2)
% 5.17/5.47 thf(fact_6066_dbl__dec__simps_I2_J,axiom,
% 5.17/5.47 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(2)
% 5.17/5.47 thf(fact_6067_dbl__inc__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.17/5.47 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_inc_simps(1)
% 5.17/5.47 thf(fact_6068_dbl__inc__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.47 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_inc_simps(1)
% 5.17/5.47 thf(fact_6069_dbl__inc__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_inc_simps(1)
% 5.17/5.47 thf(fact_6070_dbl__inc__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_inc_simps(1)
% 5.17/5.47 thf(fact_6071_dbl__inc__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.17/5.47 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_inc_simps(1)
% 5.17/5.47 thf(fact_6072_dbl__dec__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.17/5.47 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(1)
% 5.17/5.47 thf(fact_6073_dbl__dec__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.47 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(1)
% 5.17/5.47 thf(fact_6074_dbl__dec__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(1)
% 5.17/5.47 thf(fact_6075_dbl__dec__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(1)
% 5.17/5.47 thf(fact_6076_dbl__dec__simps_I1_J,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.17/5.47 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_simps(1)
% 5.17/5.47 thf(fact_6077_signed__take__bit__numeral__bit0,axiom,
% 5.17/5.47 ! [L: num,K: num] :
% 5.17/5.47 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.17/5.47 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_numeral_bit0
% 5.17/5.47 thf(fact_6078_signed__take__bit__numeral__minus__bit0,axiom,
% 5.17/5.47 ! [L: num,K: num] :
% 5.17/5.47 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.17/5.47 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_numeral_minus_bit0
% 5.17/5.47 thf(fact_6079_signed__take__bit__numeral__bit1,axiom,
% 5.17/5.47 ! [L: num,K: num] :
% 5.17/5.47 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.17/5.47 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_numeral_bit1
% 5.17/5.47 thf(fact_6080_ComplD,axiom,
% 5.17/5.47 ! [C: complex,A2: set_complex] :
% 5.17/5.47 ( ( member_complex @ C @ ( uminus8566677241136511917omplex @ A2 ) )
% 5.17/5.47 => ~ ( member_complex @ C @ A2 ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplD
% 5.17/5.47 thf(fact_6081_ComplD,axiom,
% 5.17/5.47 ! [C: real,A2: set_real] :
% 5.17/5.47 ( ( member_real @ C @ ( uminus612125837232591019t_real @ A2 ) )
% 5.17/5.47 => ~ ( member_real @ C @ A2 ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplD
% 5.17/5.47 thf(fact_6082_ComplD,axiom,
% 5.17/5.47 ! [C: set_nat,A2: set_set_nat] :
% 5.17/5.47 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 5.17/5.47 => ~ ( member_set_nat @ C @ A2 ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplD
% 5.17/5.47 thf(fact_6083_ComplD,axiom,
% 5.17/5.47 ! [C: nat,A2: set_nat] :
% 5.17/5.47 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.17/5.47 => ~ ( member_nat @ C @ A2 ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplD
% 5.17/5.47 thf(fact_6084_ComplD,axiom,
% 5.17/5.47 ! [C: int,A2: set_int] :
% 5.17/5.47 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.17/5.47 => ~ ( member_int @ C @ A2 ) ) ).
% 5.17/5.47
% 5.17/5.47 % ComplD
% 5.17/5.47 thf(fact_6085_subset__code_I1_J,axiom,
% 5.17/5.47 ! [Xs: list_complex,B4: set_complex] :
% 5.17/5.47 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B4 )
% 5.17/5.47 = ( ! [X3: complex] :
% 5.17/5.47 ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 5.17/5.47 => ( member_complex @ X3 @ B4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % subset_code(1)
% 5.17/5.47 thf(fact_6086_subset__code_I1_J,axiom,
% 5.17/5.47 ! [Xs: list_set_nat,B4: set_set_nat] :
% 5.17/5.47 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B4 )
% 5.17/5.47 = ( ! [X3: set_nat] :
% 5.17/5.47 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 5.17/5.47 => ( member_set_nat @ X3 @ B4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % subset_code(1)
% 5.17/5.47 thf(fact_6087_subset__code_I1_J,axiom,
% 5.17/5.47 ! [Xs: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 5.17/5.47 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B4 )
% 5.17/5.47 = ( ! [X3: vEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.17/5.47 => ( member_VEBT_VEBT @ X3 @ B4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % subset_code(1)
% 5.17/5.47 thf(fact_6088_subset__code_I1_J,axiom,
% 5.17/5.47 ! [Xs: list_nat,B4: set_nat] :
% 5.17/5.47 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B4 )
% 5.17/5.47 = ( ! [X3: nat] :
% 5.17/5.47 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.17/5.47 => ( member_nat @ X3 @ B4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % subset_code(1)
% 5.17/5.47 thf(fact_6089_subset__code_I1_J,axiom,
% 5.17/5.47 ! [Xs: list_real,B4: set_real] :
% 5.17/5.47 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B4 )
% 5.17/5.47 = ( ! [X3: real] :
% 5.17/5.47 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.17/5.47 => ( member_real @ X3 @ B4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % subset_code(1)
% 5.17/5.47 thf(fact_6090_subset__code_I1_J,axiom,
% 5.17/5.47 ! [Xs: list_int,B4: set_int] :
% 5.17/5.47 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B4 )
% 5.17/5.47 = ( ! [X3: int] :
% 5.17/5.47 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.17/5.47 => ( member_int @ X3 @ B4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % subset_code(1)
% 5.17/5.47 thf(fact_6091_zdvd__antisym__abs,axiom,
% 5.17/5.47 ! [A: int,B: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ A @ B )
% 5.17/5.47 => ( ( dvd_dvd_int @ B @ A )
% 5.17/5.47 => ( ( abs_abs_int @ A )
% 5.17/5.47 = ( abs_abs_int @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zdvd_antisym_abs
% 5.17/5.47 thf(fact_6092_abs__zmult__eq__1,axiom,
% 5.17/5.47 ! [M: int,N: int] :
% 5.17/5.47 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.17/5.47 = one_one_int )
% 5.17/5.47 => ( ( abs_abs_int @ M )
% 5.17/5.47 = one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_zmult_eq_1
% 5.17/5.47 thf(fact_6093_abs__div,axiom,
% 5.17/5.47 ! [Y4: int,X: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ Y4 @ X )
% 5.17/5.47 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y4 ) )
% 5.17/5.47 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_div
% 5.17/5.47 thf(fact_6094_numeral__eq__Suc,axiom,
% 5.17/5.47 ( numeral_numeral_nat
% 5.17/5.47 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % numeral_eq_Suc
% 5.17/5.47 thf(fact_6095_sin__coeff__Suc,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( sin_coeff @ ( suc @ N ) )
% 5.17/5.47 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sin_coeff_Suc
% 5.17/5.47 thf(fact_6096_zabs__def,axiom,
% 5.17/5.47 ( abs_abs_int
% 5.17/5.47 = ( ^ [I2: int] : ( if_int @ ( ord_less_int @ I2 @ zero_zero_int ) @ ( uminus_uminus_int @ I2 ) @ I2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zabs_def
% 5.17/5.47 thf(fact_6097_dvd__imp__le__int,axiom,
% 5.17/5.47 ! [I: int,D: int] :
% 5.17/5.47 ( ( I != zero_zero_int )
% 5.17/5.47 => ( ( dvd_dvd_int @ D @ I )
% 5.17/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dvd_imp_le_int
% 5.17/5.47 thf(fact_6098_abs__mod__less,axiom,
% 5.17/5.47 ! [L: int,K: int] :
% 5.17/5.47 ( ( L != zero_zero_int )
% 5.17/5.47 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_mod_less
% 5.17/5.47 thf(fact_6099_cos__coeff__Suc,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( cos_coeff @ ( suc @ N ) )
% 5.17/5.47 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % cos_coeff_Suc
% 5.17/5.47 thf(fact_6100_pred__numeral__def,axiom,
% 5.17/5.47 ( pred_numeral
% 5.17/5.47 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % pred_numeral_def
% 5.17/5.47 thf(fact_6101_zdvd__mult__cancel1,axiom,
% 5.17/5.47 ! [M: int,N: int] :
% 5.17/5.47 ( ( M != zero_zero_int )
% 5.17/5.47 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.17/5.47 = ( ( abs_abs_int @ N )
% 5.17/5.47 = one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zdvd_mult_cancel1
% 5.17/5.47 thf(fact_6102_fact__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_numeral
% 5.17/5.47 thf(fact_6103_fact__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_numeral
% 5.17/5.47 thf(fact_6104_fact__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_numeral
% 5.17/5.47 thf(fact_6105_fact__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_numeral
% 5.17/5.47 thf(fact_6106_fact__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.17/5.47 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % fact_numeral
% 5.17/5.47 thf(fact_6107_even__abs__add__iff,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.17/5.47 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_abs_add_iff
% 5.17/5.47 thf(fact_6108_even__add__abs__iff,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.17/5.47 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_add_abs_iff
% 5.17/5.47 thf(fact_6109_nat__intermed__int__val,axiom,
% 5.17/5.47 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.17/5.47 ( ! [I3: nat] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.17/5.47 & ( ord_less_nat @ I3 @ N ) )
% 5.17/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.17/5.47 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.47 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.17/5.47 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.17/5.47 => ? [I3: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ M @ I3 )
% 5.17/5.47 & ( ord_less_eq_nat @ I3 @ N )
% 5.17/5.47 & ( ( F @ I3 )
% 5.17/5.47 = K ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_intermed_int_val
% 5.17/5.47 thf(fact_6110_dbl__dec__def,axiom,
% 5.17/5.47 ( neg_nu6511756317524482435omplex
% 5.17/5.47 = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_def
% 5.17/5.47 thf(fact_6111_dbl__dec__def,axiom,
% 5.17/5.47 ( neg_nu6075765906172075777c_real
% 5.17/5.47 = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_def
% 5.17/5.47 thf(fact_6112_dbl__dec__def,axiom,
% 5.17/5.47 ( neg_nu3179335615603231917ec_rat
% 5.17/5.47 = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_def
% 5.17/5.47 thf(fact_6113_dbl__dec__def,axiom,
% 5.17/5.47 ( neg_nu3811975205180677377ec_int
% 5.17/5.47 = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dbl_dec_def
% 5.17/5.47 thf(fact_6114_incr__lemma,axiom,
% 5.17/5.47 ! [D: int,Z: int,X: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.47 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % incr_lemma
% 5.17/5.47 thf(fact_6115_decr__lemma,axiom,
% 5.17/5.47 ! [D: int,X: int,Z: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.47 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.17/5.47
% 5.17/5.47 % decr_lemma
% 5.17/5.47 thf(fact_6116_compl__mono,axiom,
% 5.17/5.47 ! [X: set_int,Y4: set_int] :
% 5.17/5.47 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.47 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y4 ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % compl_mono
% 5.17/5.47 thf(fact_6117_compl__le__swap1,axiom,
% 5.17/5.47 ! [Y4: set_int,X: set_int] :
% 5.17/5.47 ( ( ord_less_eq_set_int @ Y4 @ ( uminus1532241313380277803et_int @ X ) )
% 5.17/5.47 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % compl_le_swap1
% 5.17/5.47 thf(fact_6118_compl__le__swap2,axiom,
% 5.17/5.47 ! [Y4: set_int,X: set_int] :
% 5.17/5.47 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y4 ) @ X )
% 5.17/5.47 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % compl_le_swap2
% 5.17/5.47 thf(fact_6119_nat__ivt__aux,axiom,
% 5.17/5.47 ! [N: nat,F: nat > int,K: int] :
% 5.17/5.47 ( ! [I3: nat] :
% 5.17/5.47 ( ( ord_less_nat @ I3 @ N )
% 5.17/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.17/5.47 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.17/5.47 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.17/5.47 => ? [I3: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ I3 @ N )
% 5.17/5.47 & ( ( F @ I3 )
% 5.17/5.47 = K ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_ivt_aux
% 5.17/5.47 thf(fact_6120_complex__mod__minus__le__complex__mod,axiom,
% 5.17/5.47 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % complex_mod_minus_le_complex_mod
% 5.17/5.47 thf(fact_6121_complex__mod__triangle__ineq2,axiom,
% 5.17/5.47 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % complex_mod_triangle_ineq2
% 5.17/5.47 thf(fact_6122_nat0__intermed__int__val,axiom,
% 5.17/5.47 ! [N: nat,F: nat > int,K: int] :
% 5.17/5.47 ( ! [I3: nat] :
% 5.17/5.47 ( ( ord_less_nat @ I3 @ N )
% 5.17/5.47 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.17/5.47 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.17/5.47 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.17/5.47 => ? [I3: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ I3 @ N )
% 5.17/5.47 & ( ( F @ I3 )
% 5.17/5.47 = K ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat0_intermed_int_val
% 5.17/5.47 thf(fact_6123_set__n__deg__not__0,axiom,
% 5.17/5.47 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 5.17/5.47 ( ! [X4: vEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.47 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.17/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.17/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.47 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % set_n_deg_not_0
% 5.17/5.47 thf(fact_6124_arctan__double,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.47 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.17/5.47 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_double
% 5.17/5.47 thf(fact_6125_concat__bit__Suc,axiom,
% 5.17/5.47 ! [N: nat,K: int,L: int] :
% 5.17/5.47 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 5.17/5.47 = ( 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 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_Suc
% 5.17/5.47 thf(fact_6126_modulo__int__unfold,axiom,
% 5.17/5.47 ! [L: int,K: int,N: nat,M: nat] :
% 5.17/5.47 ( ( ( ( ( sgn_sgn_int @ L )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( ( sgn_sgn_int @ K )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( N = zero_zero_nat ) )
% 5.17/5.47 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.17/5.47 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( ( sgn_sgn_int @ K )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( N = zero_zero_nat ) )
% 5.17/5.47 => ( ( ( ( sgn_sgn_int @ K )
% 5.17/5.47 = ( sgn_sgn_int @ L ) )
% 5.17/5.47 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.17/5.47 & ( ( ( sgn_sgn_int @ K )
% 5.17/5.47 != ( sgn_sgn_int @ L ) )
% 5.17/5.47 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.17/5.47 @ ( minus_minus_int
% 5.17/5.47 @ ( semiri1314217659103216013at_int
% 5.17/5.47 @ ( times_times_nat @ N
% 5.17/5.47 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.47 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.17/5.47 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % modulo_int_unfold
% 5.17/5.47 thf(fact_6127_mask__numeral,axiom,
% 5.17/5.47 ! [N: num] :
% 5.17/5.47 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.17/5.47 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_numeral
% 5.17/5.47 thf(fact_6128_mask__numeral,axiom,
% 5.17/5.47 ! [N: num] :
% 5.17/5.47 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.17/5.47 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_numeral
% 5.17/5.47 thf(fact_6129_sgn__sgn,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = ( sgn_sgn_int @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_sgn
% 5.17/5.47 thf(fact_6130_sgn__sgn,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = ( sgn_sgn_real @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_sgn
% 5.17/5.47 thf(fact_6131_sgn__sgn,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 5.17/5.47 = ( sgn_sgn_complex @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_sgn
% 5.17/5.47 thf(fact_6132_sgn__sgn,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = ( sgn_sgn_Code_integer @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_sgn
% 5.17/5.47 thf(fact_6133_sgn__sgn,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = ( sgn_sgn_rat @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_sgn
% 5.17/5.47 thf(fact_6134_mask__nat__positive__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.17/5.47 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_nat_positive_iff
% 5.17/5.47 thf(fact_6135_sgn__zero,axiom,
% 5.17/5.47 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.17/5.47 = zero_zero_complex ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_zero
% 5.17/5.47 thf(fact_6136_sgn__zero,axiom,
% 5.17/5.47 ( ( sgn_sgn_real @ zero_zero_real )
% 5.17/5.47 = zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_zero
% 5.17/5.47 thf(fact_6137_sgn__0,axiom,
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 5.17/5.47 = zero_z3403309356797280102nteger ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0
% 5.17/5.47 thf(fact_6138_sgn__0,axiom,
% 5.17/5.47 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.17/5.47 = zero_zero_complex ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0
% 5.17/5.47 thf(fact_6139_sgn__0,axiom,
% 5.17/5.47 ( ( sgn_sgn_real @ zero_zero_real )
% 5.17/5.47 = zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0
% 5.17/5.47 thf(fact_6140_sgn__0,axiom,
% 5.17/5.47 ( ( sgn_sgn_rat @ zero_zero_rat )
% 5.17/5.47 = zero_zero_rat ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0
% 5.17/5.47 thf(fact_6141_sgn__0,axiom,
% 5.17/5.47 ( ( sgn_sgn_int @ zero_zero_int )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0
% 5.17/5.47 thf(fact_6142_sgn__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_int @ one_one_int )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1
% 5.17/5.47 thf(fact_6143_sgn__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_real @ one_one_real )
% 5.17/5.47 = one_one_real ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1
% 5.17/5.47 thf(fact_6144_sgn__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_complex @ one_one_complex )
% 5.17/5.47 = one_one_complex ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1
% 5.17/5.47 thf(fact_6145_sgn__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 5.17/5.47 = one_one_Code_integer ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1
% 5.17/5.47 thf(fact_6146_sgn__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_rat @ one_one_rat )
% 5.17/5.47 = one_one_rat ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1
% 5.17/5.47 thf(fact_6147_sgn__divide,axiom,
% 5.17/5.47 ! [A: complex,B: complex] :
% 5.17/5.47 ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_divide
% 5.17/5.47 thf(fact_6148_sgn__divide,axiom,
% 5.17/5.47 ! [A: real,B: real] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.47 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_divide
% 5.17/5.47 thf(fact_6149_sgn__divide,axiom,
% 5.17/5.47 ! [A: rat,B: rat] :
% 5.17/5.47 ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.47 = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_divide
% 5.17/5.47 thf(fact_6150_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.47 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.sgn_minus
% 5.17/5.47 thf(fact_6151_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 5.17/5.47 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.sgn_minus
% 5.17/5.47 thf(fact_6152_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.sgn_minus
% 5.17/5.47 thf(fact_6153_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.sgn_minus
% 5.17/5.47 thf(fact_6154_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.47 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.sgn_minus
% 5.17/5.47 thf(fact_6155_arctan__eq__zero__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( arctan @ X )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( X = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_eq_zero_iff
% 5.17/5.47 thf(fact_6156_arctan__zero__zero,axiom,
% 5.17/5.47 ( ( arctan @ zero_zero_real )
% 5.17/5.47 = zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_zero_zero
% 5.17/5.47 thf(fact_6157_concat__bit__0,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.17/5.47 = L ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_0
% 5.17/5.47 thf(fact_6158_sgn__less,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.17/5.47 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_less
% 5.17/5.47 thf(fact_6159_sgn__less,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 5.17/5.47 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_less
% 5.17/5.47 thf(fact_6160_sgn__less,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 5.17/5.47 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_less
% 5.17/5.47 thf(fact_6161_sgn__less,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 5.17/5.47 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_less
% 5.17/5.47 thf(fact_6162_sgn__greater,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_greater
% 5.17/5.47 thf(fact_6163_sgn__greater,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_greater
% 5.17/5.47 thf(fact_6164_sgn__greater,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_greater
% 5.17/5.47 thf(fact_6165_sgn__greater,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_greater
% 5.17/5.47 thf(fact_6166_divide__sgn,axiom,
% 5.17/5.47 ! [A: real,B: real] :
% 5.17/5.47 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 5.17/5.47 = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_sgn
% 5.17/5.47 thf(fact_6167_divide__sgn,axiom,
% 5.17/5.47 ! [A: rat,B: rat] :
% 5.17/5.47 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 5.17/5.47 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_sgn
% 5.17/5.47 thf(fact_6168_mask__0,axiom,
% 5.17/5.47 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % mask_0
% 5.17/5.47 thf(fact_6169_mask__0,axiom,
% 5.17/5.47 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % mask_0
% 5.17/5.47 thf(fact_6170_mask__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.17/5.47 = zero_zero_nat )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_eq_0_iff
% 5.17/5.47 thf(fact_6171_mask__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_eq_0_iff
% 5.17/5.47 thf(fact_6172_arctan__less__zero__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 5.17/5.47 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_less_zero_iff
% 5.17/5.47 thf(fact_6173_zero__less__arctan__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 5.17/5.47 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % zero_less_arctan_iff
% 5.17/5.47 thf(fact_6174_zero__le__arctan__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.17/5.47 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % zero_le_arctan_iff
% 5.17/5.47 thf(fact_6175_arctan__le__zero__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.17/5.47 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_le_zero_iff
% 5.17/5.47 thf(fact_6176_concat__bit__nonnegative__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int,L: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 5.17/5.47 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_nonnegative_iff
% 5.17/5.47 thf(fact_6177_concat__bit__negative__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int,L: int] :
% 5.17/5.47 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 5.17/5.47 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_negative_iff
% 5.17/5.47 thf(fact_6178_sgn__pos,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.17/5.47 => ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_pos
% 5.17/5.47 thf(fact_6179_sgn__pos,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.47 => ( ( sgn_sgn_real @ A )
% 5.17/5.47 = one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_pos
% 5.17/5.47 thf(fact_6180_sgn__pos,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.47 => ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_pos
% 5.17/5.47 thf(fact_6181_sgn__pos,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.47 => ( ( sgn_sgn_int @ A )
% 5.17/5.47 = one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_pos
% 5.17/5.47 thf(fact_6182_abs__sgn__eq__1,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.47 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq_1
% 5.17/5.47 thf(fact_6183_abs__sgn__eq__1,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( A != zero_zero_real )
% 5.17/5.47 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq_1
% 5.17/5.47 thf(fact_6184_abs__sgn__eq__1,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( A != zero_zero_rat )
% 5.17/5.47 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq_1
% 5.17/5.47 thf(fact_6185_abs__sgn__eq__1,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( A != zero_zero_int )
% 5.17/5.47 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq_1
% 5.17/5.47 thf(fact_6186_sgn__mult__self__eq,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_self_eq
% 5.17/5.47 thf(fact_6187_sgn__mult__self__eq,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_self_eq
% 5.17/5.47 thf(fact_6188_sgn__mult__self__eq,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_self_eq
% 5.17/5.47 thf(fact_6189_sgn__mult__self__eq,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_self_eq
% 5.17/5.47 thf(fact_6190_mask__Suc__0,axiom,
% 5.17/5.47 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.17/5.47 = one_one_nat ) ).
% 5.17/5.47
% 5.17/5.47 % mask_Suc_0
% 5.17/5.47 thf(fact_6191_mask__Suc__0,axiom,
% 5.17/5.47 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % mask_Suc_0
% 5.17/5.47 thf(fact_6192_sgn__abs,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 5.17/5.47 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_abs
% 5.17/5.47 thf(fact_6193_sgn__abs,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_abs
% 5.17/5.47 thf(fact_6194_sgn__abs,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_abs
% 5.17/5.47 thf(fact_6195_sgn__abs,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_abs
% 5.17/5.47 thf(fact_6196_sgn__abs,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_abs
% 5.17/5.47 thf(fact_6197_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 5.17/5.47 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.abs_sgn
% 5.17/5.47 thf(fact_6198_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 5.17/5.47 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.abs_sgn
% 5.17/5.47 thf(fact_6199_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 5.17/5.47 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.abs_sgn
% 5.17/5.47 thf(fact_6200_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 5.17/5.47 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.abs_sgn
% 5.17/5.47 thf(fact_6201_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.17/5.47 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % idom_abs_sgn_class.abs_sgn
% 5.17/5.47 thf(fact_6202_sgn__mult__dvd__iff,axiom,
% 5.17/5.47 ! [R2: int,L: int,K: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 5.17/5.47 = ( ( dvd_dvd_int @ L @ K )
% 5.17/5.47 & ( ( R2 = zero_zero_int )
% 5.17/5.47 => ( K = zero_zero_int ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_dvd_iff
% 5.17/5.47 thf(fact_6203_mult__sgn__dvd__iff,axiom,
% 5.17/5.47 ! [L: int,R2: int,K: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.17/5.47 = ( ( dvd_dvd_int @ L @ K )
% 5.17/5.47 & ( ( R2 = zero_zero_int )
% 5.17/5.47 => ( K = zero_zero_int ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mult_sgn_dvd_iff
% 5.17/5.47 thf(fact_6204_dvd__sgn__mult__iff,axiom,
% 5.17/5.47 ! [L: int,R2: int,K: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.17/5.47 = ( ( dvd_dvd_int @ L @ K )
% 5.17/5.47 | ( R2 = zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dvd_sgn_mult_iff
% 5.17/5.47 thf(fact_6205_dvd__mult__sgn__iff,axiom,
% 5.17/5.47 ! [L: int,K: int,R2: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.17/5.47 = ( ( dvd_dvd_int @ L @ K )
% 5.17/5.47 | ( R2 = zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % dvd_mult_sgn_iff
% 5.17/5.47 thf(fact_6206_sgn__neg,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.47 => ( ( sgn_sgn_real @ A )
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_neg
% 5.17/5.47 thf(fact_6207_sgn__neg,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ord_less_int @ A @ zero_zero_int )
% 5.17/5.47 => ( ( sgn_sgn_int @ A )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_neg
% 5.17/5.47 thf(fact_6208_sgn__neg,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.17/5.47 => ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_neg
% 5.17/5.47 thf(fact_6209_sgn__neg,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.47 => ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_neg
% 5.17/5.47 thf(fact_6210_sgn__of__nat,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.47 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_of_nat
% 5.17/5.47 thf(fact_6211_sgn__of__nat,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.47 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_of_nat
% 5.17/5.47 thf(fact_6212_sgn__of__nat,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.47 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_of_nat
% 5.17/5.47 thf(fact_6213_sgn__of__nat,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.17/5.47 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_of_nat
% 5.17/5.47 thf(fact_6214_of__nat__mask__eq,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.17/5.47 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % of_nat_mask_eq
% 5.17/5.47 thf(fact_6215_of__nat__mask__eq,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.17/5.47 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % of_nat_mask_eq
% 5.17/5.47 thf(fact_6216_size__neq__size__imp__neq,axiom,
% 5.17/5.47 ! [X: list_real,Y4: list_real] :
% 5.17/5.47 ( ( ( size_size_list_real @ X )
% 5.17/5.47 != ( size_size_list_real @ Y4 ) )
% 5.17/5.47 => ( X != Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % size_neq_size_imp_neq
% 5.17/5.47 thf(fact_6217_size__neq__size__imp__neq,axiom,
% 5.17/5.47 ! [X: list_o,Y4: list_o] :
% 5.17/5.47 ( ( ( size_size_list_o @ X )
% 5.17/5.47 != ( size_size_list_o @ Y4 ) )
% 5.17/5.47 => ( X != Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % size_neq_size_imp_neq
% 5.17/5.47 thf(fact_6218_size__neq__size__imp__neq,axiom,
% 5.17/5.47 ! [X: list_nat,Y4: list_nat] :
% 5.17/5.47 ( ( ( size_size_list_nat @ X )
% 5.17/5.47 != ( size_size_list_nat @ Y4 ) )
% 5.17/5.47 => ( X != Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % size_neq_size_imp_neq
% 5.17/5.47 thf(fact_6219_size__neq__size__imp__neq,axiom,
% 5.17/5.47 ! [X: list_int,Y4: list_int] :
% 5.17/5.47 ( ( ( size_size_list_int @ X )
% 5.17/5.47 != ( size_size_list_int @ Y4 ) )
% 5.17/5.47 => ( X != Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % size_neq_size_imp_neq
% 5.17/5.47 thf(fact_6220_size__neq__size__imp__neq,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( ( size_size_num @ X )
% 5.17/5.47 != ( size_size_num @ Y4 ) )
% 5.17/5.47 => ( X != Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % size_neq_size_imp_neq
% 5.17/5.47 thf(fact_6221_sgn__zero__iff,axiom,
% 5.17/5.47 ! [X: complex] :
% 5.17/5.47 ( ( ( sgn_sgn_complex @ X )
% 5.17/5.47 = zero_zero_complex )
% 5.17/5.47 = ( X = zero_zero_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_zero_iff
% 5.17/5.47 thf(fact_6222_sgn__zero__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ X )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( X = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_zero_iff
% 5.17/5.47 thf(fact_6223_sgn__0__0,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = zero_z3403309356797280102nteger )
% 5.17/5.47 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0_0
% 5.17/5.47 thf(fact_6224_sgn__0__0,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ A )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( A = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0_0
% 5.17/5.47 thf(fact_6225_sgn__0__0,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = zero_zero_rat )
% 5.17/5.47 = ( A = zero_zero_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0_0
% 5.17/5.47 thf(fact_6226_sgn__0__0,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ A )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 = ( A = zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_0_0
% 5.17/5.47 thf(fact_6227_sgn__eq__0__iff,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = zero_z3403309356797280102nteger )
% 5.17/5.47 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_eq_0_iff
% 5.17/5.47 thf(fact_6228_sgn__eq__0__iff,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( ( sgn_sgn_complex @ A )
% 5.17/5.47 = zero_zero_complex )
% 5.17/5.47 = ( A = zero_zero_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_eq_0_iff
% 5.17/5.47 thf(fact_6229_sgn__eq__0__iff,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ A )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( A = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_eq_0_iff
% 5.17/5.47 thf(fact_6230_sgn__eq__0__iff,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = zero_zero_rat )
% 5.17/5.47 = ( A = zero_zero_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_eq_0_iff
% 5.17/5.47 thf(fact_6231_sgn__eq__0__iff,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ A )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 = ( A = zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_eq_0_iff
% 5.17/5.47 thf(fact_6232_Real__Vector__Spaces_Osgn__mult,axiom,
% 5.17/5.47 ! [X: complex,Y4: complex] :
% 5.17/5.47 ( ( sgn_sgn_complex @ ( times_times_complex @ X @ Y4 ) )
% 5.17/5.47 = ( times_times_complex @ ( sgn_sgn_complex @ X ) @ ( sgn_sgn_complex @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Real_Vector_Spaces.sgn_mult
% 5.17/5.47 thf(fact_6233_Real__Vector__Spaces_Osgn__mult,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.47 = ( times_times_real @ ( sgn_sgn_real @ X ) @ ( sgn_sgn_real @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % Real_Vector_Spaces.sgn_mult
% 5.17/5.47 thf(fact_6234_sgn__mult,axiom,
% 5.17/5.47 ! [A: complex,B: complex] :
% 5.17/5.47 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 5.17/5.47 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult
% 5.17/5.47 thf(fact_6235_sgn__mult,axiom,
% 5.17/5.47 ! [A: code_integer,B: code_integer] :
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.17/5.47 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult
% 5.17/5.47 thf(fact_6236_sgn__mult,axiom,
% 5.17/5.47 ! [A: real,B: real] :
% 5.17/5.47 ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 5.17/5.47 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult
% 5.17/5.47 thf(fact_6237_sgn__mult,axiom,
% 5.17/5.47 ! [A: rat,B: rat] :
% 5.17/5.47 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.47 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult
% 5.17/5.47 thf(fact_6238_sgn__mult,axiom,
% 5.17/5.47 ! [A: int,B: int] :
% 5.17/5.47 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 5.17/5.47 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult
% 5.17/5.47 thf(fact_6239_same__sgn__sgn__add,axiom,
% 5.17/5.47 ! [B: code_integer,A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ B )
% 5.17/5.47 = ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.47 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_sgn_add
% 5.17/5.47 thf(fact_6240_same__sgn__sgn__add,axiom,
% 5.17/5.47 ! [B: real,A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ B )
% 5.17/5.47 = ( sgn_sgn_real @ A ) )
% 5.17/5.47 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 5.17/5.47 = ( sgn_sgn_real @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_sgn_add
% 5.17/5.47 thf(fact_6241_same__sgn__sgn__add,axiom,
% 5.17/5.47 ! [B: rat,A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ B )
% 5.17/5.47 = ( sgn_sgn_rat @ A ) )
% 5.17/5.47 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.47 = ( sgn_sgn_rat @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_sgn_add
% 5.17/5.47 thf(fact_6242_same__sgn__sgn__add,axiom,
% 5.17/5.47 ! [B: int,A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ B )
% 5.17/5.47 = ( sgn_sgn_int @ A ) )
% 5.17/5.47 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 5.17/5.47 = ( sgn_sgn_int @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_sgn_add
% 5.17/5.47 thf(fact_6243_div__eq__sgn__abs,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ K )
% 5.17/5.47 = ( sgn_sgn_int @ L ) )
% 5.17/5.47 => ( ( divide_divide_int @ K @ L )
% 5.17/5.47 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % div_eq_sgn_abs
% 5.17/5.47 thf(fact_6244_arctan__monotone_H,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.47 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_monotone'
% 5.17/5.47 thf(fact_6245_arctan__le__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_le_iff
% 5.17/5.47 thf(fact_6246_less__eq__mask,axiom,
% 5.17/5.47 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % less_eq_mask
% 5.17/5.47 thf(fact_6247_concat__bit__assoc,axiom,
% 5.17/5.47 ! [N: nat,K: int,M: nat,L: int,R2: int] :
% 5.17/5.47 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 5.17/5.47 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R2 ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_assoc
% 5.17/5.47 thf(fact_6248_sgn__not__eq__imp,axiom,
% 5.17/5.47 ! [B: real,A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ B )
% 5.17/5.47 != ( sgn_sgn_real @ A ) )
% 5.17/5.47 => ( ( ( sgn_sgn_real @ A )
% 5.17/5.47 != zero_zero_real )
% 5.17/5.47 => ( ( ( sgn_sgn_real @ B )
% 5.17/5.47 != zero_zero_real )
% 5.17/5.47 => ( ( sgn_sgn_real @ A )
% 5.17/5.47 = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_not_eq_imp
% 5.17/5.47 thf(fact_6249_sgn__not__eq__imp,axiom,
% 5.17/5.47 ! [B: int,A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ B )
% 5.17/5.47 != ( sgn_sgn_int @ A ) )
% 5.17/5.47 => ( ( ( sgn_sgn_int @ A )
% 5.17/5.47 != zero_zero_int )
% 5.17/5.47 => ( ( ( sgn_sgn_int @ B )
% 5.17/5.47 != zero_zero_int )
% 5.17/5.47 => ( ( sgn_sgn_int @ A )
% 5.17/5.47 = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_not_eq_imp
% 5.17/5.47 thf(fact_6250_sgn__not__eq__imp,axiom,
% 5.17/5.47 ! [B: code_integer,A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ B )
% 5.17/5.47 != ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 => ( ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 != zero_z3403309356797280102nteger )
% 5.17/5.47 => ( ( ( sgn_sgn_Code_integer @ B )
% 5.17/5.47 != zero_z3403309356797280102nteger )
% 5.17/5.47 => ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_not_eq_imp
% 5.17/5.47 thf(fact_6251_sgn__not__eq__imp,axiom,
% 5.17/5.47 ! [B: rat,A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ B )
% 5.17/5.47 != ( sgn_sgn_rat @ A ) )
% 5.17/5.47 => ( ( ( sgn_sgn_rat @ A )
% 5.17/5.47 != zero_zero_rat )
% 5.17/5.47 => ( ( ( sgn_sgn_rat @ B )
% 5.17/5.47 != zero_zero_rat )
% 5.17/5.47 => ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_not_eq_imp
% 5.17/5.47 thf(fact_6252_sgn__minus__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_minus_1
% 5.17/5.47 thf(fact_6253_sgn__minus__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_minus_1
% 5.17/5.47 thf(fact_6254_sgn__minus__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.47 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_minus_1
% 5.17/5.47 thf(fact_6255_sgn__minus__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_minus_1
% 5.17/5.47 thf(fact_6256_sgn__minus__1,axiom,
% 5.17/5.47 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_minus_1
% 5.17/5.47 thf(fact_6257_linordered__idom__class_Oabs__sgn,axiom,
% 5.17/5.47 ( abs_abs_Code_integer
% 5.17/5.47 = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % linordered_idom_class.abs_sgn
% 5.17/5.47 thf(fact_6258_linordered__idom__class_Oabs__sgn,axiom,
% 5.17/5.47 ( abs_abs_real
% 5.17/5.47 = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % linordered_idom_class.abs_sgn
% 5.17/5.47 thf(fact_6259_linordered__idom__class_Oabs__sgn,axiom,
% 5.17/5.47 ( abs_abs_rat
% 5.17/5.47 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % linordered_idom_class.abs_sgn
% 5.17/5.47 thf(fact_6260_linordered__idom__class_Oabs__sgn,axiom,
% 5.17/5.47 ( abs_abs_int
% 5.17/5.47 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % linordered_idom_class.abs_sgn
% 5.17/5.47 thf(fact_6261_abs__mult__sgn,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % abs_mult_sgn
% 5.17/5.47 thf(fact_6262_abs__mult__sgn,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % abs_mult_sgn
% 5.17/5.47 thf(fact_6263_abs__mult__sgn,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % abs_mult_sgn
% 5.17/5.47 thf(fact_6264_abs__mult__sgn,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % abs_mult_sgn
% 5.17/5.47 thf(fact_6265_abs__mult__sgn,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % abs_mult_sgn
% 5.17/5.47 thf(fact_6266_sgn__mult__abs,axiom,
% 5.17/5.47 ! [A: complex] :
% 5.17/5.47 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_abs
% 5.17/5.47 thf(fact_6267_sgn__mult__abs,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_abs
% 5.17/5.47 thf(fact_6268_sgn__mult__abs,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_abs
% 5.17/5.47 thf(fact_6269_sgn__mult__abs,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_abs
% 5.17/5.47 thf(fact_6270_sgn__mult__abs,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mult_abs
% 5.17/5.47 thf(fact_6271_mult__sgn__abs,axiom,
% 5.17/5.47 ! [X: code_integer] :
% 5.17/5.47 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % mult_sgn_abs
% 5.17/5.47 thf(fact_6272_mult__sgn__abs,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( times_times_real @ ( sgn_sgn_real @ X ) @ ( abs_abs_real @ X ) )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % mult_sgn_abs
% 5.17/5.47 thf(fact_6273_mult__sgn__abs,axiom,
% 5.17/5.47 ! [X: rat] :
% 5.17/5.47 ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % mult_sgn_abs
% 5.17/5.47 thf(fact_6274_mult__sgn__abs,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % mult_sgn_abs
% 5.17/5.47 thf(fact_6275_int__sgnE,axiom,
% 5.17/5.47 ! [K: int] :
% 5.17/5.47 ~ ! [N2: nat,L2: int] :
% 5.17/5.47 ( K
% 5.17/5.47 != ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % int_sgnE
% 5.17/5.47 thf(fact_6276_same__sgn__abs__add,axiom,
% 5.17/5.47 ! [B: code_integer,A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ B )
% 5.17/5.47 = ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.17/5.47 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_abs_add
% 5.17/5.47 thf(fact_6277_same__sgn__abs__add,axiom,
% 5.17/5.47 ! [B: real,A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ B )
% 5.17/5.47 = ( sgn_sgn_real @ A ) )
% 5.17/5.47 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 5.17/5.47 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_abs_add
% 5.17/5.47 thf(fact_6278_same__sgn__abs__add,axiom,
% 5.17/5.47 ! [B: rat,A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ B )
% 5.17/5.47 = ( sgn_sgn_rat @ A ) )
% 5.17/5.47 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 5.17/5.47 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_abs_add
% 5.17/5.47 thf(fact_6279_same__sgn__abs__add,axiom,
% 5.17/5.47 ! [B: int,A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ B )
% 5.17/5.47 = ( sgn_sgn_int @ A ) )
% 5.17/5.47 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 5.17/5.47 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % same_sgn_abs_add
% 5.17/5.47 thf(fact_6280_mask__nonnegative__int,axiom,
% 5.17/5.47 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_nonnegative_int
% 5.17/5.47 thf(fact_6281_not__mask__negative__int,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % not_mask_negative_int
% 5.17/5.47 thf(fact_6282_sgn__1__pos,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = one_one_Code_integer )
% 5.17/5.47 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_pos
% 5.17/5.47 thf(fact_6283_sgn__1__pos,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ A )
% 5.17/5.47 = one_one_real )
% 5.17/5.47 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_pos
% 5.17/5.47 thf(fact_6284_sgn__1__pos,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = one_one_rat )
% 5.17/5.47 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_pos
% 5.17/5.47 thf(fact_6285_sgn__1__pos,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ A )
% 5.17/5.47 = one_one_int )
% 5.17/5.47 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_pos
% 5.17/5.47 thf(fact_6286_abs__sgn__eq,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ( A = zero_z3403309356797280102nteger )
% 5.17/5.47 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = zero_z3403309356797280102nteger ) )
% 5.17/5.47 & ( ( A != zero_z3403309356797280102nteger )
% 5.17/5.47 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.17/5.47 = one_one_Code_integer ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq
% 5.17/5.47 thf(fact_6287_abs__sgn__eq,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ( A = zero_zero_real )
% 5.17/5.47 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = zero_zero_real ) )
% 5.17/5.47 & ( ( A != zero_zero_real )
% 5.17/5.47 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.47 = one_one_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq
% 5.17/5.47 thf(fact_6288_abs__sgn__eq,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ( A = zero_zero_rat )
% 5.17/5.47 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = zero_zero_rat ) )
% 5.17/5.47 & ( ( A != zero_zero_rat )
% 5.17/5.47 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.47 = one_one_rat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq
% 5.17/5.47 thf(fact_6289_abs__sgn__eq,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ( A = zero_zero_int )
% 5.17/5.47 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = zero_zero_int ) )
% 5.17/5.47 & ( ( A != zero_zero_int )
% 5.17/5.47 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.17/5.47 = one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % abs_sgn_eq
% 5.17/5.47 thf(fact_6290_div__sgn__abs__cancel,axiom,
% 5.17/5.47 ! [V: int,K: int,L: int] :
% 5.17/5.47 ( ( V != zero_zero_int )
% 5.17/5.47 => ( ( 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 ) ) )
% 5.17/5.47 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % div_sgn_abs_cancel
% 5.17/5.47 thf(fact_6291_div__dvd__sgn__abs,axiom,
% 5.17/5.47 ! [L: int,K: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ L @ K )
% 5.17/5.47 => ( ( divide_divide_int @ K @ L )
% 5.17/5.47 = ( 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 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % div_dvd_sgn_abs
% 5.17/5.47 thf(fact_6292_sgn__mod,axiom,
% 5.17/5.47 ! [L: int,K: int] :
% 5.17/5.47 ( ( L != zero_zero_int )
% 5.17/5.47 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.17/5.47 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.17/5.47 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_mod
% 5.17/5.47 thf(fact_6293_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: complex,Xs: list_complex] :
% 5.17/5.47 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6294_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: set_nat,Xs: list_set_nat] :
% 5.17/5.47 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6295_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.17/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6296_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: real,Xs: list_real] :
% 5.17/5.47 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6297_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: $o,Xs: list_o] :
% 5.17/5.47 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6298_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: nat,Xs: list_nat] :
% 5.17/5.47 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6299_length__pos__if__in__set,axiom,
% 5.17/5.47 ! [X: int,Xs: list_int] :
% 5.17/5.47 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.17/5.47 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % length_pos_if_in_set
% 5.17/5.47 thf(fact_6300_less__mask,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.47 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % less_mask
% 5.17/5.47 thf(fact_6301_sgn__if,axiom,
% 5.17/5.47 ( sgn_sgn_real
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_if
% 5.17/5.47 thf(fact_6302_sgn__if,axiom,
% 5.17/5.47 ( sgn_sgn_int
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_if
% 5.17/5.47 thf(fact_6303_sgn__if,axiom,
% 5.17/5.47 ( sgn_sgn_Code_integer
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_if
% 5.17/5.47 thf(fact_6304_sgn__if,axiom,
% 5.17/5.47 ( sgn_sgn_rat
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_if
% 5.17/5.47 thf(fact_6305_sgn__1__neg,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( ( sgn_sgn_real @ A )
% 5.17/5.47 = ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.47 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_neg
% 5.17/5.47 thf(fact_6306_sgn__1__neg,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( ( sgn_sgn_int @ A )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_neg
% 5.17/5.47 thf(fact_6307_sgn__1__neg,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( ( sgn_sgn_Code_integer @ A )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_neg
% 5.17/5.47 thf(fact_6308_sgn__1__neg,axiom,
% 5.17/5.47 ! [A: rat] :
% 5.17/5.47 ( ( ( sgn_sgn_rat @ A )
% 5.17/5.47 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.47 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_1_neg
% 5.17/5.47 thf(fact_6309_zsgn__def,axiom,
% 5.17/5.47 ( sgn_sgn_int
% 5.17/5.47 = ( ^ [I2: int] : ( if_int @ ( I2 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I2 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zsgn_def
% 5.17/5.47 thf(fact_6310_norm__sgn,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( X = zero_zero_real )
% 5.17/5.47 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 5.17/5.47 = zero_zero_real ) )
% 5.17/5.47 & ( ( X != zero_zero_real )
% 5.17/5.47 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X ) )
% 5.17/5.47 = one_one_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % norm_sgn
% 5.17/5.47 thf(fact_6311_norm__sgn,axiom,
% 5.17/5.47 ! [X: complex] :
% 5.17/5.47 ( ( ( X = zero_zero_complex )
% 5.17/5.47 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 5.17/5.47 = zero_zero_real ) )
% 5.17/5.47 & ( ( X != zero_zero_complex )
% 5.17/5.47 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X ) )
% 5.17/5.47 = one_one_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % norm_sgn
% 5.17/5.47 thf(fact_6312_div__noneq__sgn__abs,axiom,
% 5.17/5.47 ! [L: int,K: int] :
% 5.17/5.47 ( ( L != zero_zero_int )
% 5.17/5.47 => ( ( ( sgn_sgn_int @ K )
% 5.17/5.47 != ( sgn_sgn_int @ L ) )
% 5.17/5.47 => ( ( divide_divide_int @ K @ L )
% 5.17/5.47 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.17/5.47 @ ( zero_n2684676970156552555ol_int
% 5.17/5.47 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % div_noneq_sgn_abs
% 5.17/5.47 thf(fact_6313_Suc__mask__eq__exp,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.17/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % Suc_mask_eq_exp
% 5.17/5.47 thf(fact_6314_mask__nat__less__exp,axiom,
% 5.17/5.47 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_nat_less_exp
% 5.17/5.47 thf(fact_6315_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % semiring_bit_operations_class.even_mask_iff
% 5.17/5.47 thf(fact_6316_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % semiring_bit_operations_class.even_mask_iff
% 5.17/5.47 thf(fact_6317_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % semiring_bit_operations_class.even_mask_iff
% 5.17/5.47 thf(fact_6318_mask__nat__def,axiom,
% 5.17/5.47 ( bit_se2002935070580805687sk_nat
% 5.17/5.47 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_nat_def
% 5.17/5.47 thf(fact_6319_mask__half__int,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_half_int
% 5.17/5.47 thf(fact_6320_mask__int__def,axiom,
% 5.17/5.47 ( bit_se2000444600071755411sk_int
% 5.17/5.47 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_int_def
% 5.17/5.47 thf(fact_6321_mask__eq__exp__minus__1,axiom,
% 5.17/5.47 ( bit_se2002935070580805687sk_nat
% 5.17/5.47 = ( ^ [N4: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_eq_exp_minus_1
% 5.17/5.47 thf(fact_6322_mask__eq__exp__minus__1,axiom,
% 5.17/5.47 ( bit_se2000444600071755411sk_int
% 5.17/5.47 = ( ^ [N4: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mask_eq_exp_minus_1
% 5.17/5.47 thf(fact_6323_arctan__add,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.47 => ( ( ord_less_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.47 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y4 ) )
% 5.17/5.47 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_add
% 5.17/5.47 thf(fact_6324_divide__int__unfold,axiom,
% 5.17/5.47 ! [L: int,K: int,N: nat,M: nat] :
% 5.17/5.47 ( ( ( ( ( sgn_sgn_int @ L )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( ( sgn_sgn_int @ K )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( N = zero_zero_nat ) )
% 5.17/5.47 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = zero_zero_int ) )
% 5.17/5.47 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( ( sgn_sgn_int @ K )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 | ( N = zero_zero_nat ) )
% 5.17/5.47 => ( ( ( ( sgn_sgn_int @ K )
% 5.17/5.47 = ( sgn_sgn_int @ L ) )
% 5.17/5.47 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.17/5.47 & ( ( ( sgn_sgn_int @ K )
% 5.17/5.47 != ( sgn_sgn_int @ L ) )
% 5.17/5.47 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = ( uminus_uminus_int
% 5.17/5.47 @ ( semiri1314217659103216013at_int
% 5.17/5.47 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.17/5.47 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.47 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_int_unfold
% 5.17/5.47 thf(fact_6325_divide__int__def,axiom,
% 5.17/5.47 ( divide_divide_int
% 5.17/5.47 = ( ^ [K3: int,L3: int] :
% 5.17/5.47 ( if_int @ ( L3 = zero_zero_int ) @ zero_zero_int
% 5.17/5.47 @ ( if_int
% 5.17/5.47 @ ( ( sgn_sgn_int @ K3 )
% 5.17/5.47 = ( sgn_sgn_int @ L3 ) )
% 5.17/5.47 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) )
% 5.17/5.47 @ ( uminus_uminus_int
% 5.17/5.47 @ ( semiri1314217659103216013at_int
% 5.17/5.47 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) )
% 5.17/5.47 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.47 @ ~ ( dvd_dvd_int @ L3 @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % divide_int_def
% 5.17/5.47 thf(fact_6326_take__bit__rec,axiom,
% 5.17/5.47 ( bit_se1745604003318907178nteger
% 5.17/5.47 = ( ^ [N4: nat,A3: 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 @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_rec
% 5.17/5.47 thf(fact_6327_take__bit__rec,axiom,
% 5.17/5.47 ( bit_se2923211474154528505it_int
% 5.17/5.47 = ( ^ [N4: nat,A3: 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 @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_rec
% 5.17/5.47 thf(fact_6328_take__bit__rec,axiom,
% 5.17/5.47 ( bit_se2925701944663578781it_nat
% 5.17/5.47 = ( ^ [N4: nat,A3: 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 @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_rec
% 5.17/5.47 thf(fact_6329_tanh__real__altdef,axiom,
% 5.17/5.47 ( tanh_real
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % tanh_real_altdef
% 5.17/5.47 thf(fact_6330_power__numeral,axiom,
% 5.17/5.47 ! [K: num,L: num] :
% 5.17/5.47 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.17/5.47 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_numeral
% 5.17/5.47 thf(fact_6331_power__numeral,axiom,
% 5.17/5.47 ! [K: num,L: num] :
% 5.17/5.47 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.17/5.47 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_numeral
% 5.17/5.47 thf(fact_6332_power__numeral,axiom,
% 5.17/5.47 ! [K: num,L: num] :
% 5.17/5.47 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.17/5.47 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_numeral
% 5.17/5.47 thf(fact_6333_power__numeral,axiom,
% 5.17/5.47 ! [K: num,L: num] :
% 5.17/5.47 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.17/5.47 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_numeral
% 5.17/5.47 thf(fact_6334_power__numeral,axiom,
% 5.17/5.47 ! [K: num,L: num] :
% 5.17/5.47 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.17/5.47 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % power_numeral
% 5.17/5.47 thf(fact_6335_and__int__unfold,axiom,
% 5.17/5.47 ( bit_se725231765392027082nd_int
% 5.17/5.47 = ( ^ [K3: int,L3: int] :
% 5.17/5.47 ( if_int
% 5.17/5.47 @ ( ( K3 = zero_zero_int )
% 5.17/5.47 | ( L3 = zero_zero_int ) )
% 5.17/5.47 @ zero_zero_int
% 5.17/5.47 @ ( if_int
% 5.17/5.47 @ ( K3
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 @ L3
% 5.17/5.47 @ ( if_int
% 5.17/5.47 @ ( L3
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 @ K3
% 5.17/5.47 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_int_unfold
% 5.17/5.47 thf(fact_6336_arctan__half,axiom,
% 5.17/5.47 ( arctan
% 5.17/5.47 = ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % arctan_half
% 5.17/5.47 thf(fact_6337_and_Oright__idem,axiom,
% 5.17/5.47 ! [A: int,B: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.17/5.47 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.right_idem
% 5.17/5.47 thf(fact_6338_and_Oright__idem,axiom,
% 5.17/5.47 ! [A: nat,B: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.17/5.47 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.right_idem
% 5.17/5.47 thf(fact_6339_and_Oleft__idem,axiom,
% 5.17/5.47 ! [A: int,B: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.17/5.47 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.left_idem
% 5.17/5.47 thf(fact_6340_and_Oleft__idem,axiom,
% 5.17/5.47 ! [A: nat,B: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.17/5.47 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.left_idem
% 5.17/5.47 thf(fact_6341_and_Oidem,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % and.idem
% 5.17/5.47 thf(fact_6342_and_Oidem,axiom,
% 5.17/5.47 ! [A: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % and.idem
% 5.17/5.47 thf(fact_6343_real__sqrt__eq__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ( sqrt @ X )
% 5.17/5.47 = ( sqrt @ Y4 ) )
% 5.17/5.47 = ( X = Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_eq_iff
% 5.17/5.47 thf(fact_6344_sgn__le__0__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 5.17/5.47 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % sgn_le_0_iff
% 5.17/5.47 thf(fact_6345_zero__le__sgn__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 5.17/5.47 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % zero_le_sgn_iff
% 5.17/5.47 thf(fact_6346_take__bit__of__0,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_0
% 5.17/5.47 thf(fact_6347_take__bit__of__0,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_0
% 5.17/5.47 thf(fact_6348_bit_Oconj__zero__right,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % bit.conj_zero_right
% 5.17/5.47 thf(fact_6349_bit_Oconj__zero__left,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % bit.conj_zero_left
% 5.17/5.47 thf(fact_6350_zero__and__eq,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % zero_and_eq
% 5.17/5.47 thf(fact_6351_zero__and__eq,axiom,
% 5.17/5.47 ! [A: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % zero_and_eq
% 5.17/5.47 thf(fact_6352_and__zero__eq,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_zero_eq
% 5.17/5.47 thf(fact_6353_and__zero__eq,axiom,
% 5.17/5.47 ! [A: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % and_zero_eq
% 5.17/5.47 thf(fact_6354_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( sqrt @ X )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 = ( X = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_eq_zero_cancel_iff
% 5.17/5.47 thf(fact_6355_real__sqrt__zero,axiom,
% 5.17/5.47 ( ( sqrt @ zero_zero_real )
% 5.17/5.47 = zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_zero
% 5.17/5.47 thf(fact_6356_real__sqrt__less__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) )
% 5.17/5.47 = ( ord_less_real @ X @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_less_iff
% 5.17/5.47 thf(fact_6357_real__sqrt__le__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_le_iff
% 5.17/5.47 thf(fact_6358_real__sqrt__eq__1__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( sqrt @ X )
% 5.17/5.47 = one_one_real )
% 5.17/5.47 = ( X = one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_eq_1_iff
% 5.17/5.47 thf(fact_6359_real__sqrt__one,axiom,
% 5.17/5.47 ( ( sqrt @ one_one_real )
% 5.17/5.47 = one_one_real ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_one
% 5.17/5.47 thf(fact_6360_nat__int,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( nat2 @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.47 = N ) ).
% 5.17/5.47
% 5.17/5.47 % nat_int
% 5.17/5.47 thf(fact_6361_take__bit__and,axiom,
% 5.17/5.47 ! [N: nat,A: int,B: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.17/5.47 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_and
% 5.17/5.47 thf(fact_6362_take__bit__and,axiom,
% 5.17/5.47 ! [N: nat,A: nat,B: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.17/5.47 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_and
% 5.17/5.47 thf(fact_6363_exp__le__cancel__iff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_le_cancel_iff
% 5.17/5.47 thf(fact_6364_concat__bit__of__zero__2,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_of_zero_2
% 5.17/5.47 thf(fact_6365_exp__zero,axiom,
% 5.17/5.47 ( ( exp_complex @ zero_zero_complex )
% 5.17/5.47 = one_one_complex ) ).
% 5.17/5.47
% 5.17/5.47 % exp_zero
% 5.17/5.47 thf(fact_6366_exp__zero,axiom,
% 5.17/5.47 ( ( exp_real @ zero_zero_real )
% 5.17/5.47 = one_one_real ) ).
% 5.17/5.47
% 5.17/5.47 % exp_zero
% 5.17/5.47 thf(fact_6367_take__bit__0,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_0
% 5.17/5.47 thf(fact_6368_take__bit__0,axiom,
% 5.17/5.47 ! [A: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_0
% 5.17/5.47 thf(fact_6369_take__bit__Suc__1,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_Suc_1
% 5.17/5.47 thf(fact_6370_take__bit__Suc__1,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.17/5.47 = one_one_nat ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_Suc_1
% 5.17/5.47 thf(fact_6371_bit_Oconj__one__right,axiom,
% 5.17/5.47 ! [X: code_integer] :
% 5.17/5.47 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % bit.conj_one_right
% 5.17/5.47 thf(fact_6372_bit_Oconj__one__right,axiom,
% 5.17/5.47 ! [X: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % bit.conj_one_right
% 5.17/5.47 thf(fact_6373_and_Oright__neutral,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % and.right_neutral
% 5.17/5.47 thf(fact_6374_and_Oright__neutral,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % and.right_neutral
% 5.17/5.47 thf(fact_6375_and_Oleft__neutral,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % and.left_neutral
% 5.17/5.47 thf(fact_6376_and_Oleft__neutral,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.17/5.47 = A ) ).
% 5.17/5.47
% 5.17/5.47 % and.left_neutral
% 5.17/5.47 thf(fact_6377_take__bit__numeral__1,axiom,
% 5.17/5.47 ! [L: num] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_numeral_1
% 5.17/5.47 thf(fact_6378_take__bit__numeral__1,axiom,
% 5.17/5.47 ! [L: num] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.17/5.47 = one_one_nat ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_numeral_1
% 5.17/5.47 thf(fact_6379_nat__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.17/5.47 = ( numeral_numeral_nat @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_numeral
% 5.17/5.47 thf(fact_6380_real__sqrt__lt__0__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.17/5.47 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_lt_0_iff
% 5.17/5.47 thf(fact_6381_real__sqrt__gt__0__iff,axiom,
% 5.17/5.47 ! [Y4: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y4 ) )
% 5.17/5.47 = ( ord_less_real @ zero_zero_real @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_gt_0_iff
% 5.17/5.47 thf(fact_6382_real__sqrt__ge__0__iff,axiom,
% 5.17/5.47 ! [Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_ge_0_iff
% 5.17/5.47 thf(fact_6383_real__sqrt__le__0__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.17/5.47 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_le_0_iff
% 5.17/5.47 thf(fact_6384_real__sqrt__lt__1__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.17/5.47 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_lt_1_iff
% 5.17/5.47 thf(fact_6385_real__sqrt__gt__1__iff,axiom,
% 5.17/5.47 ! [Y4: real] :
% 5.17/5.47 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y4 ) )
% 5.17/5.47 = ( ord_less_real @ one_one_real @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_gt_1_iff
% 5.17/5.47 thf(fact_6386_real__sqrt__ge__1__iff,axiom,
% 5.17/5.47 ! [Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y4 ) )
% 5.17/5.47 = ( ord_less_eq_real @ one_one_real @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_ge_1_iff
% 5.17/5.47 thf(fact_6387_real__sqrt__le__1__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.17/5.47 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_le_1_iff
% 5.17/5.47 thf(fact_6388_exp__eq__one__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( exp_real @ X )
% 5.17/5.47 = one_one_real )
% 5.17/5.47 = ( X = zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_eq_one_iff
% 5.17/5.47 thf(fact_6389_and__nonnegative__int__iff,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.17/5.47 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.47 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_nonnegative_int_iff
% 5.17/5.47 thf(fact_6390_and__negative__int__iff,axiom,
% 5.17/5.47 ! [K: int,L: int] :
% 5.17/5.47 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.17/5.47 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.47 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_negative_int_iff
% 5.17/5.47 thf(fact_6391_real__sqrt__mult__self,axiom,
% 5.17/5.47 ! [A: real] :
% 5.17/5.47 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.17/5.47 = ( abs_abs_real @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_mult_self
% 5.17/5.47 thf(fact_6392_real__sqrt__abs2,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.17/5.47 = ( abs_abs_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_abs2
% 5.17/5.47 thf(fact_6393_nat__of__bool,axiom,
% 5.17/5.47 ! [P: $o] :
% 5.17/5.47 ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.47 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_of_bool
% 5.17/5.47 thf(fact_6394_take__bit__of__1__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.17/5.47 = zero_zero_int )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_1_eq_0_iff
% 5.17/5.47 thf(fact_6395_take__bit__of__1__eq__0__iff,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.17/5.47 = zero_zero_nat )
% 5.17/5.47 = ( N = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_1_eq_0_iff
% 5.17/5.47 thf(fact_6396_and__numerals_I2_J,axiom,
% 5.17/5.47 ! [Y4: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(2)
% 5.17/5.47 thf(fact_6397_and__numerals_I2_J,axiom,
% 5.17/5.47 ! [Y4: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.47 = one_one_nat ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(2)
% 5.17/5.47 thf(fact_6398_and__numerals_I8_J,axiom,
% 5.17/5.47 ! [X: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(8)
% 5.17/5.47 thf(fact_6399_and__numerals_I8_J,axiom,
% 5.17/5.47 ! [X: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.17/5.47 = one_one_nat ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(8)
% 5.17/5.47 thf(fact_6400_real__sqrt__four,axiom,
% 5.17/5.47 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_four
% 5.17/5.47 thf(fact_6401_nat__1,axiom,
% 5.17/5.47 ( ( nat2 @ one_one_int )
% 5.17/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_1
% 5.17/5.47 thf(fact_6402_nat__0__iff,axiom,
% 5.17/5.47 ! [I: int] :
% 5.17/5.47 ( ( ( nat2 @ I )
% 5.17/5.47 = zero_zero_nat )
% 5.17/5.47 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_0_iff
% 5.17/5.47 thf(fact_6403_nat__le__0,axiom,
% 5.17/5.47 ! [Z: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.17/5.47 => ( ( nat2 @ Z )
% 5.17/5.47 = zero_zero_nat ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_le_0
% 5.17/5.47 thf(fact_6404_zless__nat__conj,axiom,
% 5.17/5.47 ! [W: int,Z: int] :
% 5.17/5.47 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.17/5.47 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.47 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % zless_nat_conj
% 5.17/5.47 thf(fact_6405_nat__neg__numeral,axiom,
% 5.17/5.47 ! [K: num] :
% 5.17/5.47 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % nat_neg_numeral
% 5.17/5.47 thf(fact_6406_one__less__exp__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 5.17/5.47 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % one_less_exp_iff
% 5.17/5.47 thf(fact_6407_exp__less__one__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 5.17/5.47 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_less_one_iff
% 5.17/5.47 thf(fact_6408_exp__le__one__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.17/5.47 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_le_one_iff
% 5.17/5.47 thf(fact_6409_one__le__exp__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.17/5.47 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % one_le_exp_iff
% 5.17/5.47 thf(fact_6410_nat__zminus__int,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % nat_zminus_int
% 5.17/5.47 thf(fact_6411_int__nat__eq,axiom,
% 5.17/5.47 ! [Z: int] :
% 5.17/5.47 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.47 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.17/5.47 = Z ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.47 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.17/5.47 = zero_zero_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % int_nat_eq
% 5.17/5.47 thf(fact_6412_take__bit__minus__one__eq__mask,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_minus_one_eq_mask
% 5.17/5.47 thf(fact_6413_take__bit__minus__one__eq__mask,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_minus_one_eq_mask
% 5.17/5.47 thf(fact_6414_exp__ln,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.17/5.47 = X ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_ln
% 5.17/5.47 thf(fact_6415_exp__ln__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.17/5.47 = X )
% 5.17/5.47 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_ln_iff
% 5.17/5.47 thf(fact_6416_take__bit__of__Suc__0,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.47 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_Suc_0
% 5.17/5.47 thf(fact_6417_and__numerals_I1_J,axiom,
% 5.17/5.47 ! [Y4: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(1)
% 5.17/5.47 thf(fact_6418_and__numerals_I1_J,axiom,
% 5.17/5.47 ! [Y4: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(1)
% 5.17/5.47 thf(fact_6419_and__numerals_I5_J,axiom,
% 5.17/5.47 ! [X: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(5)
% 5.17/5.47 thf(fact_6420_and__numerals_I5_J,axiom,
% 5.17/5.47 ! [X: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.17/5.47 = zero_zero_nat ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(5)
% 5.17/5.47 thf(fact_6421_and__numerals_I3_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(3)
% 5.17/5.47 thf(fact_6422_and__numerals_I3_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(3)
% 5.17/5.47 thf(fact_6423_zero__less__nat__eq,axiom,
% 5.17/5.47 ! [Z: int] :
% 5.17/5.47 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.17/5.47 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.47
% 5.17/5.47 % zero_less_nat_eq
% 5.17/5.47 thf(fact_6424_take__bit__of__1,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.17/5.47 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_1
% 5.17/5.47 thf(fact_6425_take__bit__of__1,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.17/5.47 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_1
% 5.17/5.47 thf(fact_6426_take__bit__of__1,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.17/5.47 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_1
% 5.17/5.47 thf(fact_6427_diff__nat__numeral,axiom,
% 5.17/5.47 ! [V: num,V2: num] :
% 5.17/5.47 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V2 ) )
% 5.17/5.47 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % diff_nat_numeral
% 5.17/5.47 thf(fact_6428_and__minus__numerals_I6_J,axiom,
% 5.17/5.47 ! [N: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_minus_numerals(6)
% 5.17/5.47 thf(fact_6429_and__minus__numerals_I2_J,axiom,
% 5.17/5.47 ! [N: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.47 = one_one_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_minus_numerals(2)
% 5.17/5.47 thf(fact_6430_nat__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.47 ! [Y4: int,X: num,N: nat] :
% 5.17/5.47 ( ( ( nat2 @ Y4 )
% 5.17/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.17/5.47 = ( Y4
% 5.17/5.47 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_eq_numeral_power_cancel_iff
% 5.17/5.47 thf(fact_6431_numeral__power__eq__nat__cancel__iff,axiom,
% 5.17/5.47 ! [X: num,N: nat,Y4: int] :
% 5.17/5.47 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.17/5.47 = ( nat2 @ Y4 ) )
% 5.17/5.47 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.47 = Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % numeral_power_eq_nat_cancel_iff
% 5.17/5.47 thf(fact_6432_dvd__nat__abs__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( dvd_dvd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.17/5.47 = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % dvd_nat_abs_iff
% 5.17/5.47 thf(fact_6433_nat__abs__dvd__iff,axiom,
% 5.17/5.47 ! [K: int,N: nat] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.17/5.47 = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_abs_dvd_iff
% 5.17/5.47 thf(fact_6434_and__numerals_I4_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(4)
% 5.17/5.47 thf(fact_6435_and__numerals_I4_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(4)
% 5.17/5.47 thf(fact_6436_and__numerals_I6_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(6)
% 5.17/5.47 thf(fact_6437_and__numerals_I6_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(6)
% 5.17/5.47 thf(fact_6438_even__take__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,A: code_integer] :
% 5.17/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.17/5.47 = ( ( N = zero_zero_nat )
% 5.17/5.47 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_take_bit_eq
% 5.17/5.47 thf(fact_6439_even__take__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,A: int] :
% 5.17/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.17/5.47 = ( ( N = zero_zero_nat )
% 5.17/5.47 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_take_bit_eq
% 5.17/5.47 thf(fact_6440_even__take__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,A: nat] :
% 5.17/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.17/5.47 = ( ( N = zero_zero_nat )
% 5.17/5.47 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % even_take_bit_eq
% 5.17/5.47 thf(fact_6441_one__less__nat__eq,axiom,
% 5.17/5.47 ! [Z: int] :
% 5.17/5.47 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.17/5.47 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.17/5.47
% 5.17/5.47 % one_less_nat_eq
% 5.17/5.47 thf(fact_6442_real__sqrt__abs,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.47 = ( abs_abs_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_abs
% 5.17/5.47 thf(fact_6443_and__minus__numerals_I5_J,axiom,
% 5.17/5.47 ! [N: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_minus_numerals(5)
% 5.17/5.47 thf(fact_6444_and__minus__numerals_I1_J,axiom,
% 5.17/5.47 ! [N: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.47 = zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % and_minus_numerals(1)
% 5.17/5.47 thf(fact_6445_take__bit__Suc__0,axiom,
% 5.17/5.47 ! [A: code_integer] :
% 5.17/5.47 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.17/5.47 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_Suc_0
% 5.17/5.47 thf(fact_6446_take__bit__Suc__0,axiom,
% 5.17/5.47 ! [A: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.17/5.47 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_Suc_0
% 5.17/5.47 thf(fact_6447_take__bit__Suc__0,axiom,
% 5.17/5.47 ! [A: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.17/5.47 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_Suc_0
% 5.17/5.47 thf(fact_6448_real__sqrt__pow2__iff,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = X )
% 5.17/5.47 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_pow2_iff
% 5.17/5.47 thf(fact_6449_real__sqrt__pow2,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = X ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_pow2
% 5.17/5.47 thf(fact_6450_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.17/5.47 ! [X: real,Y4: real,Xa: real,Ya: real] :
% 5.17/5.47 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( 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 ) ) )
% 5.17/5.47 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( 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 ) ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_sum_squares_mult_squared_eq
% 5.17/5.47 thf(fact_6451_nat__numeral__diff__1,axiom,
% 5.17/5.47 ! [V: num] :
% 5.17/5.47 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.17/5.47 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_numeral_diff_1
% 5.17/5.47 thf(fact_6452_numeral__power__less__nat__cancel__iff,axiom,
% 5.17/5.47 ! [X: num,N: nat,A: int] :
% 5.17/5.47 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.17/5.47 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % numeral_power_less_nat_cancel_iff
% 5.17/5.47 thf(fact_6453_nat__less__numeral__power__cancel__iff,axiom,
% 5.17/5.47 ! [A: int,X: num,N: nat] :
% 5.17/5.47 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.17/5.47 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_less_numeral_power_cancel_iff
% 5.17/5.47 thf(fact_6454_nat__le__numeral__power__cancel__iff,axiom,
% 5.17/5.47 ! [A: int,X: num,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.17/5.47 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_le_numeral_power_cancel_iff
% 5.17/5.47 thf(fact_6455_numeral__power__le__nat__cancel__iff,axiom,
% 5.17/5.47 ! [X: num,N: nat,A: int] :
% 5.17/5.47 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.17/5.47 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % numeral_power_le_nat_cancel_iff
% 5.17/5.47 thf(fact_6456_and__numerals_I7_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.47 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(7)
% 5.17/5.47 thf(fact_6457_and__numerals_I7_J,axiom,
% 5.17/5.47 ! [X: num,Y4: num] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.47 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_numerals(7)
% 5.17/5.47 thf(fact_6458_take__bit__of__exp,axiom,
% 5.17/5.47 ! [M: nat,N: nat] :
% 5.17/5.47 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.47 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_exp
% 5.17/5.47 thf(fact_6459_take__bit__of__exp,axiom,
% 5.17/5.47 ! [M: nat,N: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.47 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_exp
% 5.17/5.47 thf(fact_6460_take__bit__of__exp,axiom,
% 5.17/5.47 ! [M: nat,N: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.47 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_exp
% 5.17/5.47 thf(fact_6461_take__bit__of__2,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_2
% 5.17/5.47 thf(fact_6462_take__bit__of__2,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_2
% 5.17/5.47 thf(fact_6463_take__bit__of__2,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.47 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_2
% 5.17/5.47 thf(fact_6464_take__bit__eq__mask,axiom,
% 5.17/5.47 ( bit_se2923211474154528505it_int
% 5.17/5.47 = ( ^ [N4: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_eq_mask
% 5.17/5.47 thf(fact_6465_take__bit__eq__mask,axiom,
% 5.17/5.47 ( bit_se2925701944663578781it_nat
% 5.17/5.47 = ( ^ [N4: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_eq_mask
% 5.17/5.47 thf(fact_6466_nat__mask__eq,axiom,
% 5.17/5.47 ! [N: nat] :
% 5.17/5.47 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.17/5.47 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_mask_eq
% 5.17/5.47 thf(fact_6467_and_Oleft__commute,axiom,
% 5.17/5.47 ! [B: int,A: int,C: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.17/5.47 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.left_commute
% 5.17/5.47 thf(fact_6468_and_Oleft__commute,axiom,
% 5.17/5.47 ! [B: nat,A: nat,C: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.17/5.47 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.left_commute
% 5.17/5.47 thf(fact_6469_and_Ocommute,axiom,
% 5.17/5.47 ( bit_se725231765392027082nd_int
% 5.17/5.47 = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.commute
% 5.17/5.47 thf(fact_6470_and_Ocommute,axiom,
% 5.17/5.47 ( bit_se727722235901077358nd_nat
% 5.17/5.47 = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.commute
% 5.17/5.47 thf(fact_6471_and_Oassoc,axiom,
% 5.17/5.47 ! [A: int,B: int,C: int] :
% 5.17/5.47 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.17/5.47 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.assoc
% 5.17/5.47 thf(fact_6472_and_Oassoc,axiom,
% 5.17/5.47 ! [A: nat,B: nat,C: nat] :
% 5.17/5.47 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.17/5.47 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and.assoc
% 5.17/5.47 thf(fact_6473_of__nat__and__eq,axiom,
% 5.17/5.47 ! [M: nat,N: nat] :
% 5.17/5.47 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.17/5.47 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % of_nat_and_eq
% 5.17/5.47 thf(fact_6474_of__nat__and__eq,axiom,
% 5.17/5.47 ! [M: nat,N: nat] :
% 5.17/5.47 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.17/5.47 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % of_nat_and_eq
% 5.17/5.47 thf(fact_6475_take__bit__of__nat,axiom,
% 5.17/5.47 ! [N: nat,M: nat] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.17/5.47 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_nat
% 5.17/5.47 thf(fact_6476_take__bit__of__nat,axiom,
% 5.17/5.47 ! [N: nat,M: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.17/5.47 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_of_nat
% 5.17/5.47 thf(fact_6477_nat__take__bit__eq,axiom,
% 5.17/5.47 ! [K: int,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.47 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_take_bit_eq
% 5.17/5.47 thf(fact_6478_take__bit__nat__eq,axiom,
% 5.17/5.47 ! [K: int,N: nat] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.17/5.47 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_nat_eq
% 5.17/5.47 thf(fact_6479_norm__exp,axiom,
% 5.17/5.47 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % norm_exp
% 5.17/5.47 thf(fact_6480_norm__exp,axiom,
% 5.17/5.47 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % norm_exp
% 5.17/5.47 thf(fact_6481_take__bit__add,axiom,
% 5.17/5.47 ! [N: nat,A: int,B: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_add
% 5.17/5.47 thf(fact_6482_take__bit__add,axiom,
% 5.17/5.47 ! [N: nat,A: nat,B: nat] :
% 5.17/5.47 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_add
% 5.17/5.47 thf(fact_6483_take__bit__tightened,axiom,
% 5.17/5.47 ! [N: nat,A: int,B: int,M: nat] :
% 5.17/5.47 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.17/5.47 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_tightened
% 5.17/5.47 thf(fact_6484_take__bit__tightened,axiom,
% 5.17/5.47 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.17/5.47 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.17/5.47 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_tightened
% 5.17/5.47 thf(fact_6485_take__bit__nat__less__eq__self,axiom,
% 5.17/5.47 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_nat_less_eq_self
% 5.17/5.47 thf(fact_6486_take__bit__tightened__less__eq__nat,axiom,
% 5.17/5.47 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.47 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.47 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_tightened_less_eq_nat
% 5.17/5.47 thf(fact_6487_real__sqrt__less__mono,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.47 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_less_mono
% 5.17/5.47 thf(fact_6488_real__sqrt__le__mono,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.47 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_le_mono
% 5.17/5.47 thf(fact_6489_real__sqrt__divide,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( sqrt @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.47 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_divide
% 5.17/5.47 thf(fact_6490_real__sqrt__mult,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( sqrt @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.47 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_mult
% 5.17/5.47 thf(fact_6491_real__sqrt__power,axiom,
% 5.17/5.47 ! [X: real,K: nat] :
% 5.17/5.47 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 5.17/5.47 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_power
% 5.17/5.47 thf(fact_6492_real__sqrt__minus,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.17/5.47 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_minus
% 5.17/5.47 thf(fact_6493_exp__not__eq__zero,axiom,
% 5.17/5.47 ! [X: complex] :
% 5.17/5.47 ( ( exp_complex @ X )
% 5.17/5.47 != zero_zero_complex ) ).
% 5.17/5.47
% 5.17/5.47 % exp_not_eq_zero
% 5.17/5.47 thf(fact_6494_exp__not__eq__zero,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( exp_real @ X )
% 5.17/5.47 != zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % exp_not_eq_zero
% 5.17/5.47 thf(fact_6495_take__bit__minus,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_minus
% 5.17/5.47 thf(fact_6496_exp__times__arg__commute,axiom,
% 5.17/5.47 ! [A2: complex] :
% 5.17/5.47 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.17/5.47 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_times_arg_commute
% 5.17/5.47 thf(fact_6497_exp__times__arg__commute,axiom,
% 5.17/5.47 ! [A2: real] :
% 5.17/5.47 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.17/5.47 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_times_arg_commute
% 5.17/5.47 thf(fact_6498_take__bit__mult,axiom,
% 5.17/5.47 ! [N: nat,K: int,L: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_mult
% 5.17/5.47 thf(fact_6499_take__bit__diff,axiom,
% 5.17/5.47 ! [N: nat,K: int,L: int] :
% 5.17/5.47 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_diff
% 5.17/5.47 thf(fact_6500_concat__bit__take__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,B: int] :
% 5.17/5.47 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.17/5.47 = ( bit_concat_bit @ N @ B ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_take_bit_eq
% 5.17/5.47 thf(fact_6501_concat__bit__eq__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int,L: int,R2: int,S2: int] :
% 5.17/5.47 ( ( ( bit_concat_bit @ N @ K @ L )
% 5.17/5.47 = ( bit_concat_bit @ N @ R2 @ S2 ) )
% 5.17/5.47 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ R2 ) )
% 5.17/5.47 & ( L = S2 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % concat_bit_eq_iff
% 5.17/5.47 thf(fact_6502_and__eq__minus__1__iff,axiom,
% 5.17/5.47 ! [A: code_integer,B: code_integer] :
% 5.17/5.47 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 = ( ( A
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.47 & ( B
% 5.17/5.47 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_eq_minus_1_iff
% 5.17/5.47 thf(fact_6503_and__eq__minus__1__iff,axiom,
% 5.17/5.47 ! [A: int,B: int] :
% 5.17/5.47 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 = ( ( A
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.47 & ( B
% 5.17/5.47 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_eq_minus_1_iff
% 5.17/5.47 thf(fact_6504_real__sqrt__gt__zero,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_gt_zero
% 5.17/5.47 thf(fact_6505_exp__total,axiom,
% 5.17/5.47 ! [Y4: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.47 => ? [X4: real] :
% 5.17/5.47 ( ( exp_real @ X4 )
% 5.17/5.47 = Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_total
% 5.17/5.47 thf(fact_6506_exp__gt__zero,axiom,
% 5.17/5.47 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_gt_zero
% 5.17/5.47 thf(fact_6507_not__exp__less__zero,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % not_exp_less_zero
% 5.17/5.47 thf(fact_6508_real__sqrt__ge__zero,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_ge_zero
% 5.17/5.47 thf(fact_6509_real__sqrt__eq__zero__cancel,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( ( sqrt @ X )
% 5.17/5.47 = zero_zero_real )
% 5.17/5.47 => ( X = zero_zero_real ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_eq_zero_cancel
% 5.17/5.47 thf(fact_6510_exp__ge__zero,axiom,
% 5.17/5.47 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_ge_zero
% 5.17/5.47 thf(fact_6511_not__exp__le__zero,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.17/5.47
% 5.17/5.47 % not_exp_le_zero
% 5.17/5.47 thf(fact_6512_real__sqrt__ge__one,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.47 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sqrt_ge_one
% 5.17/5.47 thf(fact_6513_nat__zero__as__int,axiom,
% 5.17/5.47 ( zero_zero_nat
% 5.17/5.47 = ( nat2 @ zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_zero_as_int
% 5.17/5.47 thf(fact_6514_AND__upper2_H,axiom,
% 5.17/5.47 ! [Y4: int,Z: int,X: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.47 => ( ( ord_less_eq_int @ Y4 @ Z )
% 5.17/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_upper2'
% 5.17/5.47 thf(fact_6515_AND__upper1_H,axiom,
% 5.17/5.47 ! [Y4: int,Z: int,Ya: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.47 => ( ( ord_less_eq_int @ Y4 @ Z )
% 5.17/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y4 @ Ya ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_upper1'
% 5.17/5.47 thf(fact_6516_AND__upper2,axiom,
% 5.17/5.47 ! [Y4: int,X: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ Y4 ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_upper2
% 5.17/5.47 thf(fact_6517_AND__upper1,axiom,
% 5.17/5.47 ! [X: int,Y4: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_upper1
% 5.17/5.47 thf(fact_6518_AND__lower,axiom,
% 5.17/5.47 ! [X: int,Y4: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.47 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_lower
% 5.17/5.47 thf(fact_6519_take__bit__tightened__less__eq__int,axiom,
% 5.17/5.47 ! [M: nat,N: nat,K: int] :
% 5.17/5.47 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.47 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_tightened_less_eq_int
% 5.17/5.47 thf(fact_6520_nat__numeral__as__int,axiom,
% 5.17/5.47 ( numeral_numeral_nat
% 5.17/5.47 = ( ^ [I2: num] : ( nat2 @ ( numeral_numeral_int @ I2 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_numeral_as_int
% 5.17/5.47 thf(fact_6521_take__bit__int__less__eq__self__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.17/5.47 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_int_less_eq_self_iff
% 5.17/5.47 thf(fact_6522_take__bit__nonnegative,axiom,
% 5.17/5.47 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_nonnegative
% 5.17/5.47 thf(fact_6523_take__bit__int__greater__self__iff,axiom,
% 5.17/5.47 ! [K: int,N: nat] :
% 5.17/5.47 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.17/5.47 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_int_greater_self_iff
% 5.17/5.47 thf(fact_6524_not__take__bit__negative,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.17/5.47
% 5.17/5.47 % not_take_bit_negative
% 5.17/5.47 thf(fact_6525_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,A: int,B: int] :
% 5.17/5.47 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.17/5.47 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.17/5.47 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_eq_iff_take_bit_eq
% 5.17/5.47 thf(fact_6526_real__sgn__eq,axiom,
% 5.17/5.47 ( sgn_sgn_real
% 5.17/5.47 = ( ^ [X3: real] : ( divide_divide_real @ X3 @ ( abs_abs_real @ X3 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_sgn_eq
% 5.17/5.47 thf(fact_6527_nat__mono,axiom,
% 5.17/5.47 ! [X: int,Y4: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.47 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_mono
% 5.17/5.47 thf(fact_6528_signed__take__bit__take__bit,axiom,
% 5.17/5.47 ! [M: nat,N: nat,A: int] :
% 5.17/5.47 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.17/5.47 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.17/5.47
% 5.17/5.47 % signed_take_bit_take_bit
% 5.17/5.47 thf(fact_6529_eq__nat__nat__iff,axiom,
% 5.17/5.47 ! [Z: int,Z6: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.17/5.47 => ( ( ( nat2 @ Z )
% 5.17/5.47 = ( nat2 @ Z6 ) )
% 5.17/5.47 = ( Z = Z6 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % eq_nat_nat_iff
% 5.17/5.47 thf(fact_6530_all__nat,axiom,
% 5.17/5.47 ( ( ^ [P2: nat > $o] :
% 5.17/5.47 ! [X6: nat] : ( P2 @ X6 ) )
% 5.17/5.47 = ( ^ [P3: nat > $o] :
% 5.17/5.47 ! [X3: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.17/5.47 => ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % all_nat
% 5.17/5.47 thf(fact_6531_ex__nat,axiom,
% 5.17/5.47 ( ( ^ [P2: nat > $o] :
% 5.17/5.47 ? [X6: nat] : ( P2 @ X6 ) )
% 5.17/5.47 = ( ^ [P3: nat > $o] :
% 5.17/5.47 ? [X3: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.17/5.47 & ( P3 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % ex_nat
% 5.17/5.47 thf(fact_6532_mult__exp__exp,axiom,
% 5.17/5.47 ! [X: complex,Y4: complex] :
% 5.17/5.47 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y4 ) )
% 5.17/5.47 = ( exp_complex @ ( plus_plus_complex @ X @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mult_exp_exp
% 5.17/5.47 thf(fact_6533_mult__exp__exp,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) )
% 5.17/5.47 = ( exp_real @ ( plus_plus_real @ X @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % mult_exp_exp
% 5.17/5.47 thf(fact_6534_exp__add__commuting,axiom,
% 5.17/5.47 ! [X: complex,Y4: complex] :
% 5.17/5.47 ( ( ( times_times_complex @ X @ Y4 )
% 5.17/5.47 = ( times_times_complex @ Y4 @ X ) )
% 5.17/5.47 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.17/5.47 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_add_commuting
% 5.17/5.47 thf(fact_6535_exp__add__commuting,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ( times_times_real @ X @ Y4 )
% 5.17/5.47 = ( times_times_real @ Y4 @ X ) )
% 5.17/5.47 => ( ( exp_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.47 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_add_commuting
% 5.17/5.47 thf(fact_6536_exp__diff,axiom,
% 5.17/5.47 ! [X: complex,Y4: complex] :
% 5.17/5.47 ( ( exp_complex @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.47 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_diff
% 5.17/5.47 thf(fact_6537_exp__diff,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( exp_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.47 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y4 ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_diff
% 5.17/5.47 thf(fact_6538_nat__one__as__int,axiom,
% 5.17/5.47 ( one_one_nat
% 5.17/5.47 = ( nat2 @ one_one_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_one_as_int
% 5.17/5.47 thf(fact_6539_take__bit__unset__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: int] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.17/5.47 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_unset_bit_eq
% 5.17/5.47 thf(fact_6540_take__bit__unset__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: nat] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.17/5.47 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_unset_bit_eq
% 5.17/5.47 thf(fact_6541_take__bit__unset__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: code_integer] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.17/5.47 = ( bit_se1745604003318907178nteger @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.17/5.47 = ( bit_se8260200283734997820nteger @ M @ ( bit_se1745604003318907178nteger @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_unset_bit_eq
% 5.17/5.47 thf(fact_6542_take__bit__set__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: code_integer] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.17/5.47 = ( bit_se1745604003318907178nteger @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.17/5.47 = ( bit_se2793503036327961859nteger @ M @ ( bit_se1745604003318907178nteger @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_set_bit_eq
% 5.17/5.47 thf(fact_6543_take__bit__set__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: int] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.17/5.47 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_set_bit_eq
% 5.17/5.47 thf(fact_6544_take__bit__set__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: nat] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.17/5.47 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_set_bit_eq
% 5.17/5.47 thf(fact_6545_take__bit__flip__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: code_integer] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.17/5.47 = ( bit_se1745604003318907178nteger @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se1745604003318907178nteger @ N @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.17/5.47 = ( bit_se1345352211410354436nteger @ M @ ( bit_se1745604003318907178nteger @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_flip_bit_eq
% 5.17/5.47 thf(fact_6546_take__bit__flip__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: int] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.17/5.47 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_flip_bit_eq
% 5.17/5.47 thf(fact_6547_take__bit__flip__bit__eq,axiom,
% 5.17/5.47 ! [N: nat,M: nat,A: nat] :
% 5.17/5.47 ( ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.17/5.47 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.17/5.47 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.17/5.47 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.17/5.47 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_flip_bit_eq
% 5.17/5.47 thf(fact_6548_unset__bit__nat__def,axiom,
% 5.17/5.47 ( bit_se4205575877204974255it_nat
% 5.17/5.47 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M5 @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % unset_bit_nat_def
% 5.17/5.47 thf(fact_6549_pow_Osimps_I1_J,axiom,
% 5.17/5.47 ! [X: num] :
% 5.17/5.47 ( ( pow @ X @ one )
% 5.17/5.47 = X ) ).
% 5.17/5.47
% 5.17/5.47 % pow.simps(1)
% 5.17/5.47 thf(fact_6550_exp__gt__one,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_gt_one
% 5.17/5.47 thf(fact_6551_real__div__sqrt,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.17/5.47 = ( sqrt @ X ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % real_div_sqrt
% 5.17/5.47 thf(fact_6552_sqrt__add__le__add__sqrt,axiom,
% 5.17/5.47 ! [X: real,Y4: real] :
% 5.17/5.47 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.47 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y4 ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y4 ) ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % sqrt_add_le_add_sqrt
% 5.17/5.47 thf(fact_6553_take__bit__signed__take__bit,axiom,
% 5.17/5.47 ! [M: nat,N: nat,A: int] :
% 5.17/5.47 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.17/5.47 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.17/5.47 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_signed_take_bit
% 5.17/5.47 thf(fact_6554_exp__ge__add__one__self,axiom,
% 5.17/5.47 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.17/5.47
% 5.17/5.47 % exp_ge_add_one_self
% 5.17/5.47 thf(fact_6555_le__real__sqrt__sumsq,axiom,
% 5.17/5.47 ! [X: real,Y4: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y4 @ Y4 ) ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % le_real_sqrt_sumsq
% 5.17/5.47 thf(fact_6556_and__less__eq,axiom,
% 5.17/5.47 ! [L: int,K: int] :
% 5.17/5.47 ( ( ord_less_int @ L @ zero_zero_int )
% 5.17/5.47 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.17/5.47
% 5.17/5.47 % and_less_eq
% 5.17/5.47 thf(fact_6557_AND__upper1_H_H,axiom,
% 5.17/5.47 ! [Y4: int,Z: int,Ya: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.47 => ( ( ord_less_int @ Y4 @ Z )
% 5.17/5.47 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y4 @ Ya ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_upper1''
% 5.17/5.47 thf(fact_6558_AND__upper2_H_H,axiom,
% 5.17/5.47 ! [Y4: int,Z: int,X: int] :
% 5.17/5.47 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.47 => ( ( ord_less_int @ Y4 @ Z )
% 5.17/5.47 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % AND_upper2''
% 5.17/5.47 thf(fact_6559_nat__mono__iff,axiom,
% 5.17/5.47 ! [Z: int,W: int] :
% 5.17/5.47 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.47 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.17/5.47 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.17/5.47
% 5.17/5.47 % nat_mono_iff
% 5.17/5.47 thf(fact_6560_take__bit__eq__mask__iff,axiom,
% 5.17/5.47 ! [N: nat,K: int] :
% 5.17/5.47 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.47 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.17/5.47 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.17/5.47 = zero_zero_int ) ) ).
% 5.17/5.47
% 5.17/5.47 % take_bit_eq_mask_iff
% 5.17/5.47 thf(fact_6561_exp__minus__inverse,axiom,
% 5.17/5.47 ! [X: real] :
% 5.17/5.47 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.17/5.47 = one_one_real ) ).
% 5.17/5.47
% 5.17/5.47 % exp_minus_inverse
% 5.17/5.47 thf(fact_6562_exp__minus__inverse,axiom,
% 5.17/5.47 ! [X: complex] :
% 5.17/5.47 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.17/5.47 = one_one_complex ) ).
% 5.17/5.47
% 5.17/5.47 % exp_minus_inverse
% 5.17/5.48 thf(fact_6563_take__bit__decr__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.48 != zero_zero_int )
% 5.17/5.48 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.17/5.48 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_decr_eq
% 5.17/5.48 thf(fact_6564_zless__nat__eq__int__zless,axiom,
% 5.17/5.48 ! [M: nat,Z: int] :
% 5.17/5.48 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.17/5.48 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % zless_nat_eq_int_zless
% 5.17/5.48 thf(fact_6565_nat__le__iff,axiom,
% 5.17/5.48 ! [X: int,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 5.17/5.48 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_le_iff
% 5.17/5.48 thf(fact_6566_nat__0__le,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.17/5.48 = Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_0_le
% 5.17/5.48 thf(fact_6567_int__eq__iff,axiom,
% 5.17/5.48 ! [M: nat,Z: int] :
% 5.17/5.48 ( ( ( semiri1314217659103216013at_int @ M )
% 5.17/5.48 = Z )
% 5.17/5.48 = ( ( M
% 5.17/5.48 = ( nat2 @ Z ) )
% 5.17/5.48 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % int_eq_iff
% 5.17/5.48 thf(fact_6568_nat__int__add,axiom,
% 5.17/5.48 ! [A: nat,B: nat] :
% 5.17/5.48 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.17/5.48 = ( plus_plus_nat @ A @ B ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_int_add
% 5.17/5.48 thf(fact_6569_exp__of__nat2__mult,axiom,
% 5.17/5.48 ! [X: complex,N: nat] :
% 5.17/5.48 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.17/5.48 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_of_nat2_mult
% 5.17/5.48 thf(fact_6570_exp__of__nat2__mult,axiom,
% 5.17/5.48 ! [X: real,N: nat] :
% 5.17/5.48 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.48 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_of_nat2_mult
% 5.17/5.48 thf(fact_6571_exp__of__nat__mult,axiom,
% 5.17/5.48 ! [N: nat,X: complex] :
% 5.17/5.48 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 5.17/5.48 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_of_nat_mult
% 5.17/5.48 thf(fact_6572_exp__of__nat__mult,axiom,
% 5.17/5.48 ! [N: nat,X: real] :
% 5.17/5.48 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 5.17/5.48 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_of_nat_mult
% 5.17/5.48 thf(fact_6573_int__minus,axiom,
% 5.17/5.48 ! [N: nat,M: nat] :
% 5.17/5.48 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % int_minus
% 5.17/5.48 thf(fact_6574_nat__abs__mult__distrib,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.17/5.48 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_abs_mult_distrib
% 5.17/5.48 thf(fact_6575_even__and__iff,axiom,
% 5.17/5.48 ! [A: code_integer,B: code_integer] :
% 5.17/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.17/5.48 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % even_and_iff
% 5.17/5.48 thf(fact_6576_even__and__iff,axiom,
% 5.17/5.48 ! [A: int,B: int] :
% 5.17/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.17/5.48 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % even_and_iff
% 5.17/5.48 thf(fact_6577_even__and__iff,axiom,
% 5.17/5.48 ! [A: nat,B: nat] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.17/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % even_and_iff
% 5.17/5.48 thf(fact_6578_sqrt2__less__2,axiom,
% 5.17/5.48 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt2_less_2
% 5.17/5.48 thf(fact_6579_sgn__real__def,axiom,
% 5.17/5.48 ( sgn_sgn_real
% 5.17/5.48 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sgn_real_def
% 5.17/5.48 thf(fact_6580_exp__ge__add__one__self__aux,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_ge_add_one_self_aux
% 5.17/5.48 thf(fact_6581_even__and__iff__int,axiom,
% 5.17/5.48 ! [K: int,L: int] :
% 5.17/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.17/5.48 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.17/5.48 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % even_and_iff_int
% 5.17/5.48 thf(fact_6582_lemma__exp__total,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ one_one_real @ Y4 )
% 5.17/5.48 => ? [X4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.17/5.48 & ( ord_less_eq_real @ X4 @ ( minus_minus_real @ Y4 @ one_one_real ) )
% 5.17/5.48 & ( ( exp_real @ X4 )
% 5.17/5.48 = Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % lemma_exp_total
% 5.17/5.48 thf(fact_6583_ln__ge__iff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( ln_ln_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( exp_real @ Y4 ) @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ln_ge_iff
% 5.17/5.48 thf(fact_6584_ln__x__over__x__mono,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y4 ) @ Y4 ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ln_x_over_x_mono
% 5.17/5.48 thf(fact_6585_nat__less__eq__zless,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.17/5.48 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.17/5.48 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_less_eq_zless
% 5.17/5.48 thf(fact_6586_nat__le__eq__zle,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.17/5.48 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.17/5.48 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_le_eq_zle
% 5.17/5.48 thf(fact_6587_nat__eq__iff2,axiom,
% 5.17/5.48 ! [M: nat,W: int] :
% 5.17/5.48 ( ( M
% 5.17/5.48 = ( nat2 @ W ) )
% 5.17/5.48 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.17/5.48 => ( W
% 5.17/5.48 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.17/5.48 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.17/5.48 => ( M = zero_zero_nat ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_eq_iff2
% 5.17/5.48 thf(fact_6588_nat__eq__iff,axiom,
% 5.17/5.48 ! [W: int,M: nat] :
% 5.17/5.48 ( ( ( nat2 @ W )
% 5.17/5.48 = M )
% 5.17/5.48 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.17/5.48 => ( W
% 5.17/5.48 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.17/5.48 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.17/5.48 => ( M = zero_zero_nat ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_eq_iff
% 5.17/5.48 thf(fact_6589_split__nat,axiom,
% 5.17/5.48 ! [P: nat > $o,I: int] :
% 5.17/5.48 ( ( P @ ( nat2 @ I ) )
% 5.17/5.48 = ( ! [N4: nat] :
% 5.17/5.48 ( ( I
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N4 ) )
% 5.17/5.48 => ( P @ N4 ) )
% 5.17/5.48 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.17/5.48 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % split_nat
% 5.17/5.48 thf(fact_6590_le__nat__iff,axiom,
% 5.17/5.48 ! [K: int,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.48 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.17/5.48 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_nat_iff
% 5.17/5.48 thf(fact_6591_nat__add__distrib,axiom,
% 5.17/5.48 ! [Z: int,Z6: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.17/5.48 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.17/5.48 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_add_distrib
% 5.17/5.48 thf(fact_6592_nat__mult__distrib,axiom,
% 5.17/5.48 ! [Z: int,Z6: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.17/5.48 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_mult_distrib
% 5.17/5.48 thf(fact_6593_Suc__as__int,axiom,
% 5.17/5.48 ( suc
% 5.17/5.48 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Suc_as_int
% 5.17/5.48 thf(fact_6594_nat__diff__distrib,axiom,
% 5.17/5.48 ! [Z6: int,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.17/5.48 => ( ( ord_less_eq_int @ Z6 @ Z )
% 5.17/5.48 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 5.17/5.48 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_diff_distrib
% 5.17/5.48 thf(fact_6595_nat__diff__distrib_H,axiom,
% 5.17/5.48 ! [X: int,Y4: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.48 => ( ( nat2 @ ( minus_minus_int @ X @ Y4 ) )
% 5.17/5.48 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_diff_distrib'
% 5.17/5.48 thf(fact_6596_nat__abs__triangle__ineq,axiom,
% 5.17/5.48 ! [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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_abs_triangle_ineq
% 5.17/5.48 thf(fact_6597_nat__div__distrib,axiom,
% 5.17/5.48 ! [X: int,Y4: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.48 => ( ( nat2 @ ( divide_divide_int @ X @ Y4 ) )
% 5.17/5.48 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_div_distrib
% 5.17/5.48 thf(fact_6598_nat__div__distrib_H,axiom,
% 5.17/5.48 ! [Y4: int,X: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.48 => ( ( nat2 @ ( divide_divide_int @ X @ Y4 ) )
% 5.17/5.48 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_div_distrib'
% 5.17/5.48 thf(fact_6599_nat__power__eq,axiom,
% 5.17/5.48 ! [Z: int,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.17/5.48 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_power_eq
% 5.17/5.48 thf(fact_6600_nat__mod__distrib,axiom,
% 5.17/5.48 ! [X: int,Y4: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.48 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y4 ) )
% 5.17/5.48 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_mod_distrib
% 5.17/5.48 thf(fact_6601_div__abs__eq__div__nat,axiom,
% 5.17/5.48 ! [K: int,L: int] :
% 5.17/5.48 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % div_abs_eq_div_nat
% 5.17/5.48 thf(fact_6602_num_Osize_I4_J,axiom,
% 5.17/5.48 ( ( size_size_num @ one )
% 5.17/5.48 = zero_zero_nat ) ).
% 5.17/5.48
% 5.17/5.48 % num.size(4)
% 5.17/5.48 thf(fact_6603_mod__abs__eq__div__nat,axiom,
% 5.17/5.48 ! [K: int,L: int] :
% 5.17/5.48 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % mod_abs_eq_div_nat
% 5.17/5.48 thf(fact_6604_take__bit__Suc__bit0,axiom,
% 5.17/5.48 ! [N: nat,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.17/5.48 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_bit0
% 5.17/5.48 thf(fact_6605_take__bit__Suc__bit0,axiom,
% 5.17/5.48 ! [N: nat,K: num] :
% 5.17/5.48 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.48 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_bit0
% 5.17/5.48 thf(fact_6606_take__bit__eq__mod,axiom,
% 5.17/5.48 ( bit_se1745604003318907178nteger
% 5.17/5.48 = ( ^ [N4: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_mod
% 5.17/5.48 thf(fact_6607_take__bit__eq__mod,axiom,
% 5.17/5.48 ( bit_se2923211474154528505it_int
% 5.17/5.48 = ( ^ [N4: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_mod
% 5.17/5.48 thf(fact_6608_take__bit__eq__mod,axiom,
% 5.17/5.48 ( bit_se2925701944663578781it_nat
% 5.17/5.48 = ( ^ [N4: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_mod
% 5.17/5.48 thf(fact_6609_one__and__eq,axiom,
% 5.17/5.48 ! [A: code_integer] :
% 5.17/5.48 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.17/5.48 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_and_eq
% 5.17/5.48 thf(fact_6610_one__and__eq,axiom,
% 5.17/5.48 ! [A: int] :
% 5.17/5.48 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.17/5.48 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_and_eq
% 5.17/5.48 thf(fact_6611_one__and__eq,axiom,
% 5.17/5.48 ! [A: nat] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.17/5.48 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_and_eq
% 5.17/5.48 thf(fact_6612_and__one__eq,axiom,
% 5.17/5.48 ! [A: code_integer] :
% 5.17/5.48 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.17/5.48 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_one_eq
% 5.17/5.48 thf(fact_6613_and__one__eq,axiom,
% 5.17/5.48 ! [A: int] :
% 5.17/5.48 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.17/5.48 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_one_eq
% 5.17/5.48 thf(fact_6614_and__one__eq,axiom,
% 5.17/5.48 ! [A: nat] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.17/5.48 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_one_eq
% 5.17/5.48 thf(fact_6615_take__bit__nat__eq__self__iff,axiom,
% 5.17/5.48 ! [N: nat,M: nat] :
% 5.17/5.48 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.17/5.48 = M )
% 5.17/5.48 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_nat_eq_self_iff
% 5.17/5.48 thf(fact_6616_take__bit__nat__less__exp,axiom,
% 5.17/5.48 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_nat_less_exp
% 5.17/5.48 thf(fact_6617_take__bit__nat__eq__self,axiom,
% 5.17/5.48 ! [M: nat,N: nat] :
% 5.17/5.48 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.17/5.48 = M ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_nat_eq_self
% 5.17/5.48 thf(fact_6618_real__less__rsqrt,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 )
% 5.17/5.48 => ( ord_less_real @ X @ ( sqrt @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_less_rsqrt
% 5.17/5.48 thf(fact_6619_real__le__rsqrt,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ X @ ( sqrt @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_le_rsqrt
% 5.17/5.48 thf(fact_6620_sqrt__le__D,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ X @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt_le_D
% 5.17/5.48 thf(fact_6621_exp__le,axiom,
% 5.17/5.48 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_le
% 5.17/5.48 thf(fact_6622_take__bit__nat__def,axiom,
% 5.17/5.48 ( bit_se2925701944663578781it_nat
% 5.17/5.48 = ( ^ [N4: nat,M5: nat] : ( modulo_modulo_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_nat_def
% 5.17/5.48 thf(fact_6623_nat__2,axiom,
% 5.17/5.48 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.48 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_2
% 5.17/5.48 thf(fact_6624_sgn__power__injE,axiom,
% 5.17/5.48 ! [A: real,N: nat,X: real,B: real] :
% 5.17/5.48 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.17/5.48 = X )
% 5.17/5.48 => ( ( X
% 5.17/5.48 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.48 => ( A = B ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sgn_power_injE
% 5.17/5.48 thf(fact_6625_take__bit__int__less__exp,axiom,
% 5.17/5.48 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_less_exp
% 5.17/5.48 thf(fact_6626_Suc__nat__eq__nat__zadd1,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( ( suc @ ( nat2 @ Z ) )
% 5.17/5.48 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Suc_nat_eq_nat_zadd1
% 5.17/5.48 thf(fact_6627_nat__less__iff,axiom,
% 5.17/5.48 ! [W: int,M: nat] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.17/5.48 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.17/5.48 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_less_iff
% 5.17/5.48 thf(fact_6628_take__bit__int__def,axiom,
% 5.17/5.48 ( bit_se2923211474154528505it_int
% 5.17/5.48 = ( ^ [N4: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_def
% 5.17/5.48 thf(fact_6629_nat__mult__distrib__neg,axiom,
% 5.17/5.48 ! [Z: int,Z6: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.17/5.48 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.17/5.48 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_mult_distrib_neg
% 5.17/5.48 thf(fact_6630_exp__divide__power__eq,axiom,
% 5.17/5.48 ! [N: nat,X: complex] :
% 5.17/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.48 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.17/5.48 = ( exp_complex @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_divide_power_eq
% 5.17/5.48 thf(fact_6631_exp__divide__power__eq,axiom,
% 5.17/5.48 ! [N: nat,X: real] :
% 5.17/5.48 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.48 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.17/5.48 = ( exp_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_divide_power_eq
% 5.17/5.48 thf(fact_6632_nat__abs__int__diff,axiom,
% 5.17/5.48 ! [A: nat,B: nat] :
% 5.17/5.48 ( ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.48 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.17/5.48 = ( minus_minus_nat @ B @ A ) ) )
% 5.17/5.48 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.17/5.48 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.17/5.48 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_abs_int_diff
% 5.17/5.48 thf(fact_6633_tanh__altdef,axiom,
% 5.17/5.48 ( tanh_real
% 5.17/5.48 = ( ^ [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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tanh_altdef
% 5.17/5.48 thf(fact_6634_tanh__altdef,axiom,
% 5.17/5.48 ( tanh_complex
% 5.17/5.48 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tanh_altdef
% 5.17/5.48 thf(fact_6635_take__bit__eq__0__iff,axiom,
% 5.17/5.48 ! [N: nat,A: code_integer] :
% 5.17/5.48 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.17/5.48 = zero_z3403309356797280102nteger )
% 5.17/5.48 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_0_iff
% 5.17/5.48 thf(fact_6636_take__bit__eq__0__iff,axiom,
% 5.17/5.48 ! [N: nat,A: int] :
% 5.17/5.48 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.17/5.48 = zero_zero_int )
% 5.17/5.48 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_0_iff
% 5.17/5.48 thf(fact_6637_take__bit__eq__0__iff,axiom,
% 5.17/5.48 ! [N: nat,A: nat] :
% 5.17/5.48 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.17/5.48 = zero_zero_nat )
% 5.17/5.48 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_0_iff
% 5.17/5.48 thf(fact_6638_take__bit__numeral__bit0,axiom,
% 5.17/5.48 ! [L: num,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.17/5.48 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_bit0
% 5.17/5.48 thf(fact_6639_take__bit__numeral__bit0,axiom,
% 5.17/5.48 ! [L: num,K: num] :
% 5.17/5.48 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.48 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_bit0
% 5.17/5.48 thf(fact_6640_take__bit__nat__less__self__iff,axiom,
% 5.17/5.48 ! [N: nat,M: nat] :
% 5.17/5.48 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.17/5.48 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_nat_less_self_iff
% 5.17/5.48 thf(fact_6641_real__sqrt__unique,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.48 = X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( sqrt @ X )
% 5.17/5.48 = Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_unique
% 5.17/5.48 thf(fact_6642_real__le__lsqrt,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_le_lsqrt
% 5.17/5.48 thf(fact_6643_lemma__real__divide__sqrt__less,axiom,
% 5.17/5.48 ! [U: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ U )
% 5.17/5.48 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.17/5.48
% 5.17/5.48 % lemma_real_divide_sqrt_less
% 5.17/5.48 thf(fact_6644_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = Y4 )
% 5.17/5.48 => ( X = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_eq_cancel2
% 5.17/5.48 thf(fact_6645_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = X )
% 5.17/5.48 => ( Y4 = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_eq_cancel
% 5.17/5.48 thf(fact_6646_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.17/5.48 ! [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 ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_triangle_ineq
% 5.17/5.48 thf(fact_6647_real__sqrt__sum__squares__ge2,axiom,
% 5.17/5.48 ! [Y4: real,X: real] : ( ord_less_eq_real @ Y4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_ge2
% 5.17/5.48 thf(fact_6648_real__sqrt__sum__squares__ge1,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_ge1
% 5.17/5.48 thf(fact_6649_exp__half__le2,axiom,
% 5.17/5.48 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_half_le2
% 5.17/5.48 thf(fact_6650_sqrt__ge__absD,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y4 ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt_ge_absD
% 5.17/5.48 thf(fact_6651_take__bit__Suc__minus__bit0,axiom,
% 5.17/5.48 ! [N: nat,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.17/5.48 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_minus_bit0
% 5.17/5.48 thf(fact_6652_take__bit__int__greater__eq__self__iff,axiom,
% 5.17/5.48 ! [K: int,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.17/5.48 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_greater_eq_self_iff
% 5.17/5.48 thf(fact_6653_take__bit__int__less__self__iff,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.17/5.48 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_less_self_iff
% 5.17/5.48 thf(fact_6654_exp__double,axiom,
% 5.17/5.48 ! [Z: complex] :
% 5.17/5.48 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.17/5.48 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_double
% 5.17/5.48 thf(fact_6655_exp__double,axiom,
% 5.17/5.48 ! [Z: real] :
% 5.17/5.48 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.17/5.48 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_double
% 5.17/5.48 thf(fact_6656_nat__dvd__iff,axiom,
% 5.17/5.48 ! [Z: int,M: nat] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.17/5.48 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.17/5.48 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.48 => ( M = zero_zero_nat ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_dvd_iff
% 5.17/5.48 thf(fact_6657_real__less__lsqrt,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ ( sqrt @ X ) @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_less_lsqrt
% 5.17/5.48 thf(fact_6658_sqrt__sum__squares__le__sum,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt_sum_squares_le_sum
% 5.17/5.48 thf(fact_6659_sqrt__sum__squares__le__sum__abs,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt_sum_squares_le_sum_abs
% 5.17/5.48 thf(fact_6660_real__sqrt__ge__abs2,axiom,
% 5.17/5.48 ! [Y4: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_ge_abs2
% 5.17/5.48 thf(fact_6661_real__sqrt__ge__abs1,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_ge_abs1
% 5.17/5.48 thf(fact_6662_sqrt__even__pow2,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt_even_pow2
% 5.17/5.48 thf(fact_6663_ln__sqrt,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.17/5.48 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ln_sqrt
% 5.17/5.48 thf(fact_6664_arsinh__real__def,axiom,
% 5.17/5.48 ( arsinh_real
% 5.17/5.48 = ( ^ [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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arsinh_real_def
% 5.17/5.48 thf(fact_6665_take__bit__int__eq__self,axiom,
% 5.17/5.48 ! [K: int,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.48 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.48 = K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_eq_self
% 5.17/5.48 thf(fact_6666_take__bit__int__eq__self__iff,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.48 = K )
% 5.17/5.48 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.48 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_eq_self_iff
% 5.17/5.48 thf(fact_6667_and__int__rec,axiom,
% 5.17/5.48 ( bit_se725231765392027082nd_int
% 5.17/5.48 = ( ^ [K3: int,L3: int] :
% 5.17/5.48 ( plus_plus_int
% 5.17/5.48 @ ( zero_n2684676970156552555ol_int
% 5.17/5.48 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.17/5.48 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 5.17/5.48 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_int_rec
% 5.17/5.48 thf(fact_6668_take__bit__numeral__minus__bit0,axiom,
% 5.17/5.48 ! [L: num,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.17/5.48 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_minus_bit0
% 5.17/5.48 thf(fact_6669_take__bit__incr__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.48 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.17/5.48 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.17/5.48 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_incr_eq
% 5.17/5.48 thf(fact_6670_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.17/5.48 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.17/5.48 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_eq_mask_iff_exp_dvd
% 5.17/5.48 thf(fact_6671_exp__bound__half,axiom,
% 5.17/5.48 ! [Z: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_bound_half
% 5.17/5.48 thf(fact_6672_exp__bound__half,axiom,
% 5.17/5.48 ! [Z: complex] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_bound_half
% 5.17/5.48 thf(fact_6673_take__bit__Suc__minus__1__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.48 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_minus_1_eq
% 5.17/5.48 thf(fact_6674_take__bit__Suc__minus__1__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.48 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_minus_1_eq
% 5.17/5.48 thf(fact_6675_take__bit__Suc__bit1,axiom,
% 5.17/5.48 ! [N: nat,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.17/5.48 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_bit1
% 5.17/5.48 thf(fact_6676_take__bit__Suc__bit1,axiom,
% 5.17/5.48 ! [N: nat,K: num] :
% 5.17/5.48 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_bit1
% 5.17/5.48 thf(fact_6677_take__bit__numeral__minus__1__eq,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.48 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_minus_1_eq
% 5.17/5.48 thf(fact_6678_take__bit__numeral__minus__1__eq,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.48 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_minus_1_eq
% 5.17/5.48 thf(fact_6679_take__bit__Suc,axiom,
% 5.17/5.48 ! [N: nat,A: code_integer] :
% 5.17/5.48 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.17/5.48 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc
% 5.17/5.48 thf(fact_6680_take__bit__Suc,axiom,
% 5.17/5.48 ! [N: nat,A: int] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.17/5.48 = ( 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 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc
% 5.17/5.48 thf(fact_6681_take__bit__Suc,axiom,
% 5.17/5.48 ! [N: nat,A: nat] :
% 5.17/5.48 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.17/5.48 = ( 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 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc
% 5.17/5.48 thf(fact_6682_arsinh__real__aux,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arsinh_real_aux
% 5.17/5.48 thf(fact_6683_exp__bound,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_bound
% 5.17/5.48 thf(fact_6684_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.17/5.48 ! [X: real,Y4: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_mult_ge_zero
% 5.17/5.48 thf(fact_6685_real__sqrt__power__even,axiom,
% 5.17/5.48 ! [N: nat,X: real] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 5.17/5.48 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_power_even
% 5.17/5.48 thf(fact_6686_arith__geo__mean__sqrt,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y4 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arith_geo_mean_sqrt
% 5.17/5.48 thf(fact_6687_take__bit__int__less__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.48 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_less_eq
% 5.17/5.48 thf(fact_6688_take__bit__int__greater__eq,axiom,
% 5.17/5.48 ! [K: int,N: nat] :
% 5.17/5.48 ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_int_greater_eq
% 5.17/5.48 thf(fact_6689_even__nat__iff,axiom,
% 5.17/5.48 ! [K: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.48 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.17/5.48 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % even_nat_iff
% 5.17/5.48 thf(fact_6690_signed__take__bit__eq__take__bit__shift,axiom,
% 5.17/5.48 ( bit_ri631733984087533419it_int
% 5.17/5.48 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % signed_take_bit_eq_take_bit_shift
% 5.17/5.48 thf(fact_6691_num_Osize_I5_J,axiom,
% 5.17/5.48 ! [X2: num] :
% 5.17/5.48 ( ( size_size_num @ ( bit0 @ X2 ) )
% 5.17/5.48 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % num.size(5)
% 5.17/5.48 thf(fact_6692_stable__imp__take__bit__eq,axiom,
% 5.17/5.48 ! [A: code_integer,N: nat] :
% 5.17/5.48 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.48 = A )
% 5.17/5.48 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.17/5.48 = zero_z3403309356797280102nteger ) )
% 5.17/5.48 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.17/5.48 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % stable_imp_take_bit_eq
% 5.17/5.48 thf(fact_6693_stable__imp__take__bit__eq,axiom,
% 5.17/5.48 ! [A: int,N: nat] :
% 5.17/5.48 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.48 = A )
% 5.17/5.48 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.17/5.48 = zero_zero_int ) )
% 5.17/5.48 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.17/5.48 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % stable_imp_take_bit_eq
% 5.17/5.48 thf(fact_6694_stable__imp__take__bit__eq,axiom,
% 5.17/5.48 ! [A: nat,N: nat] :
% 5.17/5.48 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.48 = A )
% 5.17/5.48 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.17/5.48 = zero_zero_nat ) )
% 5.17/5.48 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.48 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.17/5.48 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % stable_imp_take_bit_eq
% 5.17/5.48 thf(fact_6695_num_Osize_I6_J,axiom,
% 5.17/5.48 ! [X33: num] :
% 5.17/5.48 ( ( size_size_num @ ( bit1 @ X33 ) )
% 5.17/5.48 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % num.size(6)
% 5.17/5.48 thf(fact_6696_take__bit__numeral__bit1,axiom,
% 5.17/5.48 ! [L: num,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.17/5.48 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_bit1
% 5.17/5.48 thf(fact_6697_take__bit__numeral__bit1,axiom,
% 5.17/5.48 ! [L: num,K: num] :
% 5.17/5.48 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_bit1
% 5.17/5.48 thf(fact_6698_real__exp__bound__lemma,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_exp_bound_lemma
% 5.17/5.48 thf(fact_6699_cos__x__y__le__one,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_x_y_le_one
% 5.17/5.48 thf(fact_6700_real__sqrt__sum__squares__less,axiom,
% 5.17/5.48 ! [X: real,U: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ ( abs_abs_real @ Y4 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_sqrt_sum_squares_less
% 5.17/5.48 thf(fact_6701_arcosh__real__def,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.48 => ( ( arcosh_real @ X )
% 5.17/5.48 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcosh_real_def
% 5.17/5.48 thf(fact_6702_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.17/5.48 ! [N: nat,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.48 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_ge_one_plus_x_over_n_power_n
% 5.17/5.48 thf(fact_6703_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.17/5.48 ! [X: real,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.48 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_ge_one_minus_x_over_n_power_n
% 5.17/5.48 thf(fact_6704_take__bit__minus__small__eq,axiom,
% 5.17/5.48 ! [K: int,N: nat] :
% 5.17/5.48 ( ( ord_less_int @ zero_zero_int @ K )
% 5.17/5.48 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.17/5.48 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_minus_small_eq
% 5.17/5.48 thf(fact_6705_exp__bound__lemma,axiom,
% 5.17/5.48 ! [Z: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( 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 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_bound_lemma
% 5.17/5.48 thf(fact_6706_exp__bound__lemma,axiom,
% 5.17/5.48 ! [Z: complex] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( 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 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_bound_lemma
% 5.17/5.48 thf(fact_6707_modulo__int__def,axiom,
% 5.17/5.48 ( modulo_modulo_int
% 5.17/5.48 = ( ^ [K3: int,L3: int] :
% 5.17/5.48 ( if_int @ ( L3 = zero_zero_int ) @ K3
% 5.17/5.48 @ ( if_int
% 5.17/5.48 @ ( ( sgn_sgn_int @ K3 )
% 5.17/5.48 = ( sgn_sgn_int @ L3 ) )
% 5.17/5.48 @ ( times_times_int @ ( sgn_sgn_int @ L3 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) ) )
% 5.17/5.48 @ ( times_times_int @ ( sgn_sgn_int @ L3 )
% 5.17/5.48 @ ( minus_minus_int
% 5.17/5.48 @ ( times_times_int @ ( abs_abs_int @ L3 )
% 5.17/5.48 @ ( zero_n2684676970156552555ol_int
% 5.17/5.48 @ ~ ( dvd_dvd_int @ L3 @ K3 ) ) )
% 5.17/5.48 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % modulo_int_def
% 5.17/5.48 thf(fact_6708_sqrt__sum__squares__half__less,axiom,
% 5.17/5.48 ! [X: real,U: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sqrt_sum_squares_half_less
% 5.17/5.48 thf(fact_6709_exp__lower__Taylor__quadratic,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % exp_lower_Taylor_quadratic
% 5.17/5.48 thf(fact_6710_take__bit__numeral__minus__bit1,axiom,
% 5.17/5.48 ! [L: num,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.17/5.48 = ( 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 ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_numeral_minus_bit1
% 5.17/5.48 thf(fact_6711_take__bit__Suc__minus__bit1,axiom,
% 5.17/5.48 ! [N: nat,K: num] :
% 5.17/5.48 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.17/5.48 = ( 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 ) ) ).
% 5.17/5.48
% 5.17/5.48 % take_bit_Suc_minus_bit1
% 5.17/5.48 thf(fact_6712_foldr__same__int,axiom,
% 5.17/5.48 ! [Xs: list_nat,Y4: nat] :
% 5.17/5.48 ( ! [X4: nat,Y: nat] :
% 5.17/5.48 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.17/5.48 => ( ( member_nat @ Y @ ( set_nat2 @ Xs ) )
% 5.17/5.48 => ( X4 = Y ) ) )
% 5.17/5.48 => ( ! [X4: nat] :
% 5.17/5.48 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.17/5.48 => ( X4 = Y4 ) )
% 5.17/5.48 => ( ( foldr_nat_nat @ plus_plus_nat @ Xs @ zero_zero_nat )
% 5.17/5.48 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % foldr_same_int
% 5.17/5.48 thf(fact_6713_log__base__10__eq1,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 = ( 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 @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_base_10_eq1
% 5.17/5.48 thf(fact_6714_log__base__10__eq2,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_base_10_eq2
% 5.17/5.48 thf(fact_6715_machin,axiom,
% 5.17/5.48 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % machin
% 5.17/5.48 thf(fact_6716_foldr__one,axiom,
% 5.17/5.48 ! [D: nat,Ys: list_nat] : ( ord_less_eq_nat @ D @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ).
% 5.17/5.48
% 5.17/5.48 % foldr_one
% 5.17/5.48 thf(fact_6717_log__one,axiom,
% 5.17/5.48 ! [A: real] :
% 5.17/5.48 ( ( log @ A @ one_one_real )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % log_one
% 5.17/5.48 thf(fact_6718_pred__numeral__inc,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( pred_numeral @ ( inc @ K ) )
% 5.17/5.48 = ( numeral_numeral_nat @ K ) ) ).
% 5.17/5.48
% 5.17/5.48 % pred_numeral_inc
% 5.17/5.48 thf(fact_6719_log__eq__one,axiom,
% 5.17/5.48 ! [A: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( log @ A @ A )
% 5.17/5.48 = one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_eq_one
% 5.17/5.48 thf(fact_6720_log__less__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) )
% 5.17/5.48 = ( ord_less_real @ X @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_less_cancel_iff
% 5.17/5.48 thf(fact_6721_log__less__one__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 5.17/5.48 = ( ord_less_real @ X @ A ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_less_one_cancel_iff
% 5.17/5.48 thf(fact_6722_one__less__log__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 5.17/5.48 = ( ord_less_real @ A @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_less_log_cancel_iff
% 5.17/5.48 thf(fact_6723_log__less__zero__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.17/5.48 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_less_zero_cancel_iff
% 5.17/5.48 thf(fact_6724_zero__less__log__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.17/5.48 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_less_log_cancel_iff
% 5.17/5.48 thf(fact_6725_log__le__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_le_cancel_iff
% 5.17/5.48 thf(fact_6726_log__le__one__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.17/5.48 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_le_one_cancel_iff
% 5.17/5.48 thf(fact_6727_one__le__log__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_le_log_cancel_iff
% 5.17/5.48 thf(fact_6728_log__le__zero__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.17/5.48 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_le_zero_cancel_iff
% 5.17/5.48 thf(fact_6729_zero__le__log__cancel__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_le_log_cancel_iff
% 5.17/5.48 thf(fact_6730_add__neg__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(6)
% 5.17/5.48 thf(fact_6731_add__neg__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(6)
% 5.17/5.48 thf(fact_6732_add__neg__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(6)
% 5.17/5.48 thf(fact_6733_add__neg__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.48 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(6)
% 5.17/5.48 thf(fact_6734_add__neg__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.48 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(6)
% 5.17/5.48 thf(fact_6735_add__neg__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(5)
% 5.17/5.48 thf(fact_6736_add__neg__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(5)
% 5.17/5.48 thf(fact_6737_add__neg__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.17/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(5)
% 5.17/5.48 thf(fact_6738_add__neg__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.48 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(5)
% 5.17/5.48 thf(fact_6739_add__neg__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.48 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_neg_numeral_special(5)
% 5.17/5.48 thf(fact_6740_diff__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.48 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(6)
% 5.17/5.48 thf(fact_6741_diff__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.48 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(6)
% 5.17/5.48 thf(fact_6742_diff__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.48 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(6)
% 5.17/5.48 thf(fact_6743_diff__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.48 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(6)
% 5.17/5.48 thf(fact_6744_diff__numeral__special_I6_J,axiom,
% 5.17/5.48 ! [M: num] :
% 5.17/5.48 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.17/5.48 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(6)
% 5.17/5.48 thf(fact_6745_diff__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(5)
% 5.17/5.48 thf(fact_6746_diff__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(5)
% 5.17/5.48 thf(fact_6747_diff__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.17/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(5)
% 5.17/5.48 thf(fact_6748_diff__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.17/5.48 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(5)
% 5.17/5.48 thf(fact_6749_diff__numeral__special_I5_J,axiom,
% 5.17/5.48 ! [N: num] :
% 5.17/5.48 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.48 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % diff_numeral_special(5)
% 5.17/5.48 thf(fact_6750_and__nat__numerals_I3_J,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.48 = zero_zero_nat ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_numerals(3)
% 5.17/5.48 thf(fact_6751_and__nat__numerals_I1_J,axiom,
% 5.17/5.48 ! [Y4: num] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.48 = zero_zero_nat ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_numerals(1)
% 5.17/5.48 thf(fact_6752_log__pow__cancel,axiom,
% 5.17/5.48 ! [A: real,B: nat] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.17/5.48 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_pow_cancel
% 5.17/5.48 thf(fact_6753_and__nat__numerals_I4_J,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.48 = one_one_nat ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_numerals(4)
% 5.17/5.48 thf(fact_6754_and__nat__numerals_I2_J,axiom,
% 5.17/5.48 ! [Y4: num] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.48 = one_one_nat ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_numerals(2)
% 5.17/5.48 thf(fact_6755_Suc__0__and__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.48 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Suc_0_and_eq
% 5.17/5.48 thf(fact_6756_and__Suc__0__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.48 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_Suc_0_eq
% 5.17/5.48 thf(fact_6757_pi__neq__zero,axiom,
% 5.17/5.48 pi != zero_zero_real ).
% 5.17/5.48
% 5.17/5.48 % pi_neq_zero
% 5.17/5.48 thf(fact_6758_num__induct,axiom,
% 5.17/5.48 ! [P: num > $o,X: num] :
% 5.17/5.48 ( ( P @ one )
% 5.17/5.48 => ( ! [X4: num] :
% 5.17/5.48 ( ( P @ X4 )
% 5.17/5.48 => ( P @ ( inc @ X4 ) ) )
% 5.17/5.48 => ( P @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % num_induct
% 5.17/5.48 thf(fact_6759_add__inc,axiom,
% 5.17/5.48 ! [X: num,Y4: num] :
% 5.17/5.48 ( ( plus_plus_num @ X @ ( inc @ Y4 ) )
% 5.17/5.48 = ( inc @ ( plus_plus_num @ X @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_inc
% 5.17/5.48 thf(fact_6760_log__def,axiom,
% 5.17/5.48 ( log
% 5.17/5.48 = ( ^ [A3: real,X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_def
% 5.17/5.48 thf(fact_6761_pi__gt__zero,axiom,
% 5.17/5.48 ord_less_real @ zero_zero_real @ pi ).
% 5.17/5.48
% 5.17/5.48 % pi_gt_zero
% 5.17/5.48 thf(fact_6762_pi__not__less__zero,axiom,
% 5.17/5.48 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % pi_not_less_zero
% 5.17/5.48 thf(fact_6763_pi__ge__zero,axiom,
% 5.17/5.48 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.17/5.48
% 5.17/5.48 % pi_ge_zero
% 5.17/5.48 thf(fact_6764_inc_Osimps_I1_J,axiom,
% 5.17/5.48 ( ( inc @ one )
% 5.17/5.48 = ( bit0 @ one ) ) ).
% 5.17/5.48
% 5.17/5.48 % inc.simps(1)
% 5.17/5.48 thf(fact_6765_inc_Osimps_I3_J,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( inc @ ( bit1 @ X ) )
% 5.17/5.48 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % inc.simps(3)
% 5.17/5.48 thf(fact_6766_inc_Osimps_I2_J,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( inc @ ( bit0 @ X ) )
% 5.17/5.48 = ( bit1 @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % inc.simps(2)
% 5.17/5.48 thf(fact_6767_add__One,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( plus_plus_num @ X @ one )
% 5.17/5.48 = ( inc @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_One
% 5.17/5.48 thf(fact_6768_and__nat__def,axiom,
% 5.17/5.48 ( bit_se727722235901077358nd_nat
% 5.17/5.48 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_def
% 5.17/5.48 thf(fact_6769_mult__inc,axiom,
% 5.17/5.48 ! [X: num,Y4: num] :
% 5.17/5.48 ( ( times_times_num @ X @ ( inc @ Y4 ) )
% 5.17/5.48 = ( plus_plus_num @ ( times_times_num @ X @ Y4 ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % mult_inc
% 5.17/5.48 thf(fact_6770_log__base__change,axiom,
% 5.17/5.48 ! [A: real,B: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( log @ B @ X )
% 5.17/5.48 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_base_change
% 5.17/5.48 thf(fact_6771_log__of__power__eq,axiom,
% 5.17/5.48 ! [M: nat,B: real,N: nat] :
% 5.17/5.48 ( ( ( semiri5074537144036343181t_real @ M )
% 5.17/5.48 = ( power_power_real @ B @ N ) )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( semiri5074537144036343181t_real @ N )
% 5.17/5.48 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_of_power_eq
% 5.17/5.48 thf(fact_6772_less__log__of__power,axiom,
% 5.17/5.48 ! [B: real,N: nat,M: real] :
% 5.17/5.48 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % less_log_of_power
% 5.17/5.48 thf(fact_6773_numeral__inc,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 5.17/5.48 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_inc
% 5.17/5.48 thf(fact_6774_numeral__inc,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( numeral_numeral_real @ ( inc @ X ) )
% 5.17/5.48 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_inc
% 5.17/5.48 thf(fact_6775_numeral__inc,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 5.17/5.48 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_inc
% 5.17/5.48 thf(fact_6776_numeral__inc,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 5.17/5.48 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_inc
% 5.17/5.48 thf(fact_6777_numeral__inc,axiom,
% 5.17/5.48 ! [X: num] :
% 5.17/5.48 ( ( numeral_numeral_int @ ( inc @ X ) )
% 5.17/5.48 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_inc
% 5.17/5.48 thf(fact_6778_pi__less__4,axiom,
% 5.17/5.48 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % pi_less_4
% 5.17/5.48 thf(fact_6779_pi__ge__two,axiom,
% 5.17/5.48 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.17/5.48
% 5.17/5.48 % pi_ge_two
% 5.17/5.48 thf(fact_6780_pi__half__neq__two,axiom,
% 5.17/5.48 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % pi_half_neq_two
% 5.17/5.48 thf(fact_6781_log__mult,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( log @ A @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.48 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_mult
% 5.17/5.48 thf(fact_6782_log__divide,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( log @ A @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.48 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_divide
% 5.17/5.48 thf(fact_6783_le__log__of__power,axiom,
% 5.17/5.48 ! [B: real,N: nat,M: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_log_of_power
% 5.17/5.48 thf(fact_6784_log__base__pow,axiom,
% 5.17/5.48 ! [A: real,N: nat,X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 5.17/5.48 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_base_pow
% 5.17/5.48 thf(fact_6785_log__nat__power,axiom,
% 5.17/5.48 ! [X: real,B: real,N: nat] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 5.17/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_nat_power
% 5.17/5.48 thf(fact_6786_pi__half__neq__zero,axiom,
% 5.17/5.48 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 != zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % pi_half_neq_zero
% 5.17/5.48 thf(fact_6787_pi__half__less__two,axiom,
% 5.17/5.48 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.17/5.48
% 5.17/5.48 % pi_half_less_two
% 5.17/5.48 thf(fact_6788_pi__half__le__two,axiom,
% 5.17/5.48 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.17/5.48
% 5.17/5.48 % pi_half_le_two
% 5.17/5.48 thf(fact_6789_log2__of__power__eq,axiom,
% 5.17/5.48 ! [M: nat,N: nat] :
% 5.17/5.48 ( ( M
% 5.17/5.48 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 => ( ( semiri5074537144036343181t_real @ N )
% 5.17/5.48 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log2_of_power_eq
% 5.17/5.48 thf(fact_6790_log__of__power__less,axiom,
% 5.17/5.48 ! [M: nat,B: real,N: nat] :
% 5.17/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.48 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_of_power_less
% 5.17/5.48 thf(fact_6791_log__eq__div__ln__mult__log,axiom,
% 5.17/5.48 ! [A: real,B: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ( B != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( log @ A @ X )
% 5.17/5.48 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_eq_div_ln_mult_log
% 5.17/5.48 thf(fact_6792_pi__half__gt__zero,axiom,
% 5.17/5.48 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % pi_half_gt_zero
% 5.17/5.48 thf(fact_6793_pi__half__ge__zero,axiom,
% 5.17/5.48 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % pi_half_ge_zero
% 5.17/5.48 thf(fact_6794_m2pi__less__pi,axiom,
% 5.17/5.48 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.17/5.48
% 5.17/5.48 % m2pi_less_pi
% 5.17/5.48 thf(fact_6795_arctan__ubound,axiom,
% 5.17/5.48 ! [Y4: real] : ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_ubound
% 5.17/5.48 thf(fact_6796_arctan__one,axiom,
% 5.17/5.48 ( ( arctan @ one_one_real )
% 5.17/5.48 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_one
% 5.17/5.48 thf(fact_6797_log__of__power__le,axiom,
% 5.17/5.48 ! [M: nat,B: real,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.48 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_of_power_le
% 5.17/5.48 thf(fact_6798_minus__pi__half__less__zero,axiom,
% 5.17/5.48 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.17/5.48
% 5.17/5.48 % minus_pi_half_less_zero
% 5.17/5.48 thf(fact_6799_arctan__lbound,axiom,
% 5.17/5.48 ! [Y4: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_lbound
% 5.17/5.48 thf(fact_6800_arctan__bounded,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) )
% 5.17/5.48 & ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_bounded
% 5.17/5.48 thf(fact_6801_and__nat__unfold,axiom,
% 5.17/5.48 ( bit_se727722235901077358nd_nat
% 5.17/5.48 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.48 ( if_nat
% 5.17/5.48 @ ( ( M5 = zero_zero_nat )
% 5.17/5.48 | ( N4 = zero_zero_nat ) )
% 5.17/5.48 @ zero_zero_nat
% 5.17/5.48 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M5 @ ( 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 @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_unfold
% 5.17/5.48 thf(fact_6802_less__log2__of__power,axiom,
% 5.17/5.48 ! [N: nat,M: nat] :
% 5.17/5.48 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.17/5.48 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % less_log2_of_power
% 5.17/5.48 thf(fact_6803_le__log2__of__power,axiom,
% 5.17/5.48 ! [N: nat,M: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.17/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_log2_of_power
% 5.17/5.48 thf(fact_6804_and__nat__rec,axiom,
% 5.17/5.48 ( bit_se727722235901077358nd_nat
% 5.17/5.48 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.48 ( plus_plus_nat
% 5.17/5.48 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.48 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 )
% 5.17/5.48 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.17/5.48 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % and_nat_rec
% 5.17/5.48 thf(fact_6805_log2__of__power__less,axiom,
% 5.17/5.48 ! [M: nat,N: nat] :
% 5.17/5.48 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.48 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log2_of_power_less
% 5.17/5.48 thf(fact_6806_log2__of__power__le,axiom,
% 5.17/5.48 ! [M: nat,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.48 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log2_of_power_le
% 5.17/5.48 thf(fact_6807_machin__Euler,axiom,
% 5.17/5.48 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % machin_Euler
% 5.17/5.48 thf(fact_6808_arctan__inverse,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( X != zero_zero_real )
% 5.17/5.48 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.17/5.48 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_inverse
% 5.17/5.48 thf(fact_6809_sin__cos__npi,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( 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 ) ) ) )
% 5.17/5.48 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_npi
% 5.17/5.48 thf(fact_6810_ceiling__log__nat__eq__powr__iff,axiom,
% 5.17/5.48 ! [B: nat,K: nat,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.48 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.17/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.17/5.48 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.17/5.48 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_log_nat_eq_powr_iff
% 5.17/5.48 thf(fact_6811_cos__pi__eq__zero,axiom,
% 5.17/5.48 ! [M: nat] :
% 5.17/5.48 ( ( 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 ) ) ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_pi_eq_zero
% 5.17/5.48 thf(fact_6812_ceiling__log__nat__eq__if,axiom,
% 5.17/5.48 ! [B: nat,N: nat,K: nat] :
% 5.17/5.48 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.17/5.48 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.17/5.48 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.48 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.17/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_log_nat_eq_if
% 5.17/5.48 thf(fact_6813_ceiling__log2__div2,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.48 = ( 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 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_log2_div2
% 5.17/5.48 thf(fact_6814_floor__log__nat__eq__powr__iff,axiom,
% 5.17/5.48 ! [B: nat,K: nat,N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.48 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.48 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.48 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.17/5.48 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_log_nat_eq_powr_iff
% 5.17/5.48 thf(fact_6815_sin__zero,axiom,
% 5.17/5.48 ( ( sin_complex @ zero_zero_complex )
% 5.17/5.48 = zero_zero_complex ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero
% 5.17/5.48 thf(fact_6816_sin__zero,axiom,
% 5.17/5.48 ( ( sin_real @ zero_zero_real )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero
% 5.17/5.48 thf(fact_6817_cos__zero,axiom,
% 5.17/5.48 ( ( cos_complex @ zero_zero_complex )
% 5.17/5.48 = one_one_complex ) ).
% 5.17/5.48
% 5.17/5.48 % cos_zero
% 5.17/5.48 thf(fact_6818_cos__zero,axiom,
% 5.17/5.48 ( ( cos_real @ zero_zero_real )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_zero
% 5.17/5.48 thf(fact_6819_floor__zero,axiom,
% 5.17/5.48 ( ( archim6058952711729229775r_real @ zero_zero_real )
% 5.17/5.48 = zero_zero_int ) ).
% 5.17/5.48
% 5.17/5.48 % floor_zero
% 5.17/5.48 thf(fact_6820_floor__zero,axiom,
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ zero_zero_rat )
% 5.17/5.48 = zero_zero_int ) ).
% 5.17/5.48
% 5.17/5.48 % floor_zero
% 5.17/5.48 thf(fact_6821_floor__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.17/5.48 = ( numeral_numeral_int @ V ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_numeral
% 5.17/5.48 thf(fact_6822_floor__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.17/5.48 = ( numeral_numeral_int @ V ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_numeral
% 5.17/5.48 thf(fact_6823_ceiling__zero,axiom,
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ zero_zero_rat )
% 5.17/5.48 = zero_zero_int ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_zero
% 5.17/5.48 thf(fact_6824_ceiling__zero,axiom,
% 5.17/5.48 ( ( archim7802044766580827645g_real @ zero_zero_real )
% 5.17/5.48 = zero_zero_int ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_zero
% 5.17/5.48 thf(fact_6825_ceiling__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.17/5.48 = ( numeral_numeral_int @ V ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_numeral
% 5.17/5.48 thf(fact_6826_ceiling__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.17/5.48 = ( numeral_numeral_int @ V ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_numeral
% 5.17/5.48 thf(fact_6827_sin__pi,axiom,
% 5.17/5.48 ( ( sin_real @ pi )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_pi
% 5.17/5.48 thf(fact_6828_floor__of__nat,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_of_nat
% 5.17/5.48 thf(fact_6829_floor__of__nat,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_of_nat
% 5.17/5.48 thf(fact_6830_ceiling__of__nat,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_of_nat
% 5.17/5.48 thf(fact_6831_ceiling__of__nat,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_of_nat
% 5.17/5.48 thf(fact_6832_sin__pi__minus,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 5.17/5.48 = ( sin_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_pi_minus
% 5.17/5.48 thf(fact_6833_cos__minus__pi,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_minus_pi
% 5.17/5.48 thf(fact_6834_cos__pi__minus,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_pi_minus
% 5.17/5.48 thf(fact_6835_sin__minus__pi,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_minus_pi
% 5.17/5.48 thf(fact_6836_zero__le__floor,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_le_floor
% 5.17/5.48 thf(fact_6837_zero__le__floor,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_le_floor
% 5.17/5.48 thf(fact_6838_sin__cos__squared__add3,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 5.17/5.48 = one_one_complex ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_squared_add3
% 5.17/5.48 thf(fact_6839_sin__cos__squared__add3,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_squared_add3
% 5.17/5.48 thf(fact_6840_floor__less__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_less_zero
% 5.17/5.48 thf(fact_6841_floor__less__zero,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_less_zero
% 5.17/5.48 thf(fact_6842_numeral__le__floor,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_le_floor
% 5.17/5.48 thf(fact_6843_numeral__le__floor,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_le_floor
% 5.17/5.48 thf(fact_6844_zero__less__floor,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_less_floor
% 5.17/5.48 thf(fact_6845_zero__less__floor,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_less_floor
% 5.17/5.48 thf(fact_6846_floor__le__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_zero
% 5.17/5.48 thf(fact_6847_floor__le__zero,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_zero
% 5.17/5.48 thf(fact_6848_ceiling__le__zero,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_zero
% 5.17/5.48 thf(fact_6849_ceiling__le__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_zero
% 5.17/5.48 thf(fact_6850_floor__less__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_less_numeral
% 5.17/5.48 thf(fact_6851_floor__less__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_less_numeral
% 5.17/5.48 thf(fact_6852_zero__less__ceiling,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_less_ceiling
% 5.17/5.48 thf(fact_6853_zero__less__ceiling,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_less_ceiling
% 5.17/5.48 thf(fact_6854_one__le__floor,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ one_one_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_le_floor
% 5.17/5.48 thf(fact_6855_one__le__floor,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_le_floor
% 5.17/5.48 thf(fact_6856_ceiling__le__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_numeral
% 5.17/5.48 thf(fact_6857_ceiling__le__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( numeral_numeral_real @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_numeral
% 5.17/5.48 thf(fact_6858_ceiling__less__one,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_one
% 5.17/5.48 thf(fact_6859_ceiling__less__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.17/5.48 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_one
% 5.17/5.48 thf(fact_6860_one__le__ceiling,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_le_ceiling
% 5.17/5.48 thf(fact_6861_one__le__ceiling,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_le_ceiling
% 5.17/5.48 thf(fact_6862_numeral__less__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_less_ceiling
% 5.17/5.48 thf(fact_6863_numeral__less__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_less_ceiling
% 5.17/5.48 thf(fact_6864_floor__neg__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_neg_numeral
% 5.17/5.48 thf(fact_6865_floor__neg__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_neg_numeral
% 5.17/5.48 thf(fact_6866_ceiling__le__one,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_one
% 5.17/5.48 thf(fact_6867_ceiling__le__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int )
% 5.17/5.48 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_one
% 5.17/5.48 thf(fact_6868_ceiling__add__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.48 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_add_numeral
% 5.17/5.48 thf(fact_6869_ceiling__add__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.48 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_add_numeral
% 5.17/5.48 thf(fact_6870_floor__diff__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_diff_numeral
% 5.17/5.48 thf(fact_6871_floor__diff__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_diff_numeral
% 5.17/5.48 thf(fact_6872_ceiling__neg__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_neg_numeral
% 5.17/5.48 thf(fact_6873_ceiling__neg__numeral,axiom,
% 5.17/5.48 ! [V: num] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_neg_numeral
% 5.17/5.48 thf(fact_6874_floor__diff__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_diff_one
% 5.17/5.48 thf(fact_6875_floor__diff__one,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_diff_one
% 5.17/5.48 thf(fact_6876_ceiling__diff__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_numeral
% 5.17/5.48 thf(fact_6877_ceiling__diff__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_numeral
% 5.17/5.48 thf(fact_6878_ceiling__diff__one,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_one
% 5.17/5.48 thf(fact_6879_ceiling__diff__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ one_one_real ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_one
% 5.17/5.48 thf(fact_6880_floor__numeral__power,axiom,
% 5.17/5.48 ! [X: num,N: nat] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.17/5.48 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_numeral_power
% 5.17/5.48 thf(fact_6881_floor__numeral__power,axiom,
% 5.17/5.48 ! [X: num,N: nat] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.17/5.48 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_numeral_power
% 5.17/5.48 thf(fact_6882_ceiling__numeral__power,axiom,
% 5.17/5.48 ! [X: num,N: nat] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.17/5.48 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_numeral_power
% 5.17/5.48 thf(fact_6883_ceiling__numeral__power,axiom,
% 5.17/5.48 ! [X: num,N: nat] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.17/5.48 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_numeral_power
% 5.17/5.48 thf(fact_6884_sin__npi2,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_npi2
% 5.17/5.48 thf(fact_6885_sin__npi,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_npi
% 5.17/5.48 thf(fact_6886_floor__divide__eq__div__numeral,axiom,
% 5.17/5.48 ! [A: num,B: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.17/5.48 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_divide_eq_div_numeral
% 5.17/5.48 thf(fact_6887_nat__ceiling__le__eq,axiom,
% 5.17/5.48 ! [X: real,A: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_ceiling_le_eq
% 5.17/5.48 thf(fact_6888_ceiling__less__zero,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_zero
% 5.17/5.48 thf(fact_6889_ceiling__less__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_zero
% 5.17/5.48 thf(fact_6890_zero__le__ceiling,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_le_ceiling
% 5.17/5.48 thf(fact_6891_zero__le__ceiling,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_le_ceiling
% 5.17/5.48 thf(fact_6892_ceiling__divide__eq__div__numeral,axiom,
% 5.17/5.48 ! [A: num,B: num] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_divide_eq_div_numeral
% 5.17/5.48 thf(fact_6893_numeral__less__floor,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_less_floor
% 5.17/5.48 thf(fact_6894_numeral__less__floor,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_less_floor
% 5.17/5.48 thf(fact_6895_floor__le__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_real @ X @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_numeral
% 5.17/5.48 thf(fact_6896_floor__le__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_numeral
% 5.17/5.48 thf(fact_6897_one__less__floor,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_less_floor
% 5.17/5.48 thf(fact_6898_one__less__floor,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_less_floor
% 5.17/5.48 thf(fact_6899_floor__le__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int )
% 5.17/5.48 = ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_one
% 5.17/5.48 thf(fact_6900_floor__le__one,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.17/5.48 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_one
% 5.17/5.48 thf(fact_6901_ceiling__less__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_numeral
% 5.17/5.48 thf(fact_6902_ceiling__less__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_numeral
% 5.17/5.48 thf(fact_6903_numeral__le__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_le_ceiling
% 5.17/5.48 thf(fact_6904_numeral__le__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_le_ceiling
% 5.17/5.48 thf(fact_6905_neg__numeral__le__floor,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_le_floor
% 5.17/5.48 thf(fact_6906_neg__numeral__le__floor,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_le_floor
% 5.17/5.48 thf(fact_6907_floor__less__neg__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_less_neg_numeral
% 5.17/5.48 thf(fact_6908_floor__less__neg__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_less_neg_numeral
% 5.17/5.48 thf(fact_6909_ceiling__le__neg__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_neg_numeral
% 5.17/5.48 thf(fact_6910_ceiling__le__neg__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_le_neg_numeral
% 5.17/5.48 thf(fact_6911_neg__numeral__less__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_less_ceiling
% 5.17/5.48 thf(fact_6912_neg__numeral__less__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_less_ceiling
% 5.17/5.48 thf(fact_6913_cos__pi__half,axiom,
% 5.17/5.48 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_pi_half
% 5.17/5.48 thf(fact_6914_sin__two__pi,axiom,
% 5.17/5.48 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_two_pi
% 5.17/5.48 thf(fact_6915_sin__pi__half,axiom,
% 5.17/5.48 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_pi_half
% 5.17/5.48 thf(fact_6916_cos__two__pi,axiom,
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_two_pi
% 5.17/5.48 thf(fact_6917_cos__periodic,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.17/5.48 = ( cos_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_periodic
% 5.17/5.48 thf(fact_6918_sin__periodic,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.17/5.48 = ( sin_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_periodic
% 5.17/5.48 thf(fact_6919_cos__2pi__minus,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.17/5.48 = ( cos_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_2pi_minus
% 5.17/5.48 thf(fact_6920_cos__npi2,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.48 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_npi2
% 5.17/5.48 thf(fact_6921_cos__npi,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.17/5.48 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_npi
% 5.17/5.48 thf(fact_6922_floor__one__divide__eq__div__numeral,axiom,
% 5.17/5.48 ! [B: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.17/5.48 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_one_divide_eq_div_numeral
% 5.17/5.48 thf(fact_6923_floor__minus__divide__eq__div__numeral,axiom,
% 5.17/5.48 ! [A: num,B: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.17/5.48 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_minus_divide_eq_div_numeral
% 5.17/5.48 thf(fact_6924_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.17/5.48 ! [A: num,B: num] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_minus_divide_eq_div_numeral
% 5.17/5.48 thf(fact_6925_sin__cos__squared__add2,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_squared_add2
% 5.17/5.48 thf(fact_6926_sin__cos__squared__add2,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_complex ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_squared_add2
% 5.17/5.48 thf(fact_6927_sin__cos__squared__add,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_squared_add
% 5.17/5.48 thf(fact_6928_sin__cos__squared__add,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_complex ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_squared_add
% 5.17/5.48 thf(fact_6929_sin__2npi,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_2npi
% 5.17/5.48 thf(fact_6930_cos__2npi,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_2npi
% 5.17/5.48 thf(fact_6931_sin__2pi__minus,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_2pi_minus
% 5.17/5.48 thf(fact_6932_neg__numeral__less__floor,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_less_floor
% 5.17/5.48 thf(fact_6933_neg__numeral__less__floor,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_less_floor
% 5.17/5.48 thf(fact_6934_floor__le__neg__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_real @ X @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_neg_numeral
% 5.17/5.48 thf(fact_6935_floor__le__neg__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_neg_numeral
% 5.17/5.48 thf(fact_6936_ceiling__less__neg__numeral,axiom,
% 5.17/5.48 ! [X: rat,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_neg_numeral
% 5.17/5.48 thf(fact_6937_ceiling__less__neg__numeral,axiom,
% 5.17/5.48 ! [X: real,V: num] :
% 5.17/5.48 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_less_neg_numeral
% 5.17/5.48 thf(fact_6938_neg__numeral__le__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: real] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_le_ceiling
% 5.17/5.48 thf(fact_6939_neg__numeral__le__ceiling,axiom,
% 5.17/5.48 ! [V: num,X: rat] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % neg_numeral_le_ceiling
% 5.17/5.48 thf(fact_6940_cos__3over2__pi,axiom,
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_3over2_pi
% 5.17/5.48 thf(fact_6941_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.17/5.48 ! [B: num] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.17/5.48 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_minus_one_divide_eq_div_numeral
% 5.17/5.48 thf(fact_6942_sin__3over2__pi,axiom,
% 5.17/5.48 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.17/5.48 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_3over2_pi
% 5.17/5.48 thf(fact_6943_sin__add,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( sin_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.48 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_add
% 5.17/5.48 thf(fact_6944_floor__le__ceiling,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim7802044766580827645g_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_ceiling
% 5.17/5.48 thf(fact_6945_floor__le__ceiling,axiom,
% 5.17/5.48 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim2889992004027027881ng_rat @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_le_ceiling
% 5.17/5.48 thf(fact_6946_polar__Ex,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ? [R3: real,A4: real] :
% 5.17/5.48 ( ( X
% 5.17/5.48 = ( times_times_real @ R3 @ ( cos_real @ A4 ) ) )
% 5.17/5.48 & ( Y4
% 5.17/5.48 = ( times_times_real @ R3 @ ( sin_real @ A4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % polar_Ex
% 5.17/5.48 thf(fact_6947_sin__diff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( sin_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.48 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_diff
% 5.17/5.48 thf(fact_6948_cos__one__sin__zero,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( ( cos_complex @ X )
% 5.17/5.48 = one_one_complex )
% 5.17/5.48 => ( ( sin_complex @ X )
% 5.17/5.48 = zero_zero_complex ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_one_sin_zero
% 5.17/5.48 thf(fact_6949_cos__one__sin__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 => ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_one_sin_zero
% 5.17/5.48 thf(fact_6950_cos__add,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( cos_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.48 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_add
% 5.17/5.48 thf(fact_6951_cos__diff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( cos_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.48 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_diff
% 5.17/5.48 thf(fact_6952_sin__zero__norm__cos__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 5.17/5.48 = one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero_norm_cos_one
% 5.17/5.48 thf(fact_6953_sin__zero__norm__cos__one,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( ( sin_complex @ X )
% 5.17/5.48 = zero_zero_complex )
% 5.17/5.48 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 5.17/5.48 = one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero_norm_cos_one
% 5.17/5.48 thf(fact_6954_ceiling__diff__floor__le__1,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) @ one_one_int ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_floor_le_1
% 5.17/5.48 thf(fact_6955_ceiling__diff__floor__le__1,axiom,
% 5.17/5.48 ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_floor_le_1
% 5.17/5.48 thf(fact_6956_sin__zero__abs__cos__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 5.17/5.48 = one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero_abs_cos_one
% 5.17/5.48 thf(fact_6957_sin__double,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_double
% 5.17/5.48 thf(fact_6958_sin__double,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_double
% 5.17/5.48 thf(fact_6959_sincos__principal__value,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ? [Y: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.17/5.48 & ( ord_less_eq_real @ Y @ pi )
% 5.17/5.48 & ( ( sin_real @ Y )
% 5.17/5.48 = ( sin_real @ X ) )
% 5.17/5.48 & ( ( cos_real @ Y )
% 5.17/5.48 = ( cos_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sincos_principal_value
% 5.17/5.48 thf(fact_6960_floor__mono,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_mono
% 5.17/5.48 thf(fact_6961_floor__mono,axiom,
% 5.17/5.48 ! [X: rat,Y4: rat] :
% 5.17/5.48 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.48 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_mono
% 5.17/5.48 thf(fact_6962_ceiling__mono,axiom,
% 5.17/5.48 ! [Y4: rat,X: rat] :
% 5.17/5.48 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.48 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y4 ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_mono
% 5.17/5.48 thf(fact_6963_ceiling__mono,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.48 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y4 ) @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_mono
% 5.17/5.48 thf(fact_6964_sin__x__le__x,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_x_le_x
% 5.17/5.48 thf(fact_6965_sin__le__one,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_le_one
% 5.17/5.48 thf(fact_6966_cos__le__one,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_le_one
% 5.17/5.48 thf(fact_6967_abs__sin__x__le__abs__x,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % abs_sin_x_le_abs_x
% 5.17/5.48 thf(fact_6968_cos__arctan__not__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( arctan @ X ) )
% 5.17/5.48 != zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_arctan_not_zero
% 5.17/5.48 thf(fact_6969_sin__cos__le1,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) @ one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_le1
% 5.17/5.48 thf(fact_6970_sin__squared__eq,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.48 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_squared_eq
% 5.17/5.48 thf(fact_6971_sin__squared__eq,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.48 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_squared_eq
% 5.17/5.48 thf(fact_6972_cos__squared__eq,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.48 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_squared_eq
% 5.17/5.48 thf(fact_6973_cos__squared__eq,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.48 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_squared_eq
% 5.17/5.48 thf(fact_6974_le__floor__add,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ ( archim6058952711729229775r_real @ Y4 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_floor_add
% 5.17/5.48 thf(fact_6975_le__floor__add,axiom,
% 5.17/5.48 ! [X: rat,Y4: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y4 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_floor_add
% 5.17/5.48 thf(fact_6976_of__nat__ceiling,axiom,
% 5.17/5.48 ! [R2: rat] : ( ord_less_eq_rat @ R2 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R2 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_ceiling
% 5.17/5.48 thf(fact_6977_of__nat__ceiling,axiom,
% 5.17/5.48 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R2 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_ceiling
% 5.17/5.48 thf(fact_6978_sin__gt__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ pi )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_gt_zero
% 5.17/5.48 thf(fact_6979_sin__x__ge__neg__x,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_x_ge_neg_x
% 5.17/5.48 thf(fact_6980_sin__ge__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_ge_zero
% 5.17/5.48 thf(fact_6981_real__nat__ceiling__ge,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % real_nat_ceiling_ge
% 5.17/5.48 thf(fact_6982_ceiling__add__le,axiom,
% 5.17/5.48 ! [X: rat,Y4: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y4 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_add_le
% 5.17/5.48 thf(fact_6983_ceiling__add__le,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X ) @ ( archim7802044766580827645g_real @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_add_le
% 5.17/5.48 thf(fact_6984_sin__ge__minus__one,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_ge_minus_one
% 5.17/5.48 thf(fact_6985_cos__monotone__0__pi__le,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.48 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_monotone_0_pi_le
% 5.17/5.48 thf(fact_6986_cos__mono__le__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ pi )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) )
% 5.17/5.48 = ( ord_less_eq_real @ Y4 @ X ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_mono_le_eq
% 5.17/5.48 thf(fact_6987_cos__inj__pi,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ pi )
% 5.17/5.48 => ( ( ( cos_real @ X )
% 5.17/5.48 = ( cos_real @ Y4 ) )
% 5.17/5.48 => ( X = Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_inj_pi
% 5.17/5.48 thf(fact_6988_cos__ge__minus__one,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_ge_minus_one
% 5.17/5.48 thf(fact_6989_abs__sin__le__one,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % abs_sin_le_one
% 5.17/5.48 thf(fact_6990_abs__cos__le__one,axiom,
% 5.17/5.48 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % abs_cos_le_one
% 5.17/5.48 thf(fact_6991_sin__times__sin,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_times_sin
% 5.17/5.48 thf(fact_6992_sin__times__sin,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_times_sin
% 5.17/5.48 thf(fact_6993_sin__times__cos,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_times_cos
% 5.17/5.48 thf(fact_6994_sin__times__cos,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_times_cos
% 5.17/5.48 thf(fact_6995_cos__times__sin,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_times_sin
% 5.17/5.48 thf(fact_6996_cos__times__sin,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_times_sin
% 5.17/5.48 thf(fact_6997_sin__plus__sin,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_plus_sin
% 5.17/5.48 thf(fact_6998_sin__plus__sin,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_plus_sin
% 5.17/5.48 thf(fact_6999_sin__diff__sin,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_diff_sin
% 5.17/5.48 thf(fact_7000_sin__diff__sin,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_diff_sin
% 5.17/5.48 thf(fact_7001_cos__diff__cos,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_diff_cos
% 5.17/5.48 thf(fact_7002_cos__diff__cos,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_diff_cos
% 5.17/5.48 thf(fact_7003_cos__double,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double
% 5.17/5.48 thf(fact_7004_cos__double,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double
% 5.17/5.48 thf(fact_7005_cos__double__sin,axiom,
% 5.17/5.48 ! [W: complex] :
% 5.17/5.48 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.17/5.48 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double_sin
% 5.17/5.48 thf(fact_7006_cos__double__sin,axiom,
% 5.17/5.48 ! [W: real] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double_sin
% 5.17/5.48 thf(fact_7007_of__nat__floor,axiom,
% 5.17/5.48 ! [R2: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.17/5.48 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R2 ) ) ) @ R2 ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_floor
% 5.17/5.48 thf(fact_7008_of__nat__floor,axiom,
% 5.17/5.48 ! [R2: rat] :
% 5.17/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.17/5.48 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R2 ) ) ) @ R2 ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_floor
% 5.17/5.48 thf(fact_7009_le__mult__nat__floor,axiom,
% 5.17/5.48 ! [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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_mult_nat_floor
% 5.17/5.48 thf(fact_7010_le__mult__nat__floor,axiom,
% 5.17/5.48 ! [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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_mult_nat_floor
% 5.17/5.48 thf(fact_7011_floor__divide__of__nat__eq,axiom,
% 5.17/5.48 ! [M: nat,N: nat] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_divide_of_nat_eq
% 5.17/5.48 thf(fact_7012_floor__divide__of__nat__eq,axiom,
% 5.17/5.48 ! [M: nat,N: nat] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_divide_of_nat_eq
% 5.17/5.48 thf(fact_7013_nat__floor__neg,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.48 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = zero_zero_nat ) ) ).
% 5.17/5.48
% 5.17/5.48 % nat_floor_neg
% 5.17/5.48 thf(fact_7014_cos__two__neq__zero,axiom,
% 5.17/5.48 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 != zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % cos_two_neq_zero
% 5.17/5.48 thf(fact_7015_floor__eq3,axiom,
% 5.17/5.48 ! [N: nat,X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.17/5.48 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_eq3
% 5.17/5.48 thf(fact_7016_le__nat__floor,axiom,
% 5.17/5.48 ! [X: nat,A: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.17/5.48 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_nat_floor
% 5.17/5.48 thf(fact_7017_cos__monotone__0__pi,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.48 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_monotone_0_pi
% 5.17/5.48 thf(fact_7018_cos__mono__less__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ pi )
% 5.17/5.48 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) )
% 5.17/5.48 = ( ord_less_real @ Y4 @ X ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_mono_less_eq
% 5.17/5.48 thf(fact_7019_sin__eq__0__pi,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ pi )
% 5.17/5.48 => ( ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 => ( X = zero_zero_real ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_eq_0_pi
% 5.17/5.48 thf(fact_7020_sin__zero__pi__iff,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 5.17/5.48 => ( ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 = ( X = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero_pi_iff
% 5.17/5.48 thf(fact_7021_cos__monotone__minus__pi__0_H,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.48 => ( ord_less_eq_real @ ( cos_real @ Y4 ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_monotone_minus_pi_0'
% 5.17/5.48 thf(fact_7022_sincos__total__pi,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 => ? [T3: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.48 & ( ord_less_eq_real @ T3 @ pi )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( cos_real @ T3 ) )
% 5.17/5.48 & ( Y4
% 5.17/5.48 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sincos_total_pi
% 5.17/5.48 thf(fact_7023_sin__cos__sqrt,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.17/5.48 => ( ( sin_real @ X )
% 5.17/5.48 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_cos_sqrt
% 5.17/5.48 thf(fact_7024_sin__expansion__lemma,axiom,
% 5.17/5.48 ! [X: real,M: nat] :
% 5.17/5.48 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_expansion_lemma
% 5.17/5.48 thf(fact_7025_le__mult__floor,axiom,
% 5.17/5.48 ! [A: real,B: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_mult_floor
% 5.17/5.48 thf(fact_7026_le__mult__floor,axiom,
% 5.17/5.48 ! [A: rat,B: rat] :
% 5.17/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.48 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_mult_floor
% 5.17/5.48 thf(fact_7027_cos__expansion__lemma,axiom,
% 5.17/5.48 ! [X: real,M: nat] :
% 5.17/5.48 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_expansion_lemma
% 5.17/5.48 thf(fact_7028_sin__gt__zero__02,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_gt_zero_02
% 5.17/5.48 thf(fact_7029_mult__ceiling__le,axiom,
% 5.17/5.48 ! [A: rat,B: rat] :
% 5.17/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.48 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.17/5.48 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % mult_ceiling_le
% 5.17/5.48 thf(fact_7030_mult__ceiling__le,axiom,
% 5.17/5.48 ! [A: real,B: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % mult_ceiling_le
% 5.17/5.48 thf(fact_7031_floor__eq4,axiom,
% 5.17/5.48 ! [N: nat,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.17/5.48 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_eq4
% 5.17/5.48 thf(fact_7032_cos__two__less__zero,axiom,
% 5.17/5.48 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.17/5.48
% 5.17/5.48 % cos_two_less_zero
% 5.17/5.48 thf(fact_7033_cos__two__le__zero,axiom,
% 5.17/5.48 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.17/5.48
% 5.17/5.48 % cos_two_le_zero
% 5.17/5.48 thf(fact_7034_cos__is__zero,axiom,
% 5.17/5.48 ? [X4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.17/5.48 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 & ( ( cos_real @ X4 )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 & ! [Y3: real] :
% 5.17/5.48 ( ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.17/5.48 & ( ord_less_eq_real @ Y3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 & ( ( cos_real @ Y3 )
% 5.17/5.48 = zero_zero_real ) )
% 5.17/5.48 => ( Y3 = X4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_is_zero
% 5.17/5.48 thf(fact_7035_cos__monotone__minus__pi__0,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.48 => ( ord_less_real @ ( cos_real @ Y4 ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_monotone_minus_pi_0
% 5.17/5.48 thf(fact_7036_cos__total,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ? [X4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.17/5.48 & ( ord_less_eq_real @ X4 @ pi )
% 5.17/5.48 & ( ( cos_real @ X4 )
% 5.17/5.48 = Y4 )
% 5.17/5.48 & ! [Y3: real] :
% 5.17/5.48 ( ( ( ord_less_eq_real @ zero_zero_real @ Y3 )
% 5.17/5.48 & ( ord_less_eq_real @ Y3 @ pi )
% 5.17/5.48 & ( ( cos_real @ Y3 )
% 5.17/5.48 = Y4 ) )
% 5.17/5.48 => ( Y3 = X4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_total
% 5.17/5.48 thf(fact_7037_sincos__total__pi__half,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 => ? [T3: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.48 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( cos_real @ T3 ) )
% 5.17/5.48 & ( Y4
% 5.17/5.48 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sincos_total_pi_half
% 5.17/5.48 thf(fact_7038_sincos__total__2pi__le,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 => ? [T3: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.48 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( cos_real @ T3 ) )
% 5.17/5.48 & ( Y4
% 5.17/5.48 = ( sin_real @ T3 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sincos_total_2pi_le
% 5.17/5.48 thf(fact_7039_sincos__total__2pi,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 => ~ ! [T3: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.48 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 => ( ( X
% 5.17/5.48 = ( cos_real @ T3 ) )
% 5.17/5.48 => ( Y4
% 5.17/5.48 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sincos_total_2pi
% 5.17/5.48 thf(fact_7040_sin__pi__divide__n__ge__0,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( N != zero_zero_nat )
% 5.17/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_pi_divide_n_ge_0
% 5.17/5.48 thf(fact_7041_sin__45,axiom,
% 5.17/5.48 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_45
% 5.17/5.48 thf(fact_7042_cos__45,axiom,
% 5.17/5.48 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_45
% 5.17/5.48 thf(fact_7043_cos__times__cos,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_times_cos
% 5.17/5.48 thf(fact_7044_cos__times__cos,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_times_cos
% 5.17/5.48 thf(fact_7045_cos__plus__cos,axiom,
% 5.17/5.48 ! [W: complex,Z: complex] :
% 5.17/5.48 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_plus_cos
% 5.17/5.48 thf(fact_7046_cos__plus__cos,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.17/5.48 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_plus_cos
% 5.17/5.48 thf(fact_7047_sin__gt__zero2,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_gt_zero2
% 5.17/5.48 thf(fact_7048_sin__lt__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ pi @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_lt_zero
% 5.17/5.48 thf(fact_7049_cos__double__less__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.48 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double_less_one
% 5.17/5.48 thf(fact_7050_sin__30,axiom,
% 5.17/5.48 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_30
% 5.17/5.48 thf(fact_7051_cos__gt__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_gt_zero
% 5.17/5.48 thf(fact_7052_sin__monotone__2pi__le,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( sin_real @ Y4 ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_monotone_2pi_le
% 5.17/5.48 thf(fact_7053_sin__mono__le__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_mono_le_eq
% 5.17/5.48 thf(fact_7054_sin__inj__pi,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ( sin_real @ X )
% 5.17/5.48 = ( sin_real @ Y4 ) )
% 5.17/5.48 => ( X = Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_inj_pi
% 5.17/5.48 thf(fact_7055_cos__60,axiom,
% 5.17/5.48 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_60
% 5.17/5.48 thf(fact_7056_sin__60,axiom,
% 5.17/5.48 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_60
% 5.17/5.48 thf(fact_7057_cos__30,axiom,
% 5.17/5.48 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_30
% 5.17/5.48 thf(fact_7058_cos__double__cos,axiom,
% 5.17/5.48 ! [W: complex] :
% 5.17/5.48 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.17/5.48 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double_cos
% 5.17/5.48 thf(fact_7059_cos__double__cos,axiom,
% 5.17/5.48 ! [W: real] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.17/5.48 = ( 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 ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_double_cos
% 5.17/5.48 thf(fact_7060_cos__treble__cos,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 5.17/5.48 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_treble_cos
% 5.17/5.48 thf(fact_7061_cos__treble__cos,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 5.17/5.48 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_treble_cos
% 5.17/5.48 thf(fact_7062_sin__le__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ pi @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_le_zero
% 5.17/5.48 thf(fact_7063_sin__less__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.48 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_less_zero
% 5.17/5.48 thf(fact_7064_sin__monotone__2pi,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ ( sin_real @ Y4 ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_monotone_2pi
% 5.17/5.48 thf(fact_7065_sin__mono__less__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y4 ) )
% 5.17/5.48 = ( ord_less_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_mono_less_eq
% 5.17/5.48 thf(fact_7066_sin__total,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ? [X4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.17/5.48 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( sin_real @ X4 )
% 5.17/5.48 = Y4 )
% 5.17/5.48 & ! [Y3: real] :
% 5.17/5.48 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.17/5.48 & ( ord_less_eq_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( sin_real @ Y3 )
% 5.17/5.48 = Y4 ) )
% 5.17/5.48 => ( Y3 = X4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_total
% 5.17/5.48 thf(fact_7067_cos__gt__zero__pi,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_gt_zero_pi
% 5.17/5.48 thf(fact_7068_cos__ge__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_ge_zero
% 5.17/5.48 thf(fact_7069_cos__one__2pi,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 = ( ? [X3: nat] :
% 5.17/5.48 ( X
% 5.17/5.48 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.17/5.48 | ? [X3: nat] :
% 5.17/5.48 ( X
% 5.17/5.48 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_one_2pi
% 5.17/5.48 thf(fact_7070_sin__pi__divide__n__gt__0,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_pi_divide_n_gt_0
% 5.17/5.48 thf(fact_7071_sin__arctan,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( sin_real @ ( arctan @ X ) )
% 5.17/5.48 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_arctan
% 5.17/5.48 thf(fact_7072_cos__arctan,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( cos_real @ ( arctan @ X ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_arctan
% 5.17/5.48 thf(fact_7073_floor__log2__div2,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.48 = ( 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 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_log2_div2
% 5.17/5.48 thf(fact_7074_floor__log__nat__eq__if,axiom,
% 5.17/5.48 ! [B: nat,N: nat,K: nat] :
% 5.17/5.48 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.17/5.48 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.17/5.48 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.17/5.48 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_log_nat_eq_if
% 5.17/5.48 thf(fact_7075_sin__zero__lemma,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 => ? [N2: nat] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero_lemma
% 5.17/5.48 thf(fact_7076_sin__zero__iff,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( sin_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 = ( ? [N4: nat] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.48 | ? [N4: nat] :
% 5.17/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_zero_iff
% 5.17/5.48 thf(fact_7077_cos__zero__lemma,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ( cos_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 => ? [N2: nat] :
% 5.17/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_zero_lemma
% 5.17/5.48 thf(fact_7078_cos__zero__iff,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 = ( ? [N4: nat] :
% 5.17/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.48 | ? [N4: nat] :
% 5.17/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 5.17/5.48 & ( X
% 5.17/5.48 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_zero_iff
% 5.17/5.48 thf(fact_7079_tan__double,axiom,
% 5.17/5.48 ! [X: complex] :
% 5.17/5.48 ( ( ( cos_complex @ X )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_double
% 5.17/5.48 thf(fact_7080_tan__double,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.48 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_double
% 5.17/5.48 thf(fact_7081_sin__tan,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( sin_real @ X )
% 5.17/5.48 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_tan
% 5.17/5.48 thf(fact_7082_cos__tan,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( cos_real @ X )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_tan
% 5.17/5.48 thf(fact_7083_complex__unimodular__polar,axiom,
% 5.17/5.48 ! [Z: complex] :
% 5.17/5.48 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 => ~ ! [T3: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.48 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.48 => ( Z
% 5.17/5.48 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % complex_unimodular_polar
% 5.17/5.48 thf(fact_7084_ceiling__log__eq__powr__iff,axiom,
% 5.17/5.48 ! [X: real,B: real,K: nat] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.17/5.48 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.17/5.48 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.17/5.48 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_log_eq_powr_iff
% 5.17/5.48 thf(fact_7085_cos__arcsin,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ( cos_real @ ( arcsin @ X ) )
% 5.17/5.48 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_arcsin
% 5.17/5.48 thf(fact_7086_powr__eq__0__iff,axiom,
% 5.17/5.48 ! [W: real,Z: real] :
% 5.17/5.48 ( ( ( powr_real @ W @ Z )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 = ( W = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_eq_0_iff
% 5.17/5.48 thf(fact_7087_powr__0,axiom,
% 5.17/5.48 ! [Z: real] :
% 5.17/5.48 ( ( powr_real @ zero_zero_real @ Z )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % powr_0
% 5.17/5.48 thf(fact_7088_tan__zero,axiom,
% 5.17/5.48 ( ( tan_complex @ zero_zero_complex )
% 5.17/5.48 = zero_zero_complex ) ).
% 5.17/5.48
% 5.17/5.48 % tan_zero
% 5.17/5.48 thf(fact_7089_tan__zero,axiom,
% 5.17/5.48 ( ( tan_real @ zero_zero_real )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % tan_zero
% 5.17/5.48 thf(fact_7090_arcsin__0,axiom,
% 5.17/5.48 ( ( arcsin @ zero_zero_real )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_0
% 5.17/5.48 thf(fact_7091_powr__zero__eq__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( X = zero_zero_real )
% 5.17/5.48 => ( ( powr_real @ X @ zero_zero_real )
% 5.17/5.48 = zero_zero_real ) )
% 5.17/5.48 & ( ( X != zero_zero_real )
% 5.17/5.48 => ( ( powr_real @ X @ zero_zero_real )
% 5.17/5.48 = one_one_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_zero_eq_one
% 5.17/5.48 thf(fact_7092_powr__gt__zero,axiom,
% 5.17/5.48 ! [X: real,A: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 5.17/5.48 = ( X != zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_gt_zero
% 5.17/5.48 thf(fact_7093_powr__nonneg__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.17/5.48 = ( A = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_nonneg_iff
% 5.17/5.48 thf(fact_7094_tan__pi,axiom,
% 5.17/5.48 ( ( tan_real @ pi )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % tan_pi
% 5.17/5.48 thf(fact_7095_powr__eq__one__iff,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ A )
% 5.17/5.48 => ( ( ( powr_real @ A @ X )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 = ( X = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_eq_one_iff
% 5.17/5.48 thf(fact_7096_powr__one__gt__zero__iff,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( powr_real @ X @ one_one_real )
% 5.17/5.48 = X )
% 5.17/5.48 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_one_gt_zero_iff
% 5.17/5.48 thf(fact_7097_powr__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ X @ one_one_real )
% 5.17/5.48 = X ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_one
% 5.17/5.48 thf(fact_7098_powr__le__cancel__iff,axiom,
% 5.17/5.48 ! [X: real,A: real,B: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.17/5.48 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_le_cancel_iff
% 5.17/5.48 thf(fact_7099_numeral__powr__numeral__real,axiom,
% 5.17/5.48 ! [M: num,N: num] :
% 5.17/5.48 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.48 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % numeral_powr_numeral_real
% 5.17/5.48 thf(fact_7100_powr__log__cancel,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 5.17/5.48 = X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_log_cancel
% 5.17/5.48 thf(fact_7101_log__powr__cancel,axiom,
% 5.17/5.48 ! [A: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( log @ A @ ( powr_real @ A @ Y4 ) )
% 5.17/5.48 = Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_powr_cancel
% 5.17/5.48 thf(fact_7102_tan__npi,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % tan_npi
% 5.17/5.48 thf(fact_7103_tan__periodic__n,axiom,
% 5.17/5.48 ! [X: real,N: num] :
% 5.17/5.48 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.17/5.48 = ( tan_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_periodic_n
% 5.17/5.48 thf(fact_7104_tan__periodic__nat,axiom,
% 5.17/5.48 ! [X: real,N: nat] :
% 5.17/5.48 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.17/5.48 = ( tan_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_periodic_nat
% 5.17/5.48 thf(fact_7105_sin__arcsin,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.17/5.48 = Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_arcsin
% 5.17/5.48 thf(fact_7106_powr__numeral,axiom,
% 5.17/5.48 ! [X: real,N: num] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 5.17/5.48 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_numeral
% 5.17/5.48 thf(fact_7107_arcsin__1,axiom,
% 5.17/5.48 ( ( arcsin @ one_one_real )
% 5.17/5.48 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_1
% 5.17/5.48 thf(fact_7108_tan__periodic,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.17/5.48 = ( tan_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_periodic
% 5.17/5.48 thf(fact_7109_arcsin__minus__1,axiom,
% 5.17/5.48 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_minus_1
% 5.17/5.48 thf(fact_7110_square__powr__half,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = ( abs_abs_real @ X ) ) ).
% 5.17/5.48
% 5.17/5.48 % square_powr_half
% 5.17/5.48 thf(fact_7111_powr__powr,axiom,
% 5.17/5.48 ! [X: real,A: real,B: real] :
% 5.17/5.48 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.17/5.48 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_powr
% 5.17/5.48 thf(fact_7112_Complex__eq__0,axiom,
% 5.17/5.48 ! [A: real,B: real] :
% 5.17/5.48 ( ( ( complex2 @ A @ B )
% 5.17/5.48 = zero_zero_complex )
% 5.17/5.48 = ( ( A = zero_zero_real )
% 5.17/5.48 & ( B = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Complex_eq_0
% 5.17/5.48 thf(fact_7113_zero__complex_Ocode,axiom,
% 5.17/5.48 ( zero_zero_complex
% 5.17/5.48 = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % zero_complex.code
% 5.17/5.48 thf(fact_7114_complex__diff,axiom,
% 5.17/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.48 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.17/5.48 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % complex_diff
% 5.17/5.48 thf(fact_7115_powr__less__mono2__neg,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_real @ ( powr_real @ Y4 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_less_mono2_neg
% 5.17/5.48 thf(fact_7116_powr__non__neg,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % powr_non_neg
% 5.17/5.48 thf(fact_7117_powr__ge__pzero,axiom,
% 5.17/5.48 ! [X: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y4 ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_ge_pzero
% 5.17/5.48 thf(fact_7118_powr__mono2,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_mono2
% 5.17/5.48 thf(fact_7119_powr__mono,axiom,
% 5.17/5.48 ! [A: real,B: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.48 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.48 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_mono
% 5.17/5.48 thf(fact_7120_Complex__eq__1,axiom,
% 5.17/5.48 ! [A: real,B: real] :
% 5.17/5.48 ( ( ( complex2 @ A @ B )
% 5.17/5.48 = one_one_complex )
% 5.17/5.48 = ( ( A = one_one_real )
% 5.17/5.48 & ( B = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Complex_eq_1
% 5.17/5.48 thf(fact_7121_one__complex_Ocode,axiom,
% 5.17/5.48 ( one_one_complex
% 5.17/5.48 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % one_complex.code
% 5.17/5.48 thf(fact_7122_Complex__eq__numeral,axiom,
% 5.17/5.48 ! [A: real,B: real,W: num] :
% 5.17/5.48 ( ( ( complex2 @ A @ B )
% 5.17/5.48 = ( numera6690914467698888265omplex @ W ) )
% 5.17/5.48 = ( ( A
% 5.17/5.48 = ( numeral_numeral_real @ W ) )
% 5.17/5.48 & ( B = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Complex_eq_numeral
% 5.17/5.48 thf(fact_7123_powr__less__mono2,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_less_mono2
% 5.17/5.48 thf(fact_7124_powr__mono2_H,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ ( powr_real @ Y4 @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_mono2'
% 5.17/5.48 thf(fact_7125_gr__one__powr,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % gr_one_powr
% 5.17/5.48 thf(fact_7126_powr__inj,axiom,
% 5.17/5.48 ! [A: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( A != one_one_real )
% 5.17/5.48 => ( ( ( powr_real @ A @ X )
% 5.17/5.48 = ( powr_real @ A @ Y4 ) )
% 5.17/5.48 = ( X = Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_inj
% 5.17/5.48 thf(fact_7127_ge__one__powr__ge__zero,axiom,
% 5.17/5.48 ! [X: real,A: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ge_one_powr_ge_zero
% 5.17/5.48 thf(fact_7128_powr__mono__both,axiom,
% 5.17/5.48 ! [A: real,B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.48 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_mono_both
% 5.17/5.48 thf(fact_7129_powr__le1,axiom,
% 5.17/5.48 ! [A: real,X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_le1
% 5.17/5.48 thf(fact_7130_powr__divide,axiom,
% 5.17/5.48 ! [X: real,Y4: real,A: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( powr_real @ ( divide_divide_real @ X @ Y4 ) @ A )
% 5.17/5.48 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_divide
% 5.17/5.48 thf(fact_7131_powr__mult,axiom,
% 5.17/5.48 ! [X: real,Y4: real,A: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ( ( powr_real @ ( times_times_real @ X @ Y4 ) @ A )
% 5.17/5.48 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_mult
% 5.17/5.48 thf(fact_7132_divide__powr__uminus,axiom,
% 5.17/5.48 ! [A: real,B: real,C: real] :
% 5.17/5.48 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.17/5.48 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % divide_powr_uminus
% 5.17/5.48 thf(fact_7133_ln__powr,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( X != zero_zero_real )
% 5.17/5.48 => ( ( ln_ln_real @ ( powr_real @ X @ Y4 ) )
% 5.17/5.48 = ( times_times_real @ Y4 @ ( ln_ln_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ln_powr
% 5.17/5.48 thf(fact_7134_log__base__powr,axiom,
% 5.17/5.48 ! [A: real,B: real,X: real] :
% 5.17/5.48 ( ( A != zero_zero_real )
% 5.17/5.48 => ( ( log @ ( powr_real @ A @ B ) @ X )
% 5.17/5.48 = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_base_powr
% 5.17/5.48 thf(fact_7135_log__powr,axiom,
% 5.17/5.48 ! [X: real,B: real,Y4: real] :
% 5.17/5.48 ( ( X != zero_zero_real )
% 5.17/5.48 => ( ( log @ B @ ( powr_real @ X @ Y4 ) )
% 5.17/5.48 = ( times_times_real @ Y4 @ ( log @ B @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_powr
% 5.17/5.48 thf(fact_7136_Complex__eq__neg__1,axiom,
% 5.17/5.48 ! [A: real,B: real] :
% 5.17/5.48 ( ( ( complex2 @ A @ B )
% 5.17/5.48 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.17/5.48 = ( ( A
% 5.17/5.48 = ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.48 & ( B = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Complex_eq_neg_1
% 5.17/5.48 thf(fact_7137_Complex__eq__neg__numeral,axiom,
% 5.17/5.48 ! [A: real,B: real,W: num] :
% 5.17/5.48 ( ( ( complex2 @ A @ B )
% 5.17/5.48 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.48 = ( ( A
% 5.17/5.48 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.48 & ( B = zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % Complex_eq_neg_numeral
% 5.17/5.48 thf(fact_7138_powr__add,axiom,
% 5.17/5.48 ! [X: real,A: real,B: real] :
% 5.17/5.48 ( ( powr_real @ X @ ( plus_plus_real @ A @ B ) )
% 5.17/5.48 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_add
% 5.17/5.48 thf(fact_7139_powr__diff,axiom,
% 5.17/5.48 ! [W: real,Z1: real,Z22: real] :
% 5.17/5.48 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.17/5.48 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_diff
% 5.17/5.48 thf(fact_7140_complex__mult,axiom,
% 5.17/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.48 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.17/5.48 = ( 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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % complex_mult
% 5.17/5.48 thf(fact_7141_arcsin__le__arcsin,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_le_arcsin
% 5.17/5.48 thf(fact_7142_arcsin__minus,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_minus
% 5.17/5.48 thf(fact_7143_arcsin__le__mono,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_le_mono
% 5.17/5.48 thf(fact_7144_arcsin__eq__iff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.48 => ( ( ( arcsin @ X )
% 5.17/5.48 = ( arcsin @ Y4 ) )
% 5.17/5.48 = ( X = Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_eq_iff
% 5.17/5.48 thf(fact_7145_tan__def,axiom,
% 5.17/5.48 ( tan_complex
% 5.17/5.48 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X3 ) @ ( cos_complex @ X3 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_def
% 5.17/5.48 thf(fact_7146_tan__def,axiom,
% 5.17/5.48 ( tan_real
% 5.17/5.48 = ( ^ [X3: real] : ( divide_divide_real @ ( sin_real @ X3 ) @ ( cos_real @ X3 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_def
% 5.17/5.48 thf(fact_7147_powr__realpow,axiom,
% 5.17/5.48 ! [X: real,N: nat] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.48 = ( power_power_real @ X @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_realpow
% 5.17/5.48 thf(fact_7148_powr__less__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ ( powr_real @ B @ Y4 ) @ X )
% 5.17/5.48 = ( ord_less_real @ Y4 @ ( log @ B @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_less_iff
% 5.17/5.48 thf(fact_7149_less__powr__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y4 ) )
% 5.17/5.48 = ( ord_less_real @ ( log @ B @ X ) @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % less_powr_iff
% 5.17/5.48 thf(fact_7150_log__less__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ ( log @ B @ X ) @ Y4 )
% 5.17/5.48 = ( ord_less_real @ X @ ( powr_real @ B @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_less_iff
% 5.17/5.48 thf(fact_7151_less__log__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ ( log @ B @ X ) )
% 5.17/5.48 = ( ord_less_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % less_log_iff
% 5.17/5.48 thf(fact_7152_powr__minus__divide,axiom,
% 5.17/5.48 ! [X: real,A: real] :
% 5.17/5.48 ( ( powr_real @ X @ ( uminus_uminus_real @ A ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_minus_divide
% 5.17/5.48 thf(fact_7153_powr__neg__one,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_neg_one
% 5.17/5.48 thf(fact_7154_arcsin__less__arcsin,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_less_arcsin
% 5.17/5.48 thf(fact_7155_powr__mult__base,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( times_times_real @ X @ ( powr_real @ X @ Y4 ) )
% 5.17/5.48 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_mult_base
% 5.17/5.48 thf(fact_7156_arcsin__less__mono,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y4 ) )
% 5.17/5.48 = ( ord_less_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_less_mono
% 5.17/5.48 thf(fact_7157_le__log__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( log @ B @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_log_iff
% 5.17/5.48 thf(fact_7158_log__le__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y4 )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_le_iff
% 5.17/5.48 thf(fact_7159_le__powr__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y4 ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_powr_iff
% 5.17/5.48 thf(fact_7160_powr__le__iff,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y4 ) @ X )
% 5.17/5.48 = ( ord_less_eq_real @ Y4 @ ( log @ B @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_le_iff
% 5.17/5.48 thf(fact_7161_ln__powr__bound,axiom,
% 5.17/5.48 ! [X: real,A: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ln_powr_bound
% 5.17/5.48 thf(fact_7162_ln__powr__bound2,axiom,
% 5.17/5.48 ! [X: real,A: real] :
% 5.17/5.48 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.48 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % ln_powr_bound2
% 5.17/5.48 thf(fact_7163_tan__45,axiom,
% 5.17/5.48 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % tan_45
% 5.17/5.48 thf(fact_7164_log__add__eq__powr,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ( B != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y4 )
% 5.17/5.48 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_add_eq_powr
% 5.17/5.48 thf(fact_7165_add__log__eq__powr,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ( B != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( plus_plus_real @ Y4 @ ( log @ B @ X ) )
% 5.17/5.48 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_log_eq_powr
% 5.17/5.48 thf(fact_7166_minus__log__eq__powr,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ( B != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( minus_minus_real @ Y4 @ ( log @ B @ X ) )
% 5.17/5.48 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y4 ) @ X ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % minus_log_eq_powr
% 5.17/5.48 thf(fact_7167_tan__60,axiom,
% 5.17/5.48 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.17/5.48 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_60
% 5.17/5.48 thf(fact_7168_cos__arcsin__nonzero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.48 => ( ( cos_real @ ( arcsin @ X ) )
% 5.17/5.48 != zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_arcsin_nonzero
% 5.17/5.48 thf(fact_7169_powr__def,axiom,
% 5.17/5.48 ( powr_real
% 5.17/5.48 = ( ^ [X3: real,A3: real] : ( if_real @ ( X3 = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X3 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_def
% 5.17/5.48 thf(fact_7170_lemma__tan__total,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ? [X4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.17/5.48 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ord_less_real @ Y4 @ ( tan_real @ X4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % lemma_tan_total
% 5.17/5.48 thf(fact_7171_tan__gt__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_gt_zero
% 5.17/5.48 thf(fact_7172_lemma__tan__total1,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ? [X4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.17/5.48 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( tan_real @ X4 )
% 5.17/5.48 = Y4 ) ) ).
% 5.17/5.48
% 5.17/5.48 % lemma_tan_total1
% 5.17/5.48 thf(fact_7173_tan__mono__lt__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) )
% 5.17/5.48 = ( ord_less_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_mono_lt_eq
% 5.17/5.48 thf(fact_7174_tan__monotone_H,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ X )
% 5.17/5.48 = ( ord_less_real @ ( tan_real @ Y4 ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_monotone'
% 5.17/5.48 thf(fact_7175_tan__monotone,axiom,
% 5.17/5.48 ! [Y4: real,X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_real @ ( tan_real @ Y4 ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_monotone
% 5.17/5.48 thf(fact_7176_tan__total,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ? [X4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.17/5.48 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( tan_real @ X4 )
% 5.17/5.48 = Y4 )
% 5.17/5.48 & ! [Y3: real] :
% 5.17/5.48 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y3 )
% 5.17/5.48 & ( ord_less_real @ Y3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( tan_real @ Y3 )
% 5.17/5.48 = Y4 ) )
% 5.17/5.48 => ( Y3 = X4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_total
% 5.17/5.48 thf(fact_7177_tan__minus__45,axiom,
% 5.17/5.48 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.48 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_minus_45
% 5.17/5.48 thf(fact_7178_tan__inverse,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y4 ) )
% 5.17/5.48 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_inverse
% 5.17/5.48 thf(fact_7179_log__minus__eq__powr,axiom,
% 5.17/5.48 ! [B: real,X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.48 => ( ( B != one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y4 )
% 5.17/5.48 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % log_minus_eq_powr
% 5.17/5.48 thf(fact_7180_complex__norm,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y4 ) )
% 5.17/5.48 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % complex_norm
% 5.17/5.48 thf(fact_7181_add__tan__eq,axiom,
% 5.17/5.48 ! [X: complex,Y4: complex] :
% 5.17/5.48 ( ( ( cos_complex @ X )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ Y4 )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_tan_eq
% 5.17/5.48 thf(fact_7182_add__tan__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ Y4 )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) )
% 5.17/5.48 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % add_tan_eq
% 5.17/5.48 thf(fact_7183_powr__half__sqrt,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 = ( sqrt @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_half_sqrt
% 5.17/5.48 thf(fact_7184_powr__neg__numeral,axiom,
% 5.17/5.48 ! [X: real,N: num] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % powr_neg_numeral
% 5.17/5.48 thf(fact_7185_tan__total__pos,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.48 => ? [X4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.17/5.48 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( tan_real @ X4 )
% 5.17/5.48 = Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_total_pos
% 5.17/5.48 thf(fact_7186_tan__pos__pi2__le,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_pos_pi2_le
% 5.17/5.48 thf(fact_7187_tan__less__zero,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.48 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_less_zero
% 5.17/5.48 thf(fact_7188_tan__mono__le,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_mono_le
% 5.17/5.48 thf(fact_7189_tan__mono__le__eq,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) )
% 5.17/5.48 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_mono_le_eq
% 5.17/5.48 thf(fact_7190_tan__bound__pi2,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_bound_pi2
% 5.17/5.48 thf(fact_7191_tan__30,axiom,
% 5.17/5.48 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.17/5.48 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_30
% 5.17/5.48 thf(fact_7192_arctan__unique,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ( tan_real @ X )
% 5.17/5.48 = Y4 )
% 5.17/5.48 => ( ( arctan @ Y4 )
% 5.17/5.48 = X ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_unique
% 5.17/5.48 thf(fact_7193_arctan__tan,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( arctan @ ( tan_real @ X ) )
% 5.17/5.48 = X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan_tan
% 5.17/5.48 thf(fact_7194_arctan,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) )
% 5.17/5.48 & ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( tan_real @ ( arctan @ Y4 ) )
% 5.17/5.48 = Y4 ) ) ).
% 5.17/5.48
% 5.17/5.48 % arctan
% 5.17/5.48 thf(fact_7195_lemma__tan__add1,axiom,
% 5.17/5.48 ! [X: complex,Y4: complex] :
% 5.17/5.48 ( ( ( cos_complex @ X )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ Y4 )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X @ Y4 ) ) @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % lemma_tan_add1
% 5.17/5.48 thf(fact_7196_lemma__tan__add1,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ Y4 )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) )
% 5.17/5.48 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y4 ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % lemma_tan_add1
% 5.17/5.48 thf(fact_7197_tan__diff,axiom,
% 5.17/5.48 ! [X: complex,Y4: complex] :
% 5.17/5.48 ( ( ( cos_complex @ X )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ Y4 )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( tan_complex @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_diff
% 5.17/5.48 thf(fact_7198_tan__diff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ Y4 )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( tan_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.48 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_diff
% 5.17/5.48 thf(fact_7199_tan__add,axiom,
% 5.17/5.48 ! [X: complex,Y4: complex] :
% 5.17/5.48 ( ( ( cos_complex @ X )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ Y4 )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( ( cos_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.17/5.48 != zero_zero_complex )
% 5.17/5.48 => ( ( tan_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X ) @ ( tan_complex @ Y4 ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_add
% 5.17/5.48 thf(fact_7200_tan__add,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ( cos_real @ X )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ Y4 )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( ( cos_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.48 != zero_zero_real )
% 5.17/5.48 => ( ( tan_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.48 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X ) @ ( tan_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_add
% 5.17/5.48 thf(fact_7201_tan__total__pi4,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.48 => ? [Z2: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.17/5.48 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.48 & ( ( tan_real @ Z2 )
% 5.17/5.48 = X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_total_pi4
% 5.17/5.48 thf(fact_7202_arcsin__lt__bounded,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.17/5.48 & ( ord_less_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_lt_bounded
% 5.17/5.48 thf(fact_7203_arcsin__lbound,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_lbound
% 5.17/5.48 thf(fact_7204_arcsin__ubound,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_ubound
% 5.17/5.48 thf(fact_7205_arcsin__bounded,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.17/5.48 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_bounded
% 5.17/5.48 thf(fact_7206_arcsin__sin,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( arcsin @ ( sin_real @ X ) )
% 5.17/5.48 = X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_sin
% 5.17/5.48 thf(fact_7207_tan__half,axiom,
% 5.17/5.48 ( tan_complex
% 5.17/5.48 = ( ^ [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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_half
% 5.17/5.48 thf(fact_7208_tan__half,axiom,
% 5.17/5.48 ( tan_real
% 5.17/5.48 = ( ^ [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 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % tan_half
% 5.17/5.48 thf(fact_7209_arcsin,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.17/5.48 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 & ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.17/5.48 = Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin
% 5.17/5.48 thf(fact_7210_arcsin__pi,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.17/5.48 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ pi )
% 5.17/5.48 & ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.17/5.48 = Y4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_pi
% 5.17/5.48 thf(fact_7211_arcsin__le__iff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y4 )
% 5.17/5.48 = ( ord_less_eq_real @ X @ ( sin_real @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcsin_le_iff
% 5.17/5.48 thf(fact_7212_le__arcsin__iff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.48 => ( ( ord_less_eq_real @ Y4 @ ( arcsin @ X ) )
% 5.17/5.48 = ( ord_less_eq_real @ ( sin_real @ Y4 ) @ X ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % le_arcsin_iff
% 5.17/5.48 thf(fact_7213_arcosh__def,axiom,
% 5.17/5.48 ( arcosh_real
% 5.17/5.48 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arcosh_def
% 5.17/5.48 thf(fact_7214_sin__arccos__abs,axiom,
% 5.17/5.48 ! [Y4: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.48 => ( ( sin_real @ ( arccos @ Y4 ) )
% 5.17/5.48 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_arccos_abs
% 5.17/5.48 thf(fact_7215_sin__arccos,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.48 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.48 => ( ( sin_real @ ( arccos @ X ) )
% 5.17/5.48 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % sin_arccos
% 5.17/5.48 thf(fact_7216_arsinh__def,axiom,
% 5.17/5.48 ( arsinh_real
% 5.17/5.48 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % arsinh_def
% 5.17/5.48 thf(fact_7217_cos__npi__int,axiom,
% 5.17/5.48 ! [N: int] :
% 5.17/5.48 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.17/5.48 = one_one_real ) )
% 5.17/5.48 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.48 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.17/5.48 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % cos_npi_int
% 5.17/5.48 thf(fact_7218_of__int__eq__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ W )
% 5.17/5.48 = ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( W = Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_iff
% 5.17/5.48 thf(fact_7219_of__int__eq__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ( ring_17405671764205052669omplex @ W )
% 5.17/5.48 = ( ring_17405671764205052669omplex @ Z ) )
% 5.17/5.48 = ( W = Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_iff
% 5.17/5.48 thf(fact_7220_of__int__eq__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ W )
% 5.17/5.48 = ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( W = Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_iff
% 5.17/5.48 thf(fact_7221_of__int__floor__cancel,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.48 = X )
% 5.17/5.48 = ( ? [N4: int] :
% 5.17/5.48 ( X
% 5.17/5.48 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_floor_cancel
% 5.17/5.48 thf(fact_7222_of__int__floor__cancel,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.48 = X )
% 5.17/5.48 = ( ? [N4: int] :
% 5.17/5.48 ( X
% 5.17/5.48 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_floor_cancel
% 5.17/5.48 thf(fact_7223_of__int__ceiling__cancel,axiom,
% 5.17/5.48 ! [X: rat] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.48 = X )
% 5.17/5.48 = ( ? [N4: int] :
% 5.17/5.48 ( X
% 5.17/5.48 = ( ring_1_of_int_rat @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_ceiling_cancel
% 5.17/5.48 thf(fact_7224_of__int__ceiling__cancel,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.48 = X )
% 5.17/5.48 = ( ? [N4: int] :
% 5.17/5.48 ( X
% 5.17/5.48 = ( ring_1_of_int_real @ N4 ) ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_ceiling_cancel
% 5.17/5.48 thf(fact_7225_of__int__eq__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_int @ Z )
% 5.17/5.48 = zero_zero_int )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_0_iff
% 5.17/5.48 thf(fact_7226_of__int__eq__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ Z )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_0_iff
% 5.17/5.48 thf(fact_7227_of__int__eq__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.17/5.48 = zero_zero_complex )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_0_iff
% 5.17/5.48 thf(fact_7228_of__int__eq__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ Z )
% 5.17/5.48 = zero_zero_rat )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_0_iff
% 5.17/5.48 thf(fact_7229_of__int__0__eq__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( zero_zero_int
% 5.17/5.48 = ( ring_1_of_int_int @ Z ) )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_eq_iff
% 5.17/5.48 thf(fact_7230_of__int__0__eq__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( zero_zero_real
% 5.17/5.48 = ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_eq_iff
% 5.17/5.48 thf(fact_7231_of__int__0__eq__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( zero_zero_complex
% 5.17/5.48 = ( ring_17405671764205052669omplex @ Z ) )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_eq_iff
% 5.17/5.48 thf(fact_7232_of__int__0__eq__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( zero_zero_rat
% 5.17/5.48 = ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( Z = zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_eq_iff
% 5.17/5.48 thf(fact_7233_of__int__0,axiom,
% 5.17/5.48 ( ( ring_1_of_int_int @ zero_zero_int )
% 5.17/5.48 = zero_zero_int ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0
% 5.17/5.48 thf(fact_7234_of__int__0,axiom,
% 5.17/5.48 ( ( ring_1_of_int_real @ zero_zero_int )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0
% 5.17/5.48 thf(fact_7235_of__int__0,axiom,
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 5.17/5.48 = zero_zero_complex ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0
% 5.17/5.48 thf(fact_7236_of__int__0,axiom,
% 5.17/5.48 ( ( ring_1_of_int_rat @ zero_zero_int )
% 5.17/5.48 = zero_zero_rat ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0
% 5.17/5.48 thf(fact_7237_of__real__0,axiom,
% 5.17/5.48 ( ( real_V1803761363581548252l_real @ zero_zero_real )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_0
% 5.17/5.48 thf(fact_7238_of__real__0,axiom,
% 5.17/5.48 ( ( real_V4546457046886955230omplex @ zero_zero_real )
% 5.17/5.48 = zero_zero_complex ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_0
% 5.17/5.48 thf(fact_7239_of__real__eq__0__iff,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( real_V1803761363581548252l_real @ X )
% 5.17/5.48 = zero_zero_real )
% 5.17/5.48 = ( X = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_eq_0_iff
% 5.17/5.48 thf(fact_7240_of__real__eq__0__iff,axiom,
% 5.17/5.48 ! [X: real] :
% 5.17/5.48 ( ( ( real_V4546457046886955230omplex @ X )
% 5.17/5.48 = zero_zero_complex )
% 5.17/5.48 = ( X = zero_zero_real ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_eq_0_iff
% 5.17/5.48 thf(fact_7241_of__int__le__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_iff
% 5.17/5.48 thf(fact_7242_of__int__le__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_iff
% 5.17/5.48 thf(fact_7243_of__int__le__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_iff
% 5.17/5.48 thf(fact_7244_of__int__eq__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.17/5.48 = ( numera6690914467698888265omplex @ N ) )
% 5.17/5.48 = ( Z
% 5.17/5.48 = ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_numeral_iff
% 5.17/5.48 thf(fact_7245_of__int__eq__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ Z )
% 5.17/5.48 = ( numeral_numeral_real @ N ) )
% 5.17/5.48 = ( Z
% 5.17/5.48 = ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_numeral_iff
% 5.17/5.48 thf(fact_7246_of__int__eq__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ Z )
% 5.17/5.48 = ( numeral_numeral_rat @ N ) )
% 5.17/5.48 = ( Z
% 5.17/5.48 = ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_numeral_iff
% 5.17/5.48 thf(fact_7247_of__int__eq__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ( ring_1_of_int_int @ Z )
% 5.17/5.48 = ( numeral_numeral_int @ N ) )
% 5.17/5.48 = ( Z
% 5.17/5.48 = ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_numeral_iff
% 5.17/5.48 thf(fact_7248_of__int__numeral,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.17/5.48 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral
% 5.17/5.48 thf(fact_7249_of__int__numeral,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.17/5.48 = ( numeral_numeral_real @ K ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral
% 5.17/5.48 thf(fact_7250_of__int__numeral,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.17/5.48 = ( numeral_numeral_rat @ K ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral
% 5.17/5.48 thf(fact_7251_of__int__numeral,axiom,
% 5.17/5.48 ! [K: num] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.17/5.48 = ( numeral_numeral_int @ K ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral
% 5.17/5.48 thf(fact_7252_of__int__less__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( ord_less_int @ W @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_less_iff
% 5.17/5.48 thf(fact_7253_of__int__less__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( ord_less_int @ W @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_less_iff
% 5.17/5.48 thf(fact_7254_of__int__less__iff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.48 = ( ord_less_int @ W @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_less_iff
% 5.17/5.48 thf(fact_7255_of__int__eq__1__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_int @ Z )
% 5.17/5.48 = one_one_int )
% 5.17/5.48 = ( Z = one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_1_iff
% 5.17/5.48 thf(fact_7256_of__int__eq__1__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ Z )
% 5.17/5.48 = one_one_real )
% 5.17/5.48 = ( Z = one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_1_iff
% 5.17/5.48 thf(fact_7257_of__int__eq__1__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.17/5.48 = one_one_complex )
% 5.17/5.48 = ( Z = one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_1_iff
% 5.17/5.48 thf(fact_7258_of__int__eq__1__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ Z )
% 5.17/5.48 = one_one_rat )
% 5.17/5.48 = ( Z = one_one_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_1_iff
% 5.17/5.48 thf(fact_7259_of__int__1,axiom,
% 5.17/5.48 ( ( ring_1_of_int_int @ one_one_int )
% 5.17/5.48 = one_one_int ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_1
% 5.17/5.48 thf(fact_7260_of__int__1,axiom,
% 5.17/5.48 ( ( ring_1_of_int_real @ one_one_int )
% 5.17/5.48 = one_one_real ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_1
% 5.17/5.48 thf(fact_7261_of__int__1,axiom,
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.17/5.48 = one_one_complex ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_1
% 5.17/5.48 thf(fact_7262_of__int__1,axiom,
% 5.17/5.48 ( ( ring_1_of_int_rat @ one_one_int )
% 5.17/5.48 = one_one_rat ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_1
% 5.17/5.48 thf(fact_7263_of__int__mult,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 5.17/5.48 = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_mult
% 5.17/5.48 thf(fact_7264_of__int__mult,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.17/5.48 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_mult
% 5.17/5.48 thf(fact_7265_of__int__mult,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.17/5.48 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_mult
% 5.17/5.48 thf(fact_7266_of__int__mult,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.17/5.48 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_mult
% 5.17/5.48 thf(fact_7267_of__int__add,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.17/5.48 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_add
% 5.17/5.48 thf(fact_7268_of__int__add,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.17/5.48 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_add
% 5.17/5.48 thf(fact_7269_of__int__add,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 5.17/5.48 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_add
% 5.17/5.48 thf(fact_7270_of__int__add,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.17/5.48 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_add
% 5.17/5.48 thf(fact_7271_of__int__minus,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z ) )
% 5.17/5.48 = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_minus
% 5.17/5.48 thf(fact_7272_of__int__minus,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 5.17/5.48 = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_minus
% 5.17/5.48 thf(fact_7273_of__int__minus,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ Z ) )
% 5.17/5.48 = ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_minus
% 5.17/5.48 thf(fact_7274_of__int__minus,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 5.17/5.48 = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_minus
% 5.17/5.48 thf(fact_7275_of__int__minus,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 5.17/5.48 = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_minus
% 5.17/5.48 thf(fact_7276_of__real__mult,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.48 = ( times_times_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_mult
% 5.17/5.48 thf(fact_7277_of__real__mult,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.48 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_mult
% 5.17/5.48 thf(fact_7278_of__real__numeral,axiom,
% 5.17/5.48 ! [W: num] :
% 5.17/5.48 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.48 = ( numeral_numeral_real @ W ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_numeral
% 5.17/5.48 thf(fact_7279_of__real__numeral,axiom,
% 5.17/5.48 ! [W: num] :
% 5.17/5.48 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.17/5.48 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_numeral
% 5.17/5.48 thf(fact_7280_of__real__divide,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.48 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_divide
% 5.17/5.48 thf(fact_7281_of__real__divide,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.48 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_divide
% 5.17/5.48 thf(fact_7282_of__int__diff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 5.17/5.48 = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_diff
% 5.17/5.48 thf(fact_7283_of__int__diff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.17/5.48 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_diff
% 5.17/5.48 thf(fact_7284_of__int__diff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.17/5.48 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_diff
% 5.17/5.48 thf(fact_7285_of__int__diff,axiom,
% 5.17/5.48 ! [W: int,Z: int] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.17/5.48 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_diff
% 5.17/5.48 thf(fact_7286_of__int__of__nat__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.48 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_nat_eq
% 5.17/5.48 thf(fact_7287_of__int__of__nat__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.48 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_nat_eq
% 5.17/5.48 thf(fact_7288_of__int__of__nat__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.48 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_nat_eq
% 5.17/5.48 thf(fact_7289_of__int__of__nat__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.48 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_nat_eq
% 5.17/5.48 thf(fact_7290_of__real__diff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V1803761363581548252l_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.48 = ( minus_minus_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_diff
% 5.17/5.48 thf(fact_7291_of__real__diff,axiom,
% 5.17/5.48 ! [X: real,Y4: real] :
% 5.17/5.48 ( ( real_V4546457046886955230omplex @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.48 = ( minus_minus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_diff
% 5.17/5.48 thf(fact_7292_of__real__of__nat__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( real_V4546457046886955230omplex @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.48 = ( semiri8010041392384452111omplex @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_of_nat_eq
% 5.17/5.48 thf(fact_7293_of__real__of__nat__eq,axiom,
% 5.17/5.48 ! [N: nat] :
% 5.17/5.48 ( ( real_V1803761363581548252l_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.48 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_real_of_nat_eq
% 5.17/5.48 thf(fact_7294_of__int__abs,axiom,
% 5.17/5.48 ! [X: int] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( abs_abs_int @ X ) )
% 5.17/5.48 = ( abs_abs_int @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_abs
% 5.17/5.48 thf(fact_7295_of__int__abs,axiom,
% 5.17/5.48 ! [X: int] :
% 5.17/5.48 ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X ) )
% 5.17/5.48 = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_abs
% 5.17/5.48 thf(fact_7296_of__int__abs,axiom,
% 5.17/5.48 ! [X: int] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( abs_abs_int @ X ) )
% 5.17/5.48 = ( abs_abs_real @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_abs
% 5.17/5.48 thf(fact_7297_of__int__abs,axiom,
% 5.17/5.48 ! [X: int] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( abs_abs_int @ X ) )
% 5.17/5.48 = ( abs_abs_rat @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_abs
% 5.17/5.48 thf(fact_7298_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.48 ! [X: int,B: int,W: nat] :
% 5.17/5.48 ( ( ( ring_1_of_int_rat @ X )
% 5.17/5.48 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.17/5.48 = ( X
% 5.17/5.48 = ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power_eq_of_int_cancel_iff
% 5.17/5.48 thf(fact_7299_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.48 ! [X: int,B: int,W: nat] :
% 5.17/5.48 ( ( ( ring_1_of_int_int @ X )
% 5.17/5.48 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.17/5.48 = ( X
% 5.17/5.48 = ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power_eq_of_int_cancel_iff
% 5.17/5.48 thf(fact_7300_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.48 ! [X: int,B: int,W: nat] :
% 5.17/5.48 ( ( ( ring_1_of_int_real @ X )
% 5.17/5.48 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.17/5.48 = ( X
% 5.17/5.48 = ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power_eq_of_int_cancel_iff
% 5.17/5.48 thf(fact_7301_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.48 ! [X: int,B: int,W: nat] :
% 5.17/5.48 ( ( ( ring_17405671764205052669omplex @ X )
% 5.17/5.48 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.17/5.48 = ( X
% 5.17/5.48 = ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power_eq_of_int_cancel_iff
% 5.17/5.48 thf(fact_7302_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.17/5.48 ! [B: int,W: nat,X: int] :
% 5.17/5.48 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.17/5.48 = ( ring_1_of_int_rat @ X ) )
% 5.17/5.48 = ( ( power_power_int @ B @ W )
% 5.17/5.48 = X ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_of_int_power_cancel_iff
% 5.17/5.48 thf(fact_7303_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.17/5.48 ! [B: int,W: nat,X: int] :
% 5.17/5.48 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.17/5.48 = ( ring_1_of_int_int @ X ) )
% 5.17/5.48 = ( ( power_power_int @ B @ W )
% 5.17/5.48 = X ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_of_int_power_cancel_iff
% 5.17/5.48 thf(fact_7304_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.17/5.48 ! [B: int,W: nat,X: int] :
% 5.17/5.48 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.17/5.48 = ( ring_1_of_int_real @ X ) )
% 5.17/5.48 = ( ( power_power_int @ B @ W )
% 5.17/5.48 = X ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_of_int_power_cancel_iff
% 5.17/5.48 thf(fact_7305_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.17/5.48 ! [B: int,W: nat,X: int] :
% 5.17/5.48 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.17/5.48 = ( ring_17405671764205052669omplex @ X ) )
% 5.17/5.48 = ( ( power_power_int @ B @ W )
% 5.17/5.48 = X ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_eq_of_int_power_cancel_iff
% 5.17/5.48 thf(fact_7306_of__int__power,axiom,
% 5.17/5.48 ! [Z: int,N: nat] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.17/5.48 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power
% 5.17/5.48 thf(fact_7307_of__int__power,axiom,
% 5.17/5.48 ! [Z: int,N: nat] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.17/5.48 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power
% 5.17/5.48 thf(fact_7308_of__int__power,axiom,
% 5.17/5.48 ! [Z: int,N: nat] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.17/5.48 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power
% 5.17/5.48 thf(fact_7309_of__int__power,axiom,
% 5.17/5.48 ! [Z: int,N: nat] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.17/5.48 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_power
% 5.17/5.48 thf(fact_7310_arccos__1,axiom,
% 5.17/5.48 ( ( arccos @ one_one_real )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % arccos_1
% 5.17/5.48 thf(fact_7311_of__int__of__bool,axiom,
% 5.17/5.48 ! [P: $o] :
% 5.17/5.48 ( ( ring_1_of_int_real @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.48 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_bool
% 5.17/5.48 thf(fact_7312_of__int__of__bool,axiom,
% 5.17/5.48 ! [P: $o] :
% 5.17/5.48 ( ( ring_17405671764205052669omplex @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.48 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_bool
% 5.17/5.48 thf(fact_7313_of__int__of__bool,axiom,
% 5.17/5.48 ! [P: $o] :
% 5.17/5.48 ( ( ring_1_of_int_rat @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.48 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_bool
% 5.17/5.48 thf(fact_7314_of__int__of__bool,axiom,
% 5.17/5.48 ! [P: $o] :
% 5.17/5.48 ( ( ring_1_of_int_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.48 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_bool
% 5.17/5.48 thf(fact_7315_of__int__of__bool,axiom,
% 5.17/5.48 ! [P: $o] :
% 5.17/5.48 ( ( ring_18347121197199848620nteger @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.17/5.48 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_of_bool
% 5.17/5.48 thf(fact_7316_sin__of__real__pi,axiom,
% 5.17/5.48 ( ( sin_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.17/5.48 = zero_zero_real ) ).
% 5.17/5.48
% 5.17/5.48 % sin_of_real_pi
% 5.17/5.48 thf(fact_7317_sin__of__real__pi,axiom,
% 5.17/5.48 ( ( sin_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.17/5.48 = zero_zero_complex ) ).
% 5.17/5.48
% 5.17/5.48 % sin_of_real_pi
% 5.17/5.48 thf(fact_7318_floor__diff__of__int,axiom,
% 5.17/5.48 ! [X: real,Z: int] :
% 5.17/5.48 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_diff_of_int
% 5.17/5.48 thf(fact_7319_floor__diff__of__int,axiom,
% 5.17/5.48 ! [X: rat,Z: int] :
% 5.17/5.48 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % floor_diff_of_int
% 5.17/5.48 thf(fact_7320_ceiling__diff__of__int,axiom,
% 5.17/5.48 ! [X: rat,Z: int] :
% 5.17/5.48 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ Z ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_of_int
% 5.17/5.48 thf(fact_7321_ceiling__diff__of__int,axiom,
% 5.17/5.48 ! [X: real,Z: int] :
% 5.17/5.48 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ Z ) ) )
% 5.17/5.48 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % ceiling_diff_of_int
% 5.17/5.48 thf(fact_7322_of__nat__nat__take__bit__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( semiri8010041392384452111omplex @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.17/5.48 = ( ring_17405671764205052669omplex @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_nat_take_bit_eq
% 5.17/5.48 thf(fact_7323_of__nat__nat__take__bit__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.17/5.48 = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_nat_take_bit_eq
% 5.17/5.48 thf(fact_7324_of__nat__nat__take__bit__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.17/5.48 = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_nat_take_bit_eq
% 5.17/5.48 thf(fact_7325_of__nat__nat__take__bit__eq,axiom,
% 5.17/5.48 ! [N: nat,K: int] :
% 5.17/5.48 ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.17/5.48 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_nat_nat_take_bit_eq
% 5.17/5.48 thf(fact_7326_of__int__le__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.17/5.48 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_0_iff
% 5.17/5.48 thf(fact_7327_of__int__le__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_0_iff
% 5.17/5.48 thf(fact_7328_of__int__le__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.17/5.48 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_0_iff
% 5.17/5.48 thf(fact_7329_of__int__0__le__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_le_iff
% 5.17/5.48 thf(fact_7330_of__int__0__le__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_le_iff
% 5.17/5.48 thf(fact_7331_of__int__0__le__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_le_iff
% 5.17/5.48 thf(fact_7332_of__int__less__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.17/5.48 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_less_0_iff
% 5.17/5.48 thf(fact_7333_of__int__less__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.17/5.48 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_less_0_iff
% 5.17/5.48 thf(fact_7334_of__int__less__0__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.17/5.48 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_less_0_iff
% 5.17/5.48 thf(fact_7335_of__int__0__less__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_less_iff
% 5.17/5.48 thf(fact_7336_of__int__0__less__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_less_iff
% 5.17/5.48 thf(fact_7337_of__int__0__less__iff,axiom,
% 5.17/5.48 ! [Z: int] :
% 5.17/5.48 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.48 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_0_less_iff
% 5.17/5.48 thf(fact_7338_of__int__numeral__le__iff,axiom,
% 5.17/5.48 ! [N: num,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral_le_iff
% 5.17/5.48 thf(fact_7339_of__int__numeral__le__iff,axiom,
% 5.17/5.48 ! [N: num,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral_le_iff
% 5.17/5.48 thf(fact_7340_of__int__numeral__le__iff,axiom,
% 5.17/5.48 ! [N: num,Z: int] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.48 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_numeral_le_iff
% 5.17/5.48 thf(fact_7341_of__int__le__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.48 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_numeral_iff
% 5.17/5.48 thf(fact_7342_of__int__le__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.48 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_numeral_iff
% 5.17/5.48 thf(fact_7343_of__int__le__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.48 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.48
% 5.17/5.48 % of_int_le_numeral_iff
% 5.17/5.48 thf(fact_7344_of__int__less__numeral__iff,axiom,
% 5.17/5.48 ! [Z: int,N: num] :
% 5.17/5.48 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.17/5.48 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_numeral_iff
% 5.17/5.49 thf(fact_7345_of__int__less__numeral__iff,axiom,
% 5.17/5.49 ! [Z: int,N: num] :
% 5.17/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.17/5.49 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_numeral_iff
% 5.17/5.49 thf(fact_7346_of__int__less__numeral__iff,axiom,
% 5.17/5.49 ! [Z: int,N: num] :
% 5.17/5.49 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.49 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_numeral_iff
% 5.17/5.49 thf(fact_7347_of__int__numeral__less__iff,axiom,
% 5.17/5.49 ! [N: num,Z: int] :
% 5.17/5.49 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.49 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_numeral_less_iff
% 5.17/5.49 thf(fact_7348_of__int__numeral__less__iff,axiom,
% 5.17/5.49 ! [N: num,Z: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.49 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_numeral_less_iff
% 5.17/5.49 thf(fact_7349_of__int__numeral__less__iff,axiom,
% 5.17/5.49 ! [N: num,Z: int] :
% 5.17/5.49 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.49 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_numeral_less_iff
% 5.17/5.49 thf(fact_7350_of__int__le__1__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.17/5.49 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_1_iff
% 5.17/5.49 thf(fact_7351_of__int__le__1__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.17/5.49 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_1_iff
% 5.17/5.49 thf(fact_7352_of__int__le__1__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.17/5.49 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_1_iff
% 5.17/5.49 thf(fact_7353_of__int__1__le__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.49 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_1_le_iff
% 5.17/5.49 thf(fact_7354_of__int__1__le__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.49 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_1_le_iff
% 5.17/5.49 thf(fact_7355_of__int__1__le__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.49 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_1_le_iff
% 5.17/5.49 thf(fact_7356_of__int__less__1__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.17/5.49 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_1_iff
% 5.17/5.49 thf(fact_7357_of__int__less__1__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.17/5.49 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_1_iff
% 5.17/5.49 thf(fact_7358_of__int__less__1__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.17/5.49 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_1_iff
% 5.17/5.49 thf(fact_7359_of__int__1__less__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.49 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_1_less_iff
% 5.17/5.49 thf(fact_7360_of__int__1__less__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.49 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_1_less_iff
% 5.17/5.49 thf(fact_7361_of__int__1__less__iff,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.17/5.49 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_1_less_iff
% 5.17/5.49 thf(fact_7362_of__real__neg__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_real_neg_numeral
% 5.17/5.49 thf(fact_7363_of__real__neg__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_real_neg_numeral
% 5.17/5.49 thf(fact_7364_of__int__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: int,B: int,W: nat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.17/5.49 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7365_of__int__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: int,B: int,W: nat] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.17/5.49 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7366_of__int__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: int,B: int,W: nat] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.17/5.49 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7367_of__int__le__of__int__power__cancel__iff,axiom,
% 5.17/5.49 ! [B: int,W: nat,X: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_of_int_power_cancel_iff
% 5.17/5.49 thf(fact_7368_of__int__le__of__int__power__cancel__iff,axiom,
% 5.17/5.49 ! [B: int,W: nat,X: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_of_int_power_cancel_iff
% 5.17/5.49 thf(fact_7369_of__int__le__of__int__power__cancel__iff,axiom,
% 5.17/5.49 ! [B: int,W: nat,X: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_of_int_power_cancel_iff
% 5.17/5.49 thf(fact_7370_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.17/5.49 = ( ring_17405671764205052669omplex @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7371_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.17/5.49 = ( ring_1_of_int_real @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7372_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.17/5.49 = ( ring_1_of_int_rat @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7373_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.49 = ( ring_1_of_int_int @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7374_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_17405671764205052669omplex @ Y4 )
% 5.17/5.49 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7375_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_1_of_int_real @ Y4 )
% 5.17/5.49 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7376_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_1_of_int_rat @ Y4 )
% 5.17/5.49 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7377_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_1_of_int_int @ Y4 )
% 5.17/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7378_of__int__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: int,B: int,W: nat] :
% 5.17/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.17/5.49 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7379_of__int__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: int,B: int,W: nat] :
% 5.17/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.17/5.49 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7380_of__int__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: int,B: int,W: nat] :
% 5.17/5.49 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.17/5.49 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7381_of__int__less__of__int__power__cancel__iff,axiom,
% 5.17/5.49 ! [B: int,W: nat,X: int] :
% 5.17/5.49 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_of_int_power_cancel_iff
% 5.17/5.49 thf(fact_7382_of__int__less__of__int__power__cancel__iff,axiom,
% 5.17/5.49 ! [B: int,W: nat,X: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_of_int_power_cancel_iff
% 5.17/5.49 thf(fact_7383_of__int__less__of__int__power__cancel__iff,axiom,
% 5.17/5.49 ! [B: int,W: nat,X: int] :
% 5.17/5.49 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_of_int_power_cancel_iff
% 5.17/5.49 thf(fact_7384_of__nat__nat,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ( semiri8010041392384452111omplex @ ( nat2 @ Z ) )
% 5.17/5.49 = ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_nat
% 5.17/5.49 thf(fact_7385_of__nat__nat,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 5.17/5.49 = ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_nat
% 5.17/5.49 thf(fact_7386_of__nat__nat,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 5.17/5.49 = ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_nat
% 5.17/5.49 thf(fact_7387_of__nat__nat,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.17/5.49 = ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_nat
% 5.17/5.49 thf(fact_7388_sin__npi__int,axiom,
% 5.17/5.49 ! [N: int] :
% 5.17/5.49 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % sin_npi_int
% 5.17/5.49 thf(fact_7389_cos__arccos,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ( cos_real @ ( arccos @ Y4 ) )
% 5.17/5.49 = Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_arccos
% 5.17/5.49 thf(fact_7390_tan__periodic__int,axiom,
% 5.17/5.49 ! [X: real,I: int] :
% 5.17/5.49 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.17/5.49 = ( tan_real @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % tan_periodic_int
% 5.17/5.49 thf(fact_7391_of__int__le__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7392_of__int__le__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7393_of__int__le__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7394_numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7395_numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7396_numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7397_of__int__less__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7398_of__int__less__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7399_of__int__less__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7400_numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7401_numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7402_numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7403_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_1_of_int_real @ Y4 )
% 5.17/5.49 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7404_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_1_of_int_int @ Y4 )
% 5.17/5.49 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7405_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_17405671764205052669omplex @ Y4 )
% 5.17/5.49 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7406_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_18347121197199848620nteger @ Y4 )
% 5.17/5.49 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7407_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [Y4: int,X: num,N: nat] :
% 5.17/5.49 ( ( ( ring_1_of_int_rat @ Y4 )
% 5.17/5.49 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.17/5.49 = ( Y4
% 5.17/5.49 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_eq_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7408_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 5.17/5.49 = ( ring_1_of_int_real @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7409_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.17/5.49 = ( ring_1_of_int_int @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7410_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 5.17/5.49 = ( ring_17405671764205052669omplex @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7411_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 5.17/5.49 = ( ring_18347121197199848620nteger @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7412_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,Y4: int] :
% 5.17/5.49 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 5.17/5.49 = ( ring_1_of_int_rat @ Y4 ) )
% 5.17/5.49 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_eq_of_int_cancel_iff
% 5.17/5.49 thf(fact_7413_norm__of__real__addn,axiom,
% 5.17/5.49 ! [X: real,B: num] :
% 5.17/5.49 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X ) @ ( numeral_numeral_real @ B ) ) )
% 5.17/5.49 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % norm_of_real_addn
% 5.17/5.49 thf(fact_7414_norm__of__real__addn,axiom,
% 5.17/5.49 ! [X: real,B: num] :
% 5.17/5.49 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.17/5.49 = ( abs_abs_real @ ( plus_plus_real @ X @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % norm_of_real_addn
% 5.17/5.49 thf(fact_7415_arccos__0,axiom,
% 5.17/5.49 ( ( arccos @ zero_zero_real )
% 5.17/5.49 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_0
% 5.17/5.49 thf(fact_7416_cos__of__real__pi__half,axiom,
% 5.17/5.49 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % cos_of_real_pi_half
% 5.17/5.49 thf(fact_7417_cos__of__real__pi__half,axiom,
% 5.17/5.49 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.17/5.49 = zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % cos_of_real_pi_half
% 5.17/5.49 thf(fact_7418_sin__of__real__pi__half,axiom,
% 5.17/5.49 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.49 = one_one_real ) ).
% 5.17/5.49
% 5.17/5.49 % sin_of_real_pi_half
% 5.17/5.49 thf(fact_7419_sin__of__real__pi__half,axiom,
% 5.17/5.49 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % sin_of_real_pi_half
% 5.17/5.49 thf(fact_7420_sin__int__2pin,axiom,
% 5.17/5.49 ! [N: int] :
% 5.17/5.49 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % sin_int_2pin
% 5.17/5.49 thf(fact_7421_cos__int__2pin,axiom,
% 5.17/5.49 ! [N: int] :
% 5.17/5.49 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.17/5.49 = one_one_real ) ).
% 5.17/5.49
% 5.17/5.49 % cos_int_2pin
% 5.17/5.49 thf(fact_7422_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7423_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7424_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7425_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.17/5.49 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_le_of_int_cancel_iff
% 5.17/5.49 thf(fact_7426_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7427_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7428_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7429_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_le_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7430_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7431_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7432_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7433_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.17/5.49 ! [A: int,X: num,N: nat] :
% 5.17/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.17/5.49 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_less_neg_numeral_power_cancel_iff
% 5.17/5.49 thf(fact_7434_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7435_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7436_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7437_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.17/5.49 ! [X: num,N: nat,A: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.17/5.49 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % neg_numeral_power_less_of_int_cancel_iff
% 5.17/5.49 thf(fact_7438_ex__le__of__int,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ? [Z2: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.17/5.49
% 5.17/5.49 % ex_le_of_int
% 5.17/5.49 thf(fact_7439_ex__le__of__int,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ? [Z2: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.17/5.49
% 5.17/5.49 % ex_le_of_int
% 5.17/5.49 thf(fact_7440_mult__of__int__commute,axiom,
% 5.17/5.49 ! [X: int,Y4: complex] :
% 5.17/5.49 ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y4 )
% 5.17/5.49 = ( times_times_complex @ Y4 @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_of_int_commute
% 5.17/5.49 thf(fact_7441_mult__of__int__commute,axiom,
% 5.17/5.49 ! [X: int,Y4: real] :
% 5.17/5.49 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y4 )
% 5.17/5.49 = ( times_times_real @ Y4 @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_of_int_commute
% 5.17/5.49 thf(fact_7442_mult__of__int__commute,axiom,
% 5.17/5.49 ! [X: int,Y4: rat] :
% 5.17/5.49 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y4 )
% 5.17/5.49 = ( times_times_rat @ Y4 @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_of_int_commute
% 5.17/5.49 thf(fact_7443_mult__of__int__commute,axiom,
% 5.17/5.49 ! [X: int,Y4: int] :
% 5.17/5.49 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y4 )
% 5.17/5.49 = ( times_times_int @ Y4 @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_of_int_commute
% 5.17/5.49 thf(fact_7444_cos__int__times__real,axiom,
% 5.17/5.49 ! [M: int,X: real] :
% 5.17/5.49 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.17/5.49 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_int_times_real
% 5.17/5.49 thf(fact_7445_cos__int__times__real,axiom,
% 5.17/5.49 ! [M: int,X: real] :
% 5.17/5.49 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.17/5.49 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_int_times_real
% 5.17/5.49 thf(fact_7446_sin__int__times__real,axiom,
% 5.17/5.49 ! [M: int,X: real] :
% 5.17/5.49 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X ) ) )
% 5.17/5.49 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_int_times_real
% 5.17/5.49 thf(fact_7447_sin__int__times__real,axiom,
% 5.17/5.49 ! [M: int,X: real] :
% 5.17/5.49 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X ) ) )
% 5.17/5.49 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_int_times_real
% 5.17/5.49 thf(fact_7448_of__int__floor__le,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_floor_le
% 5.17/5.49 thf(fact_7449_of__int__floor__le,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_floor_le
% 5.17/5.49 thf(fact_7450_le__of__int__ceiling,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_of_int_ceiling
% 5.17/5.49 thf(fact_7451_le__of__int__ceiling,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_of_int_ceiling
% 5.17/5.49 thf(fact_7452_complex__of__real__def,axiom,
% 5.17/5.49 ( real_V4546457046886955230omplex
% 5.17/5.49 = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % complex_of_real_def
% 5.17/5.49 thf(fact_7453_complex__of__real__code,axiom,
% 5.17/5.49 ( real_V4546457046886955230omplex
% 5.17/5.49 = ( ^ [X3: real] : ( complex2 @ X3 @ zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % complex_of_real_code
% 5.17/5.49 thf(fact_7454_complex__eq__cancel__iff2,axiom,
% 5.17/5.49 ! [X: real,Y4: real,Xa: real] :
% 5.17/5.49 ( ( ( complex2 @ X @ Y4 )
% 5.17/5.49 = ( real_V4546457046886955230omplex @ Xa ) )
% 5.17/5.49 = ( ( X = Xa )
% 5.17/5.49 & ( Y4 = zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % complex_eq_cancel_iff2
% 5.17/5.49 thf(fact_7455_complex__of__real__mult__Complex,axiom,
% 5.17/5.49 ! [R2: real,X: real,Y4: real] :
% 5.17/5.49 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X @ Y4 ) )
% 5.17/5.49 = ( complex2 @ ( times_times_real @ R2 @ X ) @ ( times_times_real @ R2 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % complex_of_real_mult_Complex
% 5.17/5.49 thf(fact_7456_Complex__mult__complex__of__real,axiom,
% 5.17/5.49 ! [X: real,Y4: real,R2: real] :
% 5.17/5.49 ( ( times_times_complex @ ( complex2 @ X @ Y4 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.17/5.49 = ( complex2 @ ( times_times_real @ X @ R2 ) @ ( times_times_real @ Y4 @ R2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Complex_mult_complex_of_real
% 5.17/5.49 thf(fact_7457_take__bit__of__int,axiom,
% 5.17/5.49 ! [N: nat,K: int] :
% 5.17/5.49 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.17/5.49 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % take_bit_of_int
% 5.17/5.49 thf(fact_7458_of__int__and__eq,axiom,
% 5.17/5.49 ! [K: int,L: int] :
% 5.17/5.49 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.17/5.49 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_and_eq
% 5.17/5.49 thf(fact_7459_of__int__mask__eq,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.17/5.49 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_mask_eq
% 5.17/5.49 thf(fact_7460_nonzero__of__real__divide,axiom,
% 5.17/5.49 ! [Y4: real,X: real] :
% 5.17/5.49 ( ( Y4 != zero_zero_real )
% 5.17/5.49 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.49 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_of_real_divide
% 5.17/5.49 thf(fact_7461_nonzero__of__real__divide,axiom,
% 5.17/5.49 ! [Y4: real,X: real] :
% 5.17/5.49 ( ( Y4 != zero_zero_real )
% 5.17/5.49 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.49 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_of_real_divide
% 5.17/5.49 thf(fact_7462_le__floor__iff,axiom,
% 5.17/5.49 ! [Z: int,X: real] :
% 5.17/5.49 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.49 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_floor_iff
% 5.17/5.49 thf(fact_7463_le__floor__iff,axiom,
% 5.17/5.49 ! [Z: int,X: rat] :
% 5.17/5.49 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.49 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_floor_iff
% 5.17/5.49 thf(fact_7464_ceiling__le__iff,axiom,
% 5.17/5.49 ! [X: rat,Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 5.17/5.49 = ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_le_iff
% 5.17/5.49 thf(fact_7465_ceiling__le__iff,axiom,
% 5.17/5.49 ! [X: real,Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 5.17/5.49 = ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_le_iff
% 5.17/5.49 thf(fact_7466_ceiling__le,axiom,
% 5.17/5.49 ! [X: rat,A: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) )
% 5.17/5.49 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_le
% 5.17/5.49 thf(fact_7467_ceiling__le,axiom,
% 5.17/5.49 ! [X: real,A: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) )
% 5.17/5.49 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X ) @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_le
% 5.17/5.49 thf(fact_7468_real__of__int__div4,axiom,
% 5.17/5.49 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_div4
% 5.17/5.49 thf(fact_7469_floor__divide__of__int__eq,axiom,
% 5.17/5.49 ! [K: int,L: int] :
% 5.17/5.49 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.17/5.49 = ( divide_divide_int @ K @ L ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_of_int_eq
% 5.17/5.49 thf(fact_7470_floor__divide__of__int__eq,axiom,
% 5.17/5.49 ! [K: int,L: int] :
% 5.17/5.49 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.17/5.49 = ( divide_divide_int @ K @ L ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_of_int_eq
% 5.17/5.49 thf(fact_7471_floor__power,axiom,
% 5.17/5.49 ! [X: real,N: nat] :
% 5.17/5.49 ( ( X
% 5.17/5.49 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) )
% 5.17/5.49 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X @ N ) )
% 5.17/5.49 = ( power_power_int @ ( archim6058952711729229775r_real @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_power
% 5.17/5.49 thf(fact_7472_floor__power,axiom,
% 5.17/5.49 ! [X: rat,N: nat] :
% 5.17/5.49 ( ( X
% 5.17/5.49 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) )
% 5.17/5.49 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X @ N ) )
% 5.17/5.49 = ( power_power_int @ ( archim3151403230148437115or_rat @ X ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_power
% 5.17/5.49 thf(fact_7473_real__of__int__div,axiom,
% 5.17/5.49 ! [D: int,N: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ D @ N )
% 5.17/5.49 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.17/5.49 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_div
% 5.17/5.49 thf(fact_7474_arccos__le__arccos,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ ( arccos @ X ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_le_arccos
% 5.17/5.49 thf(fact_7475_arccos__eq__iff,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.49 & ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real ) )
% 5.17/5.49 => ( ( ( arccos @ X )
% 5.17/5.49 = ( arccos @ Y4 ) )
% 5.17/5.49 = ( X = Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_eq_iff
% 5.17/5.49 thf(fact_7476_arccos__le__mono,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y4 ) )
% 5.17/5.49 = ( ord_less_eq_real @ Y4 @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_le_mono
% 5.17/5.49 thf(fact_7477_of__int__nonneg,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_nonneg
% 5.17/5.49 thf(fact_7478_of__int__nonneg,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_nonneg
% 5.17/5.49 thf(fact_7479_of__int__nonneg,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_nonneg
% 5.17/5.49 thf(fact_7480_of__int__leD,axiom,
% 5.17/5.49 ! [N: int,X: code_integer] :
% 5.17/5.49 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_leD
% 5.17/5.49 thf(fact_7481_of__int__leD,axiom,
% 5.17/5.49 ! [N: int,X: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_leD
% 5.17/5.49 thf(fact_7482_of__int__leD,axiom,
% 5.17/5.49 ! [N: int,X: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_leD
% 5.17/5.49 thf(fact_7483_of__int__leD,axiom,
% 5.17/5.49 ! [N: int,X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_leD
% 5.17/5.49 thf(fact_7484_of__int__pos,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_pos
% 5.17/5.49 thf(fact_7485_of__int__pos,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_pos
% 5.17/5.49 thf(fact_7486_of__int__pos,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.17/5.49 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_pos
% 5.17/5.49 thf(fact_7487_of__int__lessD,axiom,
% 5.17/5.49 ! [N: int,X: code_integer] :
% 5.17/5.49 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_lessD
% 5.17/5.49 thf(fact_7488_of__int__lessD,axiom,
% 5.17/5.49 ! [N: int,X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_lessD
% 5.17/5.49 thf(fact_7489_of__int__lessD,axiom,
% 5.17/5.49 ! [N: int,X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_lessD
% 5.17/5.49 thf(fact_7490_of__int__lessD,axiom,
% 5.17/5.49 ! [N: int,X: int] :
% 5.17/5.49 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.17/5.49 => ( ( N = zero_zero_int )
% 5.17/5.49 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_lessD
% 5.17/5.49 thf(fact_7491_floor__exists1,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ? [X4: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.17/5.49 & ! [Y3: int] :
% 5.17/5.49 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y3 ) @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y3 @ one_one_int ) ) ) )
% 5.17/5.49 => ( Y3 = X4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_exists1
% 5.17/5.49 thf(fact_7492_floor__exists1,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ? [X4: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X )
% 5.17/5.49 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.17/5.49 & ! [Y3: int] :
% 5.17/5.49 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y3 ) @ X )
% 5.17/5.49 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y3 @ one_one_int ) ) ) )
% 5.17/5.49 => ( Y3 = X4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_exists1
% 5.17/5.49 thf(fact_7493_floor__exists,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ? [Z2: int] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_exists
% 5.17/5.49 thf(fact_7494_floor__exists,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ? [Z2: int] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X )
% 5.17/5.49 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_exists
% 5.17/5.49 thf(fact_7495_of__int__ceiling__le__add__one,axiom,
% 5.17/5.49 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_ceiling_le_add_one
% 5.17/5.49 thf(fact_7496_of__int__ceiling__le__add__one,axiom,
% 5.17/5.49 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_ceiling_le_add_one
% 5.17/5.49 thf(fact_7497_of__int__neg__numeral,axiom,
% 5.17/5.49 ! [K: num] :
% 5.17/5.49 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_neg_numeral
% 5.17/5.49 thf(fact_7498_of__int__neg__numeral,axiom,
% 5.17/5.49 ! [K: num] :
% 5.17/5.49 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.49 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_neg_numeral
% 5.17/5.49 thf(fact_7499_of__int__neg__numeral,axiom,
% 5.17/5.49 ! [K: num] :
% 5.17/5.49 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_neg_numeral
% 5.17/5.49 thf(fact_7500_of__int__neg__numeral,axiom,
% 5.17/5.49 ! [K: num] :
% 5.17/5.49 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.49 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_neg_numeral
% 5.17/5.49 thf(fact_7501_of__int__neg__numeral,axiom,
% 5.17/5.49 ! [K: num] :
% 5.17/5.49 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.49 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_neg_numeral
% 5.17/5.49 thf(fact_7502_of__int__ceiling__diff__one__le,axiom,
% 5.17/5.49 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_ceiling_diff_one_le
% 5.17/5.49 thf(fact_7503_of__int__ceiling__diff__one__le,axiom,
% 5.17/5.49 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_ceiling_diff_one_le
% 5.17/5.49 thf(fact_7504_of__nat__less__of__int__iff,axiom,
% 5.17/5.49 ! [N: nat,X: int] :
% 5.17/5.49 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 5.17/5.49 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_less_of_int_iff
% 5.17/5.49 thf(fact_7505_of__nat__less__of__int__iff,axiom,
% 5.17/5.49 ! [N: nat,X: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 5.17/5.49 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_less_of_int_iff
% 5.17/5.49 thf(fact_7506_of__nat__less__of__int__iff,axiom,
% 5.17/5.49 ! [N: nat,X: int] :
% 5.17/5.49 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 5.17/5.49 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_less_of_int_iff
% 5.17/5.49 thf(fact_7507_int__le__real__less,axiom,
% 5.17/5.49 ( ord_less_eq_int
% 5.17/5.49 = ( ^ [N4: int,M5: int] : ( ord_less_real @ ( ring_1_of_int_real @ N4 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M5 ) @ one_one_real ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % int_le_real_less
% 5.17/5.49 thf(fact_7508_int__less__real__le,axiom,
% 5.17/5.49 ( ord_less_int
% 5.17/5.49 = ( ^ [N4: int,M5: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N4 ) @ one_one_real ) @ ( ring_1_of_int_real @ M5 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % int_less_real_le
% 5.17/5.49 thf(fact_7509_ceiling__divide__eq__div,axiom,
% 5.17/5.49 ! [A: int,B: int] :
% 5.17/5.49 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.17/5.49 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_divide_eq_div
% 5.17/5.49 thf(fact_7510_ceiling__divide__eq__div,axiom,
% 5.17/5.49 ! [A: int,B: int] :
% 5.17/5.49 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.17/5.49 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_divide_eq_div
% 5.17/5.49 thf(fact_7511_sin__zero__iff__int2,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( sin_real @ X )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( ? [I2: int] :
% 5.17/5.49 ( X
% 5.17/5.49 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_zero_iff_int2
% 5.17/5.49 thf(fact_7512_arccos__cos__eq__abs__2pi,axiom,
% 5.17/5.49 ! [Theta: real] :
% 5.17/5.49 ~ ! [K2: int] :
% 5.17/5.49 ( ( arccos @ ( cos_real @ Theta ) )
% 5.17/5.49 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_cos_eq_abs_2pi
% 5.17/5.49 thf(fact_7513_real__of__int__div__aux,axiom,
% 5.17/5.49 ! [X: int,D: int] :
% 5.17/5.49 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.17/5.49 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_div_aux
% 5.17/5.49 thf(fact_7514_floor__eq,axiom,
% 5.17/5.49 ! [N: int,X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.17/5.49 => ( ( archim6058952711729229775r_real @ X )
% 5.17/5.49 = N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_eq
% 5.17/5.49 thf(fact_7515_real__of__int__floor__add__one__gt,axiom,
% 5.17/5.49 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_floor_add_one_gt
% 5.17/5.49 thf(fact_7516_real__of__int__floor__add__one__ge,axiom,
% 5.17/5.49 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_floor_add_one_ge
% 5.17/5.49 thf(fact_7517_real__of__int__floor__gt__diff__one,axiom,
% 5.17/5.49 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_floor_gt_diff_one
% 5.17/5.49 thf(fact_7518_real__of__int__floor__ge__diff__one,axiom,
% 5.17/5.49 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_floor_ge_diff_one
% 5.17/5.49 thf(fact_7519_arccos__lbound,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_lbound
% 5.17/5.49 thf(fact_7520_arccos__less__arccos,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ord_less_real @ ( arccos @ Y4 ) @ ( arccos @ X ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_less_arccos
% 5.17/5.49 thf(fact_7521_arccos__less__mono,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.49 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y4 ) )
% 5.17/5.49 = ( ord_less_real @ Y4 @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_less_mono
% 5.17/5.49 thf(fact_7522_arccos__ubound,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ pi ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_ubound
% 5.17/5.49 thf(fact_7523_arccos__cos,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.49 => ( ( arccos @ ( cos_real @ X ) )
% 5.17/5.49 = X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_cos
% 5.17/5.49 thf(fact_7524_floor__split,axiom,
% 5.17/5.49 ! [P: int > $o,T: real] :
% 5.17/5.49 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.17/5.49 = ( ! [I2: int] :
% 5.17/5.49 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I2 ) @ T )
% 5.17/5.49 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) ) )
% 5.17/5.49 => ( P @ I2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_split
% 5.17/5.49 thf(fact_7525_floor__split,axiom,
% 5.17/5.49 ! [P: int > $o,T: rat] :
% 5.17/5.49 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.17/5.49 = ( ! [I2: int] :
% 5.17/5.49 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I2 ) @ T )
% 5.17/5.49 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) ) )
% 5.17/5.49 => ( P @ I2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_split
% 5.17/5.49 thf(fact_7526_floor__eq__iff,axiom,
% 5.17/5.49 ! [X: real,A: int] :
% 5.17/5.49 ( ( ( archim6058952711729229775r_real @ X )
% 5.17/5.49 = A )
% 5.17/5.49 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X )
% 5.17/5.49 & ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_eq_iff
% 5.17/5.49 thf(fact_7527_floor__eq__iff,axiom,
% 5.17/5.49 ! [X: rat,A: int] :
% 5.17/5.49 ( ( ( archim3151403230148437115or_rat @ X )
% 5.17/5.49 = A )
% 5.17/5.49 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_eq_iff
% 5.17/5.49 thf(fact_7528_floor__unique,axiom,
% 5.17/5.49 ! [Z: int,X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.17/5.49 => ( ( archim6058952711729229775r_real @ X )
% 5.17/5.49 = Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_unique
% 5.17/5.49 thf(fact_7529_floor__unique,axiom,
% 5.17/5.49 ! [Z: int,X: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 5.17/5.49 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.17/5.49 => ( ( archim3151403230148437115or_rat @ X )
% 5.17/5.49 = Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_unique
% 5.17/5.49 thf(fact_7530_cos__arccos__abs,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.17/5.49 => ( ( cos_real @ ( arccos @ Y4 ) )
% 5.17/5.49 = Y4 ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_arccos_abs
% 5.17/5.49 thf(fact_7531_norm__of__real__diff,axiom,
% 5.17/5.49 ! [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 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % norm_of_real_diff
% 5.17/5.49 thf(fact_7532_norm__of__real__diff,axiom,
% 5.17/5.49 ! [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 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % norm_of_real_diff
% 5.17/5.49 thf(fact_7533_ceiling__split,axiom,
% 5.17/5.49 ! [P: int > $o,T: rat] :
% 5.17/5.49 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.17/5.49 = ( ! [I2: int] :
% 5.17/5.49 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I2 ) @ one_one_rat ) @ T )
% 5.17/5.49 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I2 ) ) )
% 5.17/5.49 => ( P @ I2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_split
% 5.17/5.49 thf(fact_7534_ceiling__split,axiom,
% 5.17/5.49 ! [P: int > $o,T: real] :
% 5.17/5.49 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.17/5.49 = ( ! [I2: int] :
% 5.17/5.49 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I2 ) @ one_one_real ) @ T )
% 5.17/5.49 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I2 ) ) )
% 5.17/5.49 => ( P @ I2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_split
% 5.17/5.49 thf(fact_7535_ceiling__eq__iff,axiom,
% 5.17/5.49 ! [X: rat,A: int] :
% 5.17/5.49 ( ( ( archim2889992004027027881ng_rat @ X )
% 5.17/5.49 = A )
% 5.17/5.49 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 5.17/5.49 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_eq_iff
% 5.17/5.49 thf(fact_7536_ceiling__eq__iff,axiom,
% 5.17/5.49 ! [X: real,A: int] :
% 5.17/5.49 ( ( ( archim7802044766580827645g_real @ X )
% 5.17/5.49 = A )
% 5.17/5.49 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X )
% 5.17/5.49 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_eq_iff
% 5.17/5.49 thf(fact_7537_ceiling__unique,axiom,
% 5.17/5.49 ! [Z: int,X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.49 => ( ( archim2889992004027027881ng_rat @ X )
% 5.17/5.49 = Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_unique
% 5.17/5.49 thf(fact_7538_ceiling__unique,axiom,
% 5.17/5.49 ! [Z: int,X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.49 => ( ( archim7802044766580827645g_real @ X )
% 5.17/5.49 = Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_unique
% 5.17/5.49 thf(fact_7539_ceiling__correct,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 5.17/5.49 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_correct
% 5.17/5.49 thf(fact_7540_ceiling__correct,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) @ one_one_real ) @ X )
% 5.17/5.49 & ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_correct
% 5.17/5.49 thf(fact_7541_arccos__cos__eq__abs,axiom,
% 5.17/5.49 ! [Theta: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.17/5.49 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.17/5.49 = ( abs_abs_real @ Theta ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_cos_eq_abs
% 5.17/5.49 thf(fact_7542_less__floor__iff,axiom,
% 5.17/5.49 ! [Z: int,X: real] :
% 5.17/5.49 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X ) )
% 5.17/5.49 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % less_floor_iff
% 5.17/5.49 thf(fact_7543_less__floor__iff,axiom,
% 5.17/5.49 ! [Z: int,X: rat] :
% 5.17/5.49 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.17/5.49 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % less_floor_iff
% 5.17/5.49 thf(fact_7544_floor__le__iff,axiom,
% 5.17/5.49 ! [X: real,Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ Z )
% 5.17/5.49 = ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_le_iff
% 5.17/5.49 thf(fact_7545_floor__le__iff,axiom,
% 5.17/5.49 ! [X: rat,Z: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 5.17/5.49 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_le_iff
% 5.17/5.49 thf(fact_7546_ceiling__less__iff,axiom,
% 5.17/5.49 ! [X: rat,Z: int] :
% 5.17/5.49 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 5.17/5.49 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_less_iff
% 5.17/5.49 thf(fact_7547_ceiling__less__iff,axiom,
% 5.17/5.49 ! [X: real,Z: int] :
% 5.17/5.49 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X ) @ Z )
% 5.17/5.49 = ( ord_less_eq_real @ X @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_less_iff
% 5.17/5.49 thf(fact_7548_le__ceiling__iff,axiom,
% 5.17/5.49 ! [Z: int,X: rat] :
% 5.17/5.49 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 5.17/5.49 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_ceiling_iff
% 5.17/5.49 thf(fact_7549_le__ceiling__iff,axiom,
% 5.17/5.49 ! [Z: int,X: real] :
% 5.17/5.49 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X ) )
% 5.17/5.49 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_ceiling_iff
% 5.17/5.49 thf(fact_7550_floor__correct,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X ) ) @ X )
% 5.17/5.49 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X ) @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_correct
% 5.17/5.49 thf(fact_7551_floor__correct,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_correct
% 5.17/5.49 thf(fact_7552_real__of__int__div2,axiom,
% 5.17/5.49 ! [N: int,X: 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 @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_div2
% 5.17/5.49 thf(fact_7553_real__of__int__div3,axiom,
% 5.17/5.49 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 5.17/5.49
% 5.17/5.49 % real_of_int_div3
% 5.17/5.49 thf(fact_7554_floor__eq2,axiom,
% 5.17/5.49 ! [N: int,X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.17/5.49 => ( ( archim6058952711729229775r_real @ X )
% 5.17/5.49 = N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_eq2
% 5.17/5.49 thf(fact_7555_floor__divide__real__eq__div,axiom,
% 5.17/5.49 ! [B: int,A: real] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.49 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.17/5.49 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_real_eq_div
% 5.17/5.49 thf(fact_7556_floor__divide__lower,axiom,
% 5.17/5.49 ! [Q2: real,P5: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.17/5.49 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ Q2 ) @ P5 ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_lower
% 5.17/5.49 thf(fact_7557_floor__divide__lower,axiom,
% 5.17/5.49 ! [Q2: rat,P5: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.17/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P5 @ Q2 ) ) ) @ Q2 ) @ P5 ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_lower
% 5.17/5.49 thf(fact_7558_ceiling__divide__upper,axiom,
% 5.17/5.49 ! [Q2: rat,P5: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.17/5.49 => ( ord_less_eq_rat @ P5 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P5 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_divide_upper
% 5.17/5.49 thf(fact_7559_ceiling__divide__upper,axiom,
% 5.17/5.49 ! [Q2: real,P5: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.17/5.49 => ( ord_less_eq_real @ P5 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_divide_upper
% 5.17/5.49 thf(fact_7560_arccos__lt__bounded,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.49 => ( ( ord_less_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.17/5.49 & ( ord_less_real @ ( arccos @ Y4 ) @ pi ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_lt_bounded
% 5.17/5.49 thf(fact_7561_even__of__int__iff,axiom,
% 5.17/5.49 ! [K: int] :
% 5.17/5.49 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.17/5.49 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_of_int_iff
% 5.17/5.49 thf(fact_7562_even__of__int__iff,axiom,
% 5.17/5.49 ! [K: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.17/5.49 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_of_int_iff
% 5.17/5.49 thf(fact_7563_arccos__bounded,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.17/5.49 & ( ord_less_eq_real @ ( arccos @ Y4 ) @ pi ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_bounded
% 5.17/5.49 thf(fact_7564_sin__arccos__nonzero,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.49 => ( ( sin_real @ ( arccos @ X ) )
% 5.17/5.49 != zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_arccos_nonzero
% 5.17/5.49 thf(fact_7565_arccos__cos2,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.17/5.49 => ( ( arccos @ ( cos_real @ X ) )
% 5.17/5.49 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_cos2
% 5.17/5.49 thf(fact_7566_arccos__minus,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.49 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.17/5.49 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_minus
% 5.17/5.49 thf(fact_7567_of__int__of__nat,axiom,
% 5.17/5.49 ( ring_18347121197199848620nteger
% 5.17/5.49 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_of_nat
% 5.17/5.49 thf(fact_7568_of__int__of__nat,axiom,
% 5.17/5.49 ( ring_17405671764205052669omplex
% 5.17/5.49 = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_of_nat
% 5.17/5.49 thf(fact_7569_of__int__of__nat,axiom,
% 5.17/5.49 ( ring_1_of_int_real
% 5.17/5.49 = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_of_nat
% 5.17/5.49 thf(fact_7570_of__int__of__nat,axiom,
% 5.17/5.49 ( ring_1_of_int_rat
% 5.17/5.49 = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_of_nat
% 5.17/5.49 thf(fact_7571_of__int__of__nat,axiom,
% 5.17/5.49 ( ring_1_of_int_int
% 5.17/5.49 = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_of_nat
% 5.17/5.49 thf(fact_7572_floor__divide__upper,axiom,
% 5.17/5.49 ! [Q2: real,P5: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.17/5.49 => ( ord_less_real @ P5 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_upper
% 5.17/5.49 thf(fact_7573_floor__divide__upper,axiom,
% 5.17/5.49 ! [Q2: rat,P5: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.17/5.49 => ( ord_less_rat @ P5 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P5 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_divide_upper
% 5.17/5.49 thf(fact_7574_ceiling__divide__lower,axiom,
% 5.17/5.49 ! [Q2: real,P5: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ Q2 )
% 5.17/5.49 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P5 @ Q2 ) ) ) @ one_one_real ) @ Q2 ) @ P5 ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_divide_lower
% 5.17/5.49 thf(fact_7575_ceiling__divide__lower,axiom,
% 5.17/5.49 ! [Q2: rat,P5: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ Q2 )
% 5.17/5.49 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P5 @ Q2 ) ) ) @ one_one_rat ) @ Q2 ) @ P5 ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_divide_lower
% 5.17/5.49 thf(fact_7576_ceiling__eq,axiom,
% 5.17/5.49 ! [N: int,X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.17/5.49 => ( ( archim2889992004027027881ng_rat @ X )
% 5.17/5.49 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_eq
% 5.17/5.49 thf(fact_7577_ceiling__eq,axiom,
% 5.17/5.49 ! [N: int,X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.17/5.49 => ( ( archim7802044766580827645g_real @ X )
% 5.17/5.49 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_eq
% 5.17/5.49 thf(fact_7578_cos__one__2pi__int,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( cos_real @ X )
% 5.17/5.49 = one_one_real )
% 5.17/5.49 = ( ? [X3: int] :
% 5.17/5.49 ( X
% 5.17/5.49 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_one_2pi_int
% 5.17/5.49 thf(fact_7579_arccos,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.17/5.49 & ( ord_less_eq_real @ ( arccos @ Y4 ) @ pi )
% 5.17/5.49 & ( ( cos_real @ ( arccos @ Y4 ) )
% 5.17/5.49 = Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos
% 5.17/5.49 thf(fact_7580_arccos__minus__abs,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.49 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.17/5.49 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_minus_abs
% 5.17/5.49 thf(fact_7581_sin__cos__eq,axiom,
% 5.17/5.49 ( sin_real
% 5.17/5.49 = ( ^ [X3: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_cos_eq
% 5.17/5.49 thf(fact_7582_sin__cos__eq,axiom,
% 5.17/5.49 ( sin_complex
% 5.17/5.49 = ( ^ [X3: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_cos_eq
% 5.17/5.49 thf(fact_7583_cos__sin__eq,axiom,
% 5.17/5.49 ( cos_real
% 5.17/5.49 = ( ^ [X3: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_sin_eq
% 5.17/5.49 thf(fact_7584_cos__sin__eq,axiom,
% 5.17/5.49 ( cos_complex
% 5.17/5.49 = ( ^ [X3: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_sin_eq
% 5.17/5.49 thf(fact_7585_minus__sin__cos__eq,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( uminus_uminus_real @ ( sin_real @ X ) )
% 5.17/5.49 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_sin_cos_eq
% 5.17/5.49 thf(fact_7586_minus__sin__cos__eq,axiom,
% 5.17/5.49 ! [X: complex] :
% 5.17/5.49 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X ) )
% 5.17/5.49 = ( cos_complex @ ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_sin_cos_eq
% 5.17/5.49 thf(fact_7587_arccos__le__pi2,axiom,
% 5.17/5.49 ! [Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.49 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.17/5.49 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % arccos_le_pi2
% 5.17/5.49 thf(fact_7588_floor__log__eq__powr__iff,axiom,
% 5.17/5.49 ! [X: real,B: real,K: int] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.49 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.17/5.49 = K )
% 5.17/5.49 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.17/5.49 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_log_eq_powr_iff
% 5.17/5.49 thf(fact_7589_cos__zero__iff__int,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( cos_real @ X )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( ? [I2: int] :
% 5.17/5.49 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 5.17/5.49 & ( X
% 5.17/5.49 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cos_zero_iff_int
% 5.17/5.49 thf(fact_7590_sin__zero__iff__int,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( sin_real @ X )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( ? [I2: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I2 )
% 5.17/5.49 & ( X
% 5.17/5.49 = ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_zero_iff_int
% 5.17/5.49 thf(fact_7591_powr__int,axiom,
% 5.17/5.49 ! [X: real,I: int] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.17/5.49 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.17/5.49 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 5.17/5.49 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.17/5.49 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.17/5.49 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % powr_int
% 5.17/5.49 thf(fact_7592_round__unique,axiom,
% 5.17/5.49 ! [X: rat,Y4: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y4 ) )
% 5.17/5.49 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.49 => ( ( archim7778729529865785530nd_rat @ X )
% 5.17/5.49 = Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_unique
% 5.17/5.49 thf(fact_7593_round__unique,axiom,
% 5.17/5.49 ! [X: real,Y4: int] :
% 5.17/5.49 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y4 ) )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.49 => ( ( archim8280529875227126926d_real @ X )
% 5.17/5.49 = Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_unique
% 5.17/5.49 thf(fact_7594_round__unique_H,axiom,
% 5.17/5.49 ! [X: real,N: int] :
% 5.17/5.49 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.49 => ( ( archim8280529875227126926d_real @ X )
% 5.17/5.49 = N ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_unique'
% 5.17/5.49 thf(fact_7595_round__unique_H,axiom,
% 5.17/5.49 ! [X: rat,N: int] :
% 5.17/5.49 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.17/5.49 => ( ( archim7778729529865785530nd_rat @ X )
% 5.17/5.49 = N ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_unique'
% 5.17/5.49 thf(fact_7596_of__int__round__abs__le,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_abs_le
% 5.17/5.49 thf(fact_7597_of__int__round__abs__le,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_abs_le
% 5.17/5.49 thf(fact_7598_of__int__round__gt,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_gt
% 5.17/5.49 thf(fact_7599_of__int__round__gt,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_gt
% 5.17/5.49 thf(fact_7600_of__int__round__ge,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_ge
% 5.17/5.49 thf(fact_7601_of__int__round__ge,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_ge
% 5.17/5.49 thf(fact_7602_round__0,axiom,
% 5.17/5.49 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 5.17/5.49 = zero_zero_int ) ).
% 5.17/5.49
% 5.17/5.49 % round_0
% 5.17/5.49 thf(fact_7603_round__0,axiom,
% 5.17/5.49 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 5.17/5.49 = zero_zero_int ) ).
% 5.17/5.49
% 5.17/5.49 % round_0
% 5.17/5.49 thf(fact_7604_round__numeral,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.17/5.49 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_numeral
% 5.17/5.49 thf(fact_7605_round__numeral,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.17/5.49 = ( numeral_numeral_int @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_numeral
% 5.17/5.49 thf(fact_7606_round__of__nat,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( archim8280529875227126926d_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.17/5.49 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_of_nat
% 5.17/5.49 thf(fact_7607_round__of__nat,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( archim7778729529865785530nd_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.17/5.49 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_of_nat
% 5.17/5.49 thf(fact_7608_round__neg__numeral,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.17/5.49 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_neg_numeral
% 5.17/5.49 thf(fact_7609_round__neg__numeral,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.17/5.49 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_neg_numeral
% 5.17/5.49 thf(fact_7610_round__mono,axiom,
% 5.17/5.49 ! [X: rat,Y4: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.49 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_mono
% 5.17/5.49 thf(fact_7611_round__mono,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.49 => ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X ) @ ( archim8280529875227126926d_real @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_mono
% 5.17/5.49 thf(fact_7612_floor__le__round,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X ) @ ( archim8280529875227126926d_real @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_le_round
% 5.17/5.49 thf(fact_7613_floor__le__round,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim7778729529865785530nd_rat @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % floor_le_round
% 5.17/5.49 thf(fact_7614_ceiling__ge__round,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X ) @ ( archim7802044766580827645g_real @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % ceiling_ge_round
% 5.17/5.49 thf(fact_7615_round__diff__minimal,axiom,
% 5.17/5.49 ! [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 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_diff_minimal
% 5.17/5.49 thf(fact_7616_round__diff__minimal,axiom,
% 5.17/5.49 ! [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 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_diff_minimal
% 5.17/5.49 thf(fact_7617_round__def,axiom,
% 5.17/5.49 ( archim8280529875227126926d_real
% 5.17/5.49 = ( ^ [X3: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_def
% 5.17/5.49 thf(fact_7618_round__def,axiom,
% 5.17/5.49 ( archim7778729529865785530nd_rat
% 5.17/5.49 = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_def
% 5.17/5.49 thf(fact_7619_of__int__round__le,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_le
% 5.17/5.49 thf(fact_7620_of__int__round__le,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_round_le
% 5.17/5.49 thf(fact_7621_round__altdef,axiom,
% 5.17/5.49 ( archim8280529875227126926d_real
% 5.17/5.49 = ( ^ [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 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_altdef
% 5.17/5.49 thf(fact_7622_round__altdef,axiom,
% 5.17/5.49 ( archim7778729529865785530nd_rat
% 5.17/5.49 = ( ^ [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 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % round_altdef
% 5.17/5.49 thf(fact_7623_exp__two__pi__i,axiom,
% 5.17/5.49 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % exp_two_pi_i
% 5.17/5.49 thf(fact_7624_exp__two__pi__i_H,axiom,
% 5.17/5.49 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % exp_two_pi_i'
% 5.17/5.49 thf(fact_7625_cot__less__zero,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cot_less_zero
% 5.17/5.49 thf(fact_7626_cot__periodic,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.17/5.49 = ( cot_real @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % cot_periodic
% 5.17/5.49 thf(fact_7627_cot__zero,axiom,
% 5.17/5.49 ( ( cot_complex @ zero_zero_complex )
% 5.17/5.49 = zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % cot_zero
% 5.17/5.49 thf(fact_7628_cot__zero,axiom,
% 5.17/5.49 ( ( cot_real @ zero_zero_real )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % cot_zero
% 5.17/5.49 thf(fact_7629_frac__of__int,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( archim2898591450579166408c_real @ ( ring_1_of_int_real @ Z ) )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % frac_of_int
% 5.17/5.49 thf(fact_7630_frac__of__int,axiom,
% 5.17/5.49 ! [Z: int] :
% 5.17/5.49 ( ( archimedean_frac_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.17/5.49 = zero_zero_rat ) ).
% 5.17/5.49
% 5.17/5.49 % frac_of_int
% 5.17/5.49 thf(fact_7631_cot__pi,axiom,
% 5.17/5.49 ( ( cot_real @ pi )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % cot_pi
% 5.17/5.49 thf(fact_7632_cot__npi,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % cot_npi
% 5.17/5.49 thf(fact_7633_power2__i,axiom,
% 5.17/5.49 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % power2_i
% 5.17/5.49 thf(fact_7634_i__even__power,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.49 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % i_even_power
% 5.17/5.49 thf(fact_7635_complex__i__not__zero,axiom,
% 5.17/5.49 imaginary_unit != zero_zero_complex ).
% 5.17/5.49
% 5.17/5.49 % complex_i_not_zero
% 5.17/5.49 thf(fact_7636_frac__ge__0,axiom,
% 5.17/5.49 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_ge_0
% 5.17/5.49 thf(fact_7637_frac__ge__0,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_ge_0
% 5.17/5.49 thf(fact_7638_imaginary__unit_Ocode,axiom,
% 5.17/5.49 ( imaginary_unit
% 5.17/5.49 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % imaginary_unit.code
% 5.17/5.49 thf(fact_7639_Complex__eq__i,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ( complex2 @ X @ Y4 )
% 5.17/5.49 = imaginary_unit )
% 5.17/5.49 = ( ( X = zero_zero_real )
% 5.17/5.49 & ( Y4 = one_one_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Complex_eq_i
% 5.17/5.49 thf(fact_7640_frac__def,axiom,
% 5.17/5.49 ( archim2898591450579166408c_real
% 5.17/5.49 = ( ^ [X3: real] : ( minus_minus_real @ X3 @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_def
% 5.17/5.49 thf(fact_7641_frac__def,axiom,
% 5.17/5.49 ( archimedean_frac_rat
% 5.17/5.49 = ( ^ [X3: rat] : ( minus_minus_rat @ X3 @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_def
% 5.17/5.49 thf(fact_7642_cot__def,axiom,
% 5.17/5.49 ( cot_complex
% 5.17/5.49 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X3 ) @ ( sin_complex @ X3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cot_def
% 5.17/5.49 thf(fact_7643_cot__def,axiom,
% 5.17/5.49 ( cot_real
% 5.17/5.49 = ( ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cot_def
% 5.17/5.49 thf(fact_7644_complex__of__real__i,axiom,
% 5.17/5.49 ! [R2: real] :
% 5.17/5.49 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.17/5.49 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.17/5.49
% 5.17/5.49 % complex_of_real_i
% 5.17/5.49 thf(fact_7645_i__complex__of__real,axiom,
% 5.17/5.49 ! [R2: real] :
% 5.17/5.49 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.17/5.49 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.17/5.49
% 5.17/5.49 % i_complex_of_real
% 5.17/5.49 thf(fact_7646_frac__eq,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ( archimedean_frac_rat @ X )
% 5.17/5.49 = X )
% 5.17/5.49 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_eq
% 5.17/5.49 thf(fact_7647_frac__eq,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( archim2898591450579166408c_real @ X )
% 5.17/5.49 = X )
% 5.17/5.49 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.49 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_eq
% 5.17/5.49 thf(fact_7648_frac__add,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y4 ) ) @ one_one_real )
% 5.17/5.49 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.49 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y4 ) ) ) )
% 5.17/5.49 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y4 ) ) @ one_one_real )
% 5.17/5.49 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.49 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y4 ) ) @ one_one_real ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_add
% 5.17/5.49 thf(fact_7649_frac__add,axiom,
% 5.17/5.49 ! [X: rat,Y4: rat] :
% 5.17/5.49 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y4 ) ) @ one_one_rat )
% 5.17/5.49 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y4 ) )
% 5.17/5.49 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y4 ) ) ) )
% 5.17/5.49 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y4 ) ) @ one_one_rat )
% 5.17/5.49 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y4 ) )
% 5.17/5.49 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y4 ) ) @ one_one_rat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_add
% 5.17/5.49 thf(fact_7650_cot__gt__zero,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.49 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cot_gt_zero
% 5.17/5.49 thf(fact_7651_tan__cot_H,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.17/5.49 = ( cot_real @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % tan_cot'
% 5.17/5.49 thf(fact_7652_Arg__minus__ii,axiom,
% 5.17/5.49 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.17/5.49 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Arg_minus_ii
% 5.17/5.49 thf(fact_7653_csqrt__ii,axiom,
% 5.17/5.49 ( ( csqrt @ imaginary_unit )
% 5.17/5.49 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % csqrt_ii
% 5.17/5.49 thf(fact_7654_Arg__ii,axiom,
% 5.17/5.49 ( ( arg @ imaginary_unit )
% 5.17/5.49 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Arg_ii
% 5.17/5.49 thf(fact_7655_cis__minus__pi__half,axiom,
% 5.17/5.49 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.17/5.49
% 5.17/5.49 % cis_minus_pi_half
% 5.17/5.49 thf(fact_7656_signed__take__bit__eq__take__bit__minus,axiom,
% 5.17/5.49 ( bit_ri631733984087533419it_int
% 5.17/5.49 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % signed_take_bit_eq_take_bit_minus
% 5.17/5.49 thf(fact_7657_csqrt__eq__0,axiom,
% 5.17/5.49 ! [Z: complex] :
% 5.17/5.49 ( ( ( csqrt @ Z )
% 5.17/5.49 = zero_zero_complex )
% 5.17/5.49 = ( Z = zero_zero_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % csqrt_eq_0
% 5.17/5.49 thf(fact_7658_csqrt__0,axiom,
% 5.17/5.49 ( ( csqrt @ zero_zero_complex )
% 5.17/5.49 = zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % csqrt_0
% 5.17/5.49 thf(fact_7659_cis__zero,axiom,
% 5.17/5.49 ( ( cis @ zero_zero_real )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % cis_zero
% 5.17/5.49 thf(fact_7660_bit__numeral__Bit0__Suc__iff,axiom,
% 5.17/5.49 ! [M: num,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_Bit0_Suc_iff
% 5.17/5.49 thf(fact_7661_bit__numeral__Bit0__Suc__iff,axiom,
% 5.17/5.49 ! [M: num,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_Bit0_Suc_iff
% 5.17/5.49 thf(fact_7662_bit__numeral__Bit1__Suc__iff,axiom,
% 5.17/5.49 ! [M: num,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_Bit1_Suc_iff
% 5.17/5.49 thf(fact_7663_bit__numeral__Bit1__Suc__iff,axiom,
% 5.17/5.49 ! [M: num,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_Bit1_Suc_iff
% 5.17/5.49 thf(fact_7664_signed__take__bit__nonnegative__iff,axiom,
% 5.17/5.49 ! [N: nat,K: int] :
% 5.17/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.17/5.49 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % signed_take_bit_nonnegative_iff
% 5.17/5.49 thf(fact_7665_signed__take__bit__negative__iff,axiom,
% 5.17/5.49 ! [N: nat,K: int] :
% 5.17/5.49 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % signed_take_bit_negative_iff
% 5.17/5.49 thf(fact_7666_bit__numeral__simps_I2_J,axiom,
% 5.17/5.49 ! [W: num,N: num] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_simps(2)
% 5.17/5.49 thf(fact_7667_bit__numeral__simps_I2_J,axiom,
% 5.17/5.49 ! [W: num,N: num] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_simps(2)
% 5.17/5.49 thf(fact_7668_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.17/5.49 ! [W: num,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_minus_numeral_Bit0_Suc_iff
% 5.17/5.49 thf(fact_7669_bit__numeral__simps_I3_J,axiom,
% 5.17/5.49 ! [W: num,N: num] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_simps(3)
% 5.17/5.49 thf(fact_7670_bit__numeral__simps_I3_J,axiom,
% 5.17/5.49 ! [W: num,N: num] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_simps(3)
% 5.17/5.49 thf(fact_7671_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.17/5.49 ! [W: num,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.17/5.49 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_minus_numeral_Bit1_Suc_iff
% 5.17/5.49 thf(fact_7672_power2__csqrt,axiom,
% 5.17/5.49 ! [Z: complex] :
% 5.17/5.49 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.49 = Z ) ).
% 5.17/5.49
% 5.17/5.49 % power2_csqrt
% 5.17/5.49 thf(fact_7673_bit__0,axiom,
% 5.17/5.49 ! [A: code_integer] :
% 5.17/5.49 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.17/5.49 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_0
% 5.17/5.49 thf(fact_7674_bit__0,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.17/5.49 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_0
% 5.17/5.49 thf(fact_7675_bit__0,axiom,
% 5.17/5.49 ! [A: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.17/5.49 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_0
% 5.17/5.49 thf(fact_7676_bit__minus__numeral__int_I1_J,axiom,
% 5.17/5.49 ! [W: num,N: num] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_minus_numeral_int(1)
% 5.17/5.49 thf(fact_7677_bit__minus__numeral__int_I2_J,axiom,
% 5.17/5.49 ! [W: num,N: num] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.49 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_minus_numeral_int(2)
% 5.17/5.49 thf(fact_7678_bit__mod__2__iff,axiom,
% 5.17/5.49 ! [A: code_integer,N: nat] :
% 5.17/5.49 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N )
% 5.17/5.49 = ( ( N = zero_zero_nat )
% 5.17/5.49 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_mod_2_iff
% 5.17/5.49 thf(fact_7679_bit__mod__2__iff,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N )
% 5.17/5.49 = ( ( N = zero_zero_nat )
% 5.17/5.49 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_mod_2_iff
% 5.17/5.49 thf(fact_7680_bit__mod__2__iff,axiom,
% 5.17/5.49 ! [A: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.17/5.49 = ( ( N = zero_zero_nat )
% 5.17/5.49 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_mod_2_iff
% 5.17/5.49 thf(fact_7681_cis__pi__half,axiom,
% 5.17/5.49 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.49 = imaginary_unit ) ).
% 5.17/5.49
% 5.17/5.49 % cis_pi_half
% 5.17/5.49 thf(fact_7682_cis__2pi,axiom,
% 5.17/5.49 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % cis_2pi
% 5.17/5.49 thf(fact_7683_cis__Arg,axiom,
% 5.17/5.49 ! [Z: complex] :
% 5.17/5.49 ( ( Z != zero_zero_complex )
% 5.17/5.49 => ( ( cis @ ( arg @ Z ) )
% 5.17/5.49 = ( sgn_sgn_complex @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cis_Arg
% 5.17/5.49 thf(fact_7684_bit__numeral__iff,axiom,
% 5.17/5.49 ! [M: num,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_iff
% 5.17/5.49 thf(fact_7685_bit__numeral__iff,axiom,
% 5.17/5.49 ! [M: num,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_iff
% 5.17/5.49 thf(fact_7686_bit__of__nat__iff__bit,axiom,
% 5.17/5.49 ! [M: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_of_nat_iff_bit
% 5.17/5.49 thf(fact_7687_bit__of__nat__iff__bit,axiom,
% 5.17/5.49 ! [M: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ M @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_of_nat_iff_bit
% 5.17/5.49 thf(fact_7688_bit__disjunctive__add__iff,axiom,
% 5.17/5.49 ! [A: int,B: int,N: nat] :
% 5.17/5.49 ( ! [N2: nat] :
% 5.17/5.49 ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.17/5.49 | ~ ( bit_se1146084159140164899it_int @ B @ N2 ) )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 | ( bit_se1146084159140164899it_int @ B @ N ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_disjunctive_add_iff
% 5.17/5.49 thf(fact_7689_bit__disjunctive__add__iff,axiom,
% 5.17/5.49 ! [A: nat,B: nat,N: nat] :
% 5.17/5.49 ( ! [N2: nat] :
% 5.17/5.49 ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.17/5.49 | ~ ( bit_se1148574629649215175it_nat @ B @ N2 ) )
% 5.17/5.49 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.17/5.49 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 | ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_disjunctive_add_iff
% 5.17/5.49 thf(fact_7690_bit__and__iff,axiom,
% 5.17/5.49 ! [A: int,B: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 & ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_and_iff
% 5.17/5.49 thf(fact_7691_bit__and__iff,axiom,
% 5.17/5.49 ! [A: nat,B: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N )
% 5.17/5.49 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 & ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_and_iff
% 5.17/5.49 thf(fact_7692_bit__and__int__iff,axiom,
% 5.17/5.49 ! [K: int,L: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.17/5.49 & ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_and_int_iff
% 5.17/5.49 thf(fact_7693_bit__unset__bit__iff,axiom,
% 5.17/5.49 ! [M: nat,A: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 & ( M != N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_unset_bit_iff
% 5.17/5.49 thf(fact_7694_bit__unset__bit__iff,axiom,
% 5.17/5.49 ! [M: nat,A: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N )
% 5.17/5.49 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 & ( M != N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_unset_bit_iff
% 5.17/5.49 thf(fact_7695_bit__unset__bit__iff,axiom,
% 5.17/5.49 ! [M: nat,A: code_integer,N: nat] :
% 5.17/5.49 ( ( bit_se9216721137139052372nteger @ ( bit_se8260200283734997820nteger @ M @ A ) @ N )
% 5.17/5.49 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.17/5.49 & ( M != N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_unset_bit_iff
% 5.17/5.49 thf(fact_7696_cis__divide,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.17/5.49 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cis_divide
% 5.17/5.49 thf(fact_7697_cis__neq__zero,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( cis @ A )
% 5.17/5.49 != zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % cis_neq_zero
% 5.17/5.49 thf(fact_7698_not__bit__1__Suc,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % not_bit_1_Suc
% 5.17/5.49 thf(fact_7699_not__bit__1__Suc,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % not_bit_1_Suc
% 5.17/5.49 thf(fact_7700_bit__1__iff,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ one_one_int @ N )
% 5.17/5.49 = ( N = zero_zero_nat ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_1_iff
% 5.17/5.49 thf(fact_7701_bit__1__iff,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N )
% 5.17/5.49 = ( N = zero_zero_nat ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_1_iff
% 5.17/5.49 thf(fact_7702_bit__numeral__simps_I1_J,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_simps(1)
% 5.17/5.49 thf(fact_7703_bit__numeral__simps_I1_J,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_numeral_simps(1)
% 5.17/5.49 thf(fact_7704_bit__take__bit__iff,axiom,
% 5.17/5.49 ! [M: nat,A: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N )
% 5.17/5.49 = ( ( ord_less_nat @ N @ M )
% 5.17/5.49 & ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_take_bit_iff
% 5.17/5.49 thf(fact_7705_bit__take__bit__iff,axiom,
% 5.17/5.49 ! [M: nat,A: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N )
% 5.17/5.49 = ( ( ord_less_nat @ N @ M )
% 5.17/5.49 & ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_take_bit_iff
% 5.17/5.49 thf(fact_7706_bit__of__bool__iff,axiom,
% 5.17/5.49 ! [B: $o,N: nat] :
% 5.17/5.49 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N )
% 5.17/5.49 = ( B
% 5.17/5.49 & ( N = zero_zero_nat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_of_bool_iff
% 5.17/5.49 thf(fact_7707_bit__of__bool__iff,axiom,
% 5.17/5.49 ! [B: $o,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N )
% 5.17/5.49 = ( B
% 5.17/5.49 & ( N = zero_zero_nat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_of_bool_iff
% 5.17/5.49 thf(fact_7708_bit__of__bool__iff,axiom,
% 5.17/5.49 ! [B: $o,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N )
% 5.17/5.49 = ( B
% 5.17/5.49 & ( N = zero_zero_nat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_of_bool_iff
% 5.17/5.49 thf(fact_7709_signed__take__bit__eq__if__positive,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 => ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.17/5.49 = ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % signed_take_bit_eq_if_positive
% 5.17/5.49 thf(fact_7710_DeMoivre,axiom,
% 5.17/5.49 ! [A: real,N: nat] :
% 5.17/5.49 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.17/5.49 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % DeMoivre
% 5.17/5.49 thf(fact_7711_cis__Arg__unique,axiom,
% 5.17/5.49 ! [Z: complex,X: real] :
% 5.17/5.49 ( ( ( sgn_sgn_complex @ Z )
% 5.17/5.49 = ( cis @ X ) )
% 5.17/5.49 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.17/5.49 => ( ( ord_less_eq_real @ X @ pi )
% 5.17/5.49 => ( ( arg @ Z )
% 5.17/5.49 = X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % cis_Arg_unique
% 5.17/5.49 thf(fact_7712_bit__not__int__iff_H,axiom,
% 5.17/5.49 ! [K: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.17/5.49 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_not_int_iff'
% 5.17/5.49 thf(fact_7713_flip__bit__eq__if,axiom,
% 5.17/5.49 ( bit_se2159334234014336723it_int
% 5.17/5.49 = ( ^ [N4: nat,A3: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A3 @ N4 ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N4 @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % flip_bit_eq_if
% 5.17/5.49 thf(fact_7714_flip__bit__eq__if,axiom,
% 5.17/5.49 ( bit_se2161824704523386999it_nat
% 5.17/5.49 = ( ^ [N4: nat,A3: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A3 @ N4 ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N4 @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % flip_bit_eq_if
% 5.17/5.49 thf(fact_7715_flip__bit__eq__if,axiom,
% 5.17/5.49 ( bit_se1345352211410354436nteger
% 5.17/5.49 = ( ^ [N4: nat,A3: code_integer] : ( if_nat5617392847756311170nteger @ ( bit_se9216721137139052372nteger @ A3 @ N4 ) @ bit_se8260200283734997820nteger @ bit_se2793503036327961859nteger @ N4 @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % flip_bit_eq_if
% 5.17/5.49 thf(fact_7716_Arg__correct,axiom,
% 5.17/5.49 ! [Z: complex] :
% 5.17/5.49 ( ( Z != zero_zero_complex )
% 5.17/5.49 => ( ( ( sgn_sgn_complex @ Z )
% 5.17/5.49 = ( cis @ ( arg @ Z ) ) )
% 5.17/5.49 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.17/5.49 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Arg_correct
% 5.17/5.49 thf(fact_7717_Arg__zero,axiom,
% 5.17/5.49 ( ( arg @ zero_zero_complex )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % Arg_zero
% 5.17/5.49 thf(fact_7718_bit__imp__take__bit__positive,axiom,
% 5.17/5.49 ! [N: nat,M: nat,K: int] :
% 5.17/5.49 ( ( ord_less_nat @ N @ M )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.17/5.49 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_imp_take_bit_positive
% 5.17/5.49 thf(fact_7719_bit__concat__bit__iff,axiom,
% 5.17/5.49 ! [M: nat,K: int,L: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 5.17/5.49 = ( ( ( ord_less_nat @ N @ M )
% 5.17/5.49 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.17/5.49 | ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.49 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_concat_bit_iff
% 5.17/5.49 thf(fact_7720_signed__take__bit__eq__concat__bit,axiom,
% 5.17/5.49 ( bit_ri631733984087533419it_int
% 5.17/5.49 = ( ^ [N4: nat,K3: int] : ( bit_concat_bit @ N4 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % signed_take_bit_eq_concat_bit
% 5.17/5.49 thf(fact_7721_exp__eq__0__imp__not__bit,axiom,
% 5.17/5.49 ! [N: nat,A: int] :
% 5.17/5.49 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.49 = zero_zero_int )
% 5.17/5.49 => ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % exp_eq_0_imp_not_bit
% 5.17/5.49 thf(fact_7722_exp__eq__0__imp__not__bit,axiom,
% 5.17/5.49 ! [N: nat,A: nat] :
% 5.17/5.49 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.49 = zero_zero_nat )
% 5.17/5.49 => ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % exp_eq_0_imp_not_bit
% 5.17/5.49 thf(fact_7723_bit__Suc,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_Suc
% 5.17/5.49 thf(fact_7724_bit__Suc,axiom,
% 5.17/5.49 ! [A: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N ) )
% 5.17/5.49 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_Suc
% 5.17/5.49 thf(fact_7725_bit__iff__idd__imp__stable,axiom,
% 5.17/5.49 ! [A: code_integer] :
% 5.17/5.49 ( ! [N2: nat] :
% 5.17/5.49 ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.17/5.49 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.49 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.49 = A ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_iff_idd_imp_stable
% 5.17/5.49 thf(fact_7726_bit__iff__idd__imp__stable,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ! [N2: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.17/5.49 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.49 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.49 = A ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_iff_idd_imp_stable
% 5.17/5.49 thf(fact_7727_bit__iff__idd__imp__stable,axiom,
% 5.17/5.49 ! [A: nat] :
% 5.17/5.49 ( ! [N2: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.17/5.49 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.49 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.49 = A ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_iff_idd_imp_stable
% 5.17/5.49 thf(fact_7728_stable__imp__bit__iff__odd,axiom,
% 5.17/5.49 ! [A: code_integer,N: nat] :
% 5.17/5.49 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.49 = A )
% 5.17/5.49 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.17/5.49 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % stable_imp_bit_iff_odd
% 5.17/5.49 thf(fact_7729_stable__imp__bit__iff__odd,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.49 = A )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % stable_imp_bit_iff_odd
% 5.17/5.49 thf(fact_7730_stable__imp__bit__iff__odd,axiom,
% 5.17/5.49 ! [A: nat,N: nat] :
% 5.17/5.49 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.49 = A )
% 5.17/5.49 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % stable_imp_bit_iff_odd
% 5.17/5.49 thf(fact_7731_int__bit__bound,axiom,
% 5.17/5.49 ! [K: int] :
% 5.17/5.49 ~ ! [N2: nat] :
% 5.17/5.49 ( ! [M2: nat] :
% 5.17/5.49 ( ( ord_less_eq_nat @ N2 @ M2 )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.17/5.49 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 5.17/5.49 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.17/5.49 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % int_bit_bound
% 5.17/5.49 thf(fact_7732_bit__iff__odd,axiom,
% 5.17/5.49 ( bit_se9216721137139052372nteger
% 5.17/5.49 = ( ^ [A3: code_integer,N4: nat] :
% 5.17/5.49 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_iff_odd
% 5.17/5.49 thf(fact_7733_bit__iff__odd,axiom,
% 5.17/5.49 ( bit_se1146084159140164899it_int
% 5.17/5.49 = ( ^ [A3: int,N4: nat] :
% 5.17/5.49 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_iff_odd
% 5.17/5.49 thf(fact_7734_bit__iff__odd,axiom,
% 5.17/5.49 ( bit_se1148574629649215175it_nat
% 5.17/5.49 = ( ^ [A3: nat,N4: nat] :
% 5.17/5.49 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_iff_odd
% 5.17/5.49 thf(fact_7735_and__exp__eq__0__iff__not__bit,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.49 = zero_zero_int )
% 5.17/5.49 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % and_exp_eq_0_iff_not_bit
% 5.17/5.49 thf(fact_7736_and__exp__eq__0__iff__not__bit,axiom,
% 5.17/5.49 ! [A: nat,N: nat] :
% 5.17/5.49 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.49 = zero_zero_nat )
% 5.17/5.49 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % and_exp_eq_0_iff_not_bit
% 5.17/5.49 thf(fact_7737_bit__int__def,axiom,
% 5.17/5.49 ( bit_se1146084159140164899it_int
% 5.17/5.49 = ( ^ [K3: int,N4: nat] :
% 5.17/5.49 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_int_def
% 5.17/5.49 thf(fact_7738_of__real__sqrt,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 5.17/5.49 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_real_sqrt
% 5.17/5.49 thf(fact_7739_even__bit__succ__iff,axiom,
% 5.17/5.49 ! [A: code_integer,N: nat] :
% 5.17/5.49 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N )
% 5.17/5.49 = ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.17/5.49 | ( N = zero_zero_nat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_bit_succ_iff
% 5.17/5.49 thf(fact_7740_even__bit__succ__iff,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 | ( N = zero_zero_nat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_bit_succ_iff
% 5.17/5.49 thf(fact_7741_even__bit__succ__iff,axiom,
% 5.17/5.49 ! [A: nat,N: nat] :
% 5.17/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N )
% 5.17/5.49 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 | ( N = zero_zero_nat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_bit_succ_iff
% 5.17/5.49 thf(fact_7742_odd__bit__iff__bit__pred,axiom,
% 5.17/5.49 ! [A: code_integer,N: nat] :
% 5.17/5.49 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 => ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.17/5.49 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N )
% 5.17/5.49 | ( N = zero_zero_nat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % odd_bit_iff_bit_pred
% 5.17/5.49 thf(fact_7743_odd__bit__iff__bit__pred,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N )
% 5.17/5.49 | ( N = zero_zero_nat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % odd_bit_iff_bit_pred
% 5.17/5.49 thf(fact_7744_odd__bit__iff__bit__pred,axiom,
% 5.17/5.49 ! [A: nat,N: nat] :
% 5.17/5.49 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 => ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N )
% 5.17/5.49 | ( N = zero_zero_nat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % odd_bit_iff_bit_pred
% 5.17/5.49 thf(fact_7745_Arg__bounded,axiom,
% 5.17/5.49 ! [Z: complex] :
% 5.17/5.49 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.17/5.49 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.17/5.49
% 5.17/5.49 % Arg_bounded
% 5.17/5.49 thf(fact_7746_bit__sum__mult__2__cases,axiom,
% 5.17/5.49 ! [A: code_integer,B: code_integer,N: nat] :
% 5.17/5.49 ( ! [J2: nat] :
% 5.17/5.49 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.17/5.49 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.17/5.49 = ( ( ( N = zero_zero_nat )
% 5.17/5.49 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.49 & ( ( N != zero_zero_nat )
% 5.17/5.49 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_sum_mult_2_cases
% 5.17/5.49 thf(fact_7747_bit__sum__mult__2__cases,axiom,
% 5.17/5.49 ! [A: int,B: int,N: nat] :
% 5.17/5.49 ( ! [J2: nat] :
% 5.17/5.49 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.17/5.49 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.17/5.49 = ( ( ( N = zero_zero_nat )
% 5.17/5.49 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.49 & ( ( N != zero_zero_nat )
% 5.17/5.49 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_sum_mult_2_cases
% 5.17/5.49 thf(fact_7748_bit__sum__mult__2__cases,axiom,
% 5.17/5.49 ! [A: nat,B: nat,N: nat] :
% 5.17/5.49 ( ! [J2: nat] :
% 5.17/5.49 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.17/5.49 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N )
% 5.17/5.49 = ( ( ( N = zero_zero_nat )
% 5.17/5.49 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.17/5.49 & ( ( N != zero_zero_nat )
% 5.17/5.49 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_sum_mult_2_cases
% 5.17/5.49 thf(fact_7749_bit__rec,axiom,
% 5.17/5.49 ( bit_se9216721137139052372nteger
% 5.17/5.49 = ( ^ [A3: code_integer,N4: nat] :
% 5.17/5.49 ( ( ( N4 = zero_zero_nat )
% 5.17/5.49 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) )
% 5.17/5.49 & ( ( N4 != zero_zero_nat )
% 5.17/5.49 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_rec
% 5.17/5.49 thf(fact_7750_bit__rec,axiom,
% 5.17/5.49 ( bit_se1146084159140164899it_int
% 5.17/5.49 = ( ^ [A3: int,N4: nat] :
% 5.17/5.49 ( ( ( N4 = zero_zero_nat )
% 5.17/5.49 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 5.17/5.49 & ( ( N4 != zero_zero_nat )
% 5.17/5.49 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_rec
% 5.17/5.49 thf(fact_7751_bit__rec,axiom,
% 5.17/5.49 ( bit_se1148574629649215175it_nat
% 5.17/5.49 = ( ^ [A3: nat,N4: nat] :
% 5.17/5.49 ( ( ( N4 = zero_zero_nat )
% 5.17/5.49 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 5.17/5.49 & ( ( N4 != zero_zero_nat )
% 5.17/5.49 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N4 @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_rec
% 5.17/5.49 thf(fact_7752_set__bit__eq,axiom,
% 5.17/5.49 ( bit_se7879613467334960850it_int
% 5.17/5.49 = ( ^ [N4: nat,K3: int] :
% 5.17/5.49 ( plus_plus_int @ K3
% 5.17/5.49 @ ( times_times_int
% 5.17/5.49 @ ( zero_n2684676970156552555ol_int
% 5.17/5.49 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N4 ) )
% 5.17/5.49 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % set_bit_eq
% 5.17/5.49 thf(fact_7753_unset__bit__eq,axiom,
% 5.17/5.49 ( bit_se4203085406695923979it_int
% 5.17/5.49 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % unset_bit_eq
% 5.17/5.49 thf(fact_7754_take__bit__Suc__from__most,axiom,
% 5.17/5.49 ! [N: nat,K: int] :
% 5.17/5.49 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.17/5.49 = ( 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 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % take_bit_Suc_from_most
% 5.17/5.49 thf(fact_7755_cis__multiple__2pi,axiom,
% 5.17/5.49 ! [N: real] :
% 5.17/5.49 ( ( member_real @ N @ ring_1_Ints_real )
% 5.17/5.49 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.17/5.49 = one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % cis_multiple_2pi
% 5.17/5.49 thf(fact_7756_powr__real__of__int,axiom,
% 5.17/5.49 ! [X: real,N: int] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.17/5.49 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.17/5.49 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 5.17/5.49 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.17/5.49 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % powr_real_of_int
% 5.17/5.49 thf(fact_7757_Suc__0__xor__eq,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.49 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.49 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.49 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Suc_0_xor_eq
% 5.17/5.49 thf(fact_7758_xor__Suc__0__eq,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.49 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.49 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.49 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_Suc_0_eq
% 5.17/5.49 thf(fact_7759_gbinomial__absorption_H,axiom,
% 5.17/5.49 ! [K: nat,A: complex] :
% 5.17/5.49 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.49 => ( ( gbinomial_complex @ A @ K )
% 5.17/5.49 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorption'
% 5.17/5.49 thf(fact_7760_gbinomial__absorption_H,axiom,
% 5.17/5.49 ! [K: nat,A: real] :
% 5.17/5.49 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.49 => ( ( gbinomial_real @ A @ K )
% 5.17/5.49 = ( 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 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorption'
% 5.17/5.49 thf(fact_7761_gbinomial__absorption_H,axiom,
% 5.17/5.49 ! [K: nat,A: rat] :
% 5.17/5.49 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.49 => ( ( gbinomial_rat @ A @ K )
% 5.17/5.49 = ( 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 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorption'
% 5.17/5.49 thf(fact_7762_inverse__inverse__eq,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_inverse_eq
% 5.17/5.49 thf(fact_7763_inverse__inverse__eq,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_inverse_eq
% 5.17/5.49 thf(fact_7764_inverse__inverse__eq,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_inverse_eq
% 5.17/5.49 thf(fact_7765_inverse__eq__iff__eq,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ( inverse_inverse_real @ A )
% 5.17/5.49 = ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( A = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_iff_eq
% 5.17/5.49 thf(fact_7766_inverse__eq__iff__eq,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 = ( A = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_iff_eq
% 5.17/5.49 thf(fact_7767_inverse__eq__iff__eq,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( A = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_iff_eq
% 5.17/5.49 thf(fact_7768_bit_Oxor__left__self,axiom,
% 5.17/5.49 ! [X: int,Y4: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ X @ ( bit_se6526347334894502574or_int @ X @ Y4 ) )
% 5.17/5.49 = Y4 ) ).
% 5.17/5.49
% 5.17/5.49 % bit.xor_left_self
% 5.17/5.49 thf(fact_7769_inverse__nonzero__iff__nonzero,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ( inverse_inverse_real @ A )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( A = zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonzero_iff_nonzero
% 5.17/5.49 thf(fact_7770_inverse__nonzero__iff__nonzero,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = zero_zero_complex )
% 5.17/5.49 = ( A = zero_zero_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonzero_iff_nonzero
% 5.17/5.49 thf(fact_7771_inverse__nonzero__iff__nonzero,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = zero_zero_rat )
% 5.17/5.49 = ( A = zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonzero_iff_nonzero
% 5.17/5.49 thf(fact_7772_inverse__zero,axiom,
% 5.17/5.49 ( ( inverse_inverse_real @ zero_zero_real )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_zero
% 5.17/5.49 thf(fact_7773_inverse__zero,axiom,
% 5.17/5.49 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.17/5.49 = zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_zero
% 5.17/5.49 thf(fact_7774_inverse__zero,axiom,
% 5.17/5.49 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.17/5.49 = zero_zero_rat ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_zero
% 5.17/5.49 thf(fact_7775_inverse__mult__distrib,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.17/5.49 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_mult_distrib
% 5.17/5.49 thf(fact_7776_inverse__mult__distrib,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.17/5.49 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_mult_distrib
% 5.17/5.49 thf(fact_7777_inverse__mult__distrib,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.49 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_mult_distrib
% 5.17/5.49 thf(fact_7778_inverse__1,axiom,
% 5.17/5.49 ( ( inverse_inverse_real @ one_one_real )
% 5.17/5.49 = one_one_real ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_1
% 5.17/5.49 thf(fact_7779_inverse__1,axiom,
% 5.17/5.49 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_1
% 5.17/5.49 thf(fact_7780_inverse__1,axiom,
% 5.17/5.49 ( ( inverse_inverse_rat @ one_one_rat )
% 5.17/5.49 = one_one_rat ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_1
% 5.17/5.49 thf(fact_7781_inverse__eq__1__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( inverse_inverse_real @ X )
% 5.17/5.49 = one_one_real )
% 5.17/5.49 = ( X = one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_1_iff
% 5.17/5.49 thf(fact_7782_inverse__eq__1__iff,axiom,
% 5.17/5.49 ! [X: complex] :
% 5.17/5.49 ( ( ( invers8013647133539491842omplex @ X )
% 5.17/5.49 = one_one_complex )
% 5.17/5.49 = ( X = one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_1_iff
% 5.17/5.49 thf(fact_7783_inverse__eq__1__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ( inverse_inverse_rat @ X )
% 5.17/5.49 = one_one_rat )
% 5.17/5.49 = ( X = one_one_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_1_iff
% 5.17/5.49 thf(fact_7784_inverse__divide,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.17/5.49 = ( divide_divide_real @ B @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_divide
% 5.17/5.49 thf(fact_7785_inverse__divide,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.49 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_divide
% 5.17/5.49 thf(fact_7786_inverse__divide,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.17/5.49 = ( divide_divide_rat @ B @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_divide
% 5.17/5.49 thf(fact_7787_inverse__minus__eq,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_minus_eq
% 5.17/5.49 thf(fact_7788_inverse__minus__eq,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_minus_eq
% 5.17/5.49 thf(fact_7789_inverse__minus__eq,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.49 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_minus_eq
% 5.17/5.49 thf(fact_7790_xor_Oright__neutral,axiom,
% 5.17/5.49 ! [A: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % xor.right_neutral
% 5.17/5.49 thf(fact_7791_xor_Oright__neutral,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % xor.right_neutral
% 5.17/5.49 thf(fact_7792_xor_Oleft__neutral,axiom,
% 5.17/5.49 ! [A: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % xor.left_neutral
% 5.17/5.49 thf(fact_7793_xor_Oleft__neutral,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 5.17/5.49 = A ) ).
% 5.17/5.49
% 5.17/5.49 % xor.left_neutral
% 5.17/5.49 thf(fact_7794_xor__self__eq,axiom,
% 5.17/5.49 ! [A: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ A @ A )
% 5.17/5.49 = zero_zero_nat ) ).
% 5.17/5.49
% 5.17/5.49 % xor_self_eq
% 5.17/5.49 thf(fact_7795_xor__self__eq,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ A @ A )
% 5.17/5.49 = zero_zero_int ) ).
% 5.17/5.49
% 5.17/5.49 % xor_self_eq
% 5.17/5.49 thf(fact_7796_bit_Oxor__self,axiom,
% 5.17/5.49 ! [X: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ X @ X )
% 5.17/5.49 = zero_zero_int ) ).
% 5.17/5.49
% 5.17/5.49 % bit.xor_self
% 5.17/5.49 thf(fact_7797_abs__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % abs_inverse
% 5.17/5.49 thf(fact_7798_abs__inverse,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.17/5.49 = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % abs_inverse
% 5.17/5.49 thf(fact_7799_abs__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % abs_inverse
% 5.17/5.49 thf(fact_7800_inverse__sgn,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( sgn_sgn_real @ A ) )
% 5.17/5.49 = ( sgn_sgn_real @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_sgn
% 5.17/5.49 thf(fact_7801_inverse__sgn,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) )
% 5.17/5.49 = ( sgn_sgn_rat @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_sgn
% 5.17/5.49 thf(fact_7802_sgn__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( sgn_sgn_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sgn_inverse
% 5.17/5.49 thf(fact_7803_sgn__inverse,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( sgn_sgn_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.17/5.49 = ( invers8013647133539491842omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sgn_inverse
% 5.17/5.49 thf(fact_7804_sgn__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( sgn_sgn_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sgn_inverse
% 5.17/5.49 thf(fact_7805_take__bit__xor,axiom,
% 5.17/5.49 ! [N: nat,A: int,B: int] :
% 5.17/5.49 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % take_bit_xor
% 5.17/5.49 thf(fact_7806_take__bit__xor,axiom,
% 5.17/5.49 ! [N: nat,A: nat,B: nat] :
% 5.17/5.49 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.17/5.49 = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % take_bit_xor
% 5.17/5.49 thf(fact_7807_inverse__nonnegative__iff__nonnegative,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonnegative_iff_nonnegative
% 5.17/5.49 thf(fact_7808_inverse__nonnegative__iff__nonnegative,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonnegative_iff_nonnegative
% 5.17/5.49 thf(fact_7809_inverse__nonpositive__iff__nonpositive,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.17/5.49 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonpositive_iff_nonpositive
% 5.17/5.49 thf(fact_7810_inverse__nonpositive__iff__nonpositive,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.17/5.49 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_nonpositive_iff_nonpositive
% 5.17/5.49 thf(fact_7811_inverse__positive__iff__positive,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_positive_iff_positive
% 5.17/5.49 thf(fact_7812_inverse__positive__iff__positive,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_positive_iff_positive
% 5.17/5.49 thf(fact_7813_inverse__negative__iff__negative,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.17/5.49 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_negative_iff_negative
% 5.17/5.49 thf(fact_7814_inverse__negative__iff__negative,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.17/5.49 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_negative_iff_negative
% 5.17/5.49 thf(fact_7815_inverse__less__iff__less__neg,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.49 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_iff_less_neg
% 5.17/5.49 thf(fact_7816_inverse__less__iff__less__neg,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.49 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_iff_less_neg
% 5.17/5.49 thf(fact_7817_inverse__less__iff__less,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.49 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_iff_less
% 5.17/5.49 thf(fact_7818_inverse__less__iff__less,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.49 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_iff_less
% 5.17/5.49 thf(fact_7819_gbinomial__0_I2_J,axiom,
% 5.17/5.49 ! [K: nat] :
% 5.17/5.49 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.17/5.49 = zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(2)
% 5.17/5.49 thf(fact_7820_gbinomial__0_I2_J,axiom,
% 5.17/5.49 ! [K: nat] :
% 5.17/5.49 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(2)
% 5.17/5.49 thf(fact_7821_gbinomial__0_I2_J,axiom,
% 5.17/5.49 ! [K: nat] :
% 5.17/5.49 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.17/5.49 = zero_zero_rat ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(2)
% 5.17/5.49 thf(fact_7822_gbinomial__0_I2_J,axiom,
% 5.17/5.49 ! [K: nat] :
% 5.17/5.49 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.17/5.49 = zero_zero_nat ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(2)
% 5.17/5.49 thf(fact_7823_gbinomial__0_I2_J,axiom,
% 5.17/5.49 ! [K: nat] :
% 5.17/5.49 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.17/5.49 = zero_zero_int ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(2)
% 5.17/5.49 thf(fact_7824_gbinomial__0_I1_J,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.17/5.49 = one_one_complex ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(1)
% 5.17/5.49 thf(fact_7825_gbinomial__0_I1_J,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.17/5.49 = one_one_real ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(1)
% 5.17/5.49 thf(fact_7826_gbinomial__0_I1_J,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.17/5.49 = one_one_rat ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(1)
% 5.17/5.49 thf(fact_7827_gbinomial__0_I1_J,axiom,
% 5.17/5.49 ! [A: nat] :
% 5.17/5.49 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.17/5.49 = one_one_nat ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(1)
% 5.17/5.49 thf(fact_7828_gbinomial__0_I1_J,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.17/5.49 = one_one_int ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_0(1)
% 5.17/5.49 thf(fact_7829_frac__eq__0__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( archim2898591450579166408c_real @ X )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_eq_0_iff
% 5.17/5.49 thf(fact_7830_frac__eq__0__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ( archimedean_frac_rat @ X )
% 5.17/5.49 = zero_zero_rat )
% 5.17/5.49 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_eq_0_iff
% 5.17/5.49 thf(fact_7831_inverse__le__iff__le__neg,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_iff_le_neg
% 5.17/5.49 thf(fact_7832_inverse__le__iff__le__neg,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.49 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_iff_le_neg
% 5.17/5.49 thf(fact_7833_inverse__le__iff__le,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.49 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_iff_le
% 5.17/5.49 thf(fact_7834_inverse__le__iff__le,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.17/5.49 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_iff_le
% 5.17/5.49 thf(fact_7835_right__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % right_inverse
% 5.17/5.49 thf(fact_7836_right__inverse,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.17/5.49 = one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % right_inverse
% 5.17/5.49 thf(fact_7837_right__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = one_one_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % right_inverse
% 5.17/5.49 thf(fact_7838_left__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.17/5.49 = one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % left_inverse
% 5.17/5.49 thf(fact_7839_left__inverse,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.17/5.49 = one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % left_inverse
% 5.17/5.49 thf(fact_7840_left__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.17/5.49 = one_one_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % left_inverse
% 5.17/5.49 thf(fact_7841_inverse__eq__divide__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.17/5.49 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide_numeral
% 5.17/5.49 thf(fact_7842_inverse__eq__divide__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.17/5.49 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide_numeral
% 5.17/5.49 thf(fact_7843_inverse__eq__divide__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.17/5.49 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide_numeral
% 5.17/5.49 thf(fact_7844_frac__gt__0__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) )
% 5.17/5.49 = ( ~ ( member_real @ X @ ring_1_Ints_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_gt_0_iff
% 5.17/5.49 thf(fact_7845_frac__gt__0__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 5.17/5.49 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_gt_0_iff
% 5.17/5.49 thf(fact_7846_inverse__eq__divide__neg__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.17/5.49 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide_neg_numeral
% 5.17/5.49 thf(fact_7847_inverse__eq__divide__neg__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.49 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide_neg_numeral
% 5.17/5.49 thf(fact_7848_inverse__eq__divide__neg__numeral,axiom,
% 5.17/5.49 ! [W: num] :
% 5.17/5.49 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.17/5.49 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide_neg_numeral
% 5.17/5.49 thf(fact_7849_xor__numerals_I3_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(3)
% 5.17/5.49 thf(fact_7850_xor__numerals_I3_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(3)
% 5.17/5.49 thf(fact_7851_xor__numerals_I1_J,axiom,
% 5.17/5.49 ! [Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(1)
% 5.17/5.49 thf(fact_7852_xor__numerals_I1_J,axiom,
% 5.17/5.49 ! [Y4: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( numeral_numeral_int @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(1)
% 5.17/5.49 thf(fact_7853_xor__numerals_I2_J,axiom,
% 5.17/5.49 ! [Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(2)
% 5.17/5.49 thf(fact_7854_xor__numerals_I2_J,axiom,
% 5.17/5.49 ! [Y4: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( numeral_numeral_int @ ( bit0 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(2)
% 5.17/5.49 thf(fact_7855_xor__numerals_I5_J,axiom,
% 5.17/5.49 ! [X: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(5)
% 5.17/5.49 thf(fact_7856_xor__numerals_I5_J,axiom,
% 5.17/5.49 ! [X: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.17/5.49 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(5)
% 5.17/5.49 thf(fact_7857_xor__numerals_I8_J,axiom,
% 5.17/5.49 ! [X: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(8)
% 5.17/5.49 thf(fact_7858_xor__numerals_I8_J,axiom,
% 5.17/5.49 ! [X: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.17/5.49 = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(8)
% 5.17/5.49 thf(fact_7859_xor__numerals_I7_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(7)
% 5.17/5.49 thf(fact_7860_xor__numerals_I7_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(7)
% 5.17/5.49 thf(fact_7861_xor__nat__numerals_I1_J,axiom,
% 5.17/5.49 ! [Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_nat_numerals(1)
% 5.17/5.49 thf(fact_7862_xor__nat__numerals_I2_J,axiom,
% 5.17/5.49 ! [Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_nat_numerals(2)
% 5.17/5.49 thf(fact_7863_xor__nat__numerals_I3_J,axiom,
% 5.17/5.49 ! [X: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_nat_numerals(3)
% 5.17/5.49 thf(fact_7864_xor__nat__numerals_I4_J,axiom,
% 5.17/5.49 ! [X: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.49 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_nat_numerals(4)
% 5.17/5.49 thf(fact_7865_xor__numerals_I4_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(4)
% 5.17/5.49 thf(fact_7866_xor__numerals_I4_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.49 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(4)
% 5.17/5.49 thf(fact_7867_xor__numerals_I6_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(6)
% 5.17/5.49 thf(fact_7868_xor__numerals_I6_J,axiom,
% 5.17/5.49 ! [X: num,Y4: num] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.49 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor_numerals(6)
% 5.17/5.49 thf(fact_7869_Ints__power,axiom,
% 5.17/5.49 ! [A: int,N: nat] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( member_int @ ( power_power_int @ A @ N ) @ ring_1_Ints_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_power
% 5.17/5.49 thf(fact_7870_Ints__power,axiom,
% 5.17/5.49 ! [A: real,N: nat] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( member_real @ ( power_power_real @ A @ N ) @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_power
% 5.17/5.49 thf(fact_7871_Ints__power,axiom,
% 5.17/5.49 ! [A: complex,N: nat] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( member_complex @ ( power_power_complex @ A @ N ) @ ring_1_Ints_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_power
% 5.17/5.49 thf(fact_7872_nonzero__of__real__inverse,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( X != zero_zero_real )
% 5.17/5.49 => ( ( real_V1803761363581548252l_real @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( real_V1803761363581548252l_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_of_real_inverse
% 5.17/5.49 thf(fact_7873_nonzero__of__real__inverse,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( X != zero_zero_real )
% 5.17/5.49 => ( ( real_V4546457046886955230omplex @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( invers8013647133539491842omplex @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_of_real_inverse
% 5.17/5.49 thf(fact_7874_of__int__xor__eq,axiom,
% 5.17/5.49 ! [K: int,L: int] :
% 5.17/5.49 ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_xor_eq
% 5.17/5.49 thf(fact_7875_Ints__0,axiom,
% 5.17/5.49 member_complex @ zero_zero_complex @ ring_1_Ints_complex ).
% 5.17/5.49
% 5.17/5.49 % Ints_0
% 5.17/5.49 thf(fact_7876_Ints__0,axiom,
% 5.17/5.49 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 5.17/5.49
% 5.17/5.49 % Ints_0
% 5.17/5.49 thf(fact_7877_Ints__0,axiom,
% 5.17/5.49 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 5.17/5.49
% 5.17/5.49 % Ints_0
% 5.17/5.49 thf(fact_7878_Ints__0,axiom,
% 5.17/5.49 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 5.17/5.49
% 5.17/5.49 % Ints_0
% 5.17/5.49 thf(fact_7879_Ints__numeral,axiom,
% 5.17/5.49 ! [N: num] : ( member_complex @ ( numera6690914467698888265omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_numeral
% 5.17/5.49 thf(fact_7880_Ints__numeral,axiom,
% 5.17/5.49 ! [N: num] : ( member_real @ ( numeral_numeral_real @ N ) @ ring_1_Ints_real ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_numeral
% 5.17/5.49 thf(fact_7881_Ints__numeral,axiom,
% 5.17/5.49 ! [N: num] : ( member_rat @ ( numeral_numeral_rat @ N ) @ ring_1_Ints_rat ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_numeral
% 5.17/5.49 thf(fact_7882_Ints__numeral,axiom,
% 5.17/5.49 ! [N: num] : ( member_int @ ( numeral_numeral_int @ N ) @ ring_1_Ints_int ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_numeral
% 5.17/5.49 thf(fact_7883_Ints__mult,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.17/5.49 => ( member_complex @ ( times_times_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_mult
% 5.17/5.49 thf(fact_7884_Ints__mult,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.17/5.49 => ( member_real @ ( times_times_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_mult
% 5.17/5.49 thf(fact_7885_Ints__mult,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.17/5.49 => ( member_rat @ ( times_times_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_mult
% 5.17/5.49 thf(fact_7886_Ints__mult,axiom,
% 5.17/5.49 ! [A: int,B: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.17/5.49 => ( member_int @ ( times_times_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_mult
% 5.17/5.49 thf(fact_7887_Ints__add,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.17/5.49 => ( member_complex @ ( plus_plus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_add
% 5.17/5.49 thf(fact_7888_Ints__add,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.17/5.49 => ( member_real @ ( plus_plus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_add
% 5.17/5.49 thf(fact_7889_Ints__add,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.17/5.49 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_add
% 5.17/5.49 thf(fact_7890_Ints__add,axiom,
% 5.17/5.49 ! [A: int,B: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.17/5.49 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_add
% 5.17/5.49 thf(fact_7891_Ints__1,axiom,
% 5.17/5.49 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 5.17/5.49
% 5.17/5.49 % Ints_1
% 5.17/5.49 thf(fact_7892_Ints__1,axiom,
% 5.17/5.49 member_int @ one_one_int @ ring_1_Ints_int ).
% 5.17/5.49
% 5.17/5.49 % Ints_1
% 5.17/5.49 thf(fact_7893_Ints__1,axiom,
% 5.17/5.49 member_real @ one_one_real @ ring_1_Ints_real ).
% 5.17/5.49
% 5.17/5.49 % Ints_1
% 5.17/5.49 thf(fact_7894_Ints__1,axiom,
% 5.17/5.49 member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 5.17/5.49
% 5.17/5.49 % Ints_1
% 5.17/5.49 thf(fact_7895_real__sqrt__inverse,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_sqrt_inverse
% 5.17/5.49 thf(fact_7896_Ints__diff,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.17/5.49 => ( member_complex @ ( minus_minus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_diff
% 5.17/5.49 thf(fact_7897_Ints__diff,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.17/5.49 => ( member_real @ ( minus_minus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_diff
% 5.17/5.49 thf(fact_7898_Ints__diff,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.17/5.49 => ( member_rat @ ( minus_minus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_diff
% 5.17/5.49 thf(fact_7899_Ints__diff,axiom,
% 5.17/5.49 ! [A: int,B: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.17/5.49 => ( member_int @ ( minus_minus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_diff
% 5.17/5.49 thf(fact_7900_Ints__minus,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( member_real @ ( uminus_uminus_real @ A ) @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_minus
% 5.17/5.49 thf(fact_7901_Ints__minus,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( member_int @ ( uminus_uminus_int @ A ) @ ring_1_Ints_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_minus
% 5.17/5.49 thf(fact_7902_Ints__minus,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( member_complex @ ( uminus1482373934393186551omplex @ A ) @ ring_1_Ints_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_minus
% 5.17/5.49 thf(fact_7903_Ints__minus,axiom,
% 5.17/5.49 ! [A: code_integer] :
% 5.17/5.49 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.17/5.49 => ( member_Code_integer @ ( uminus1351360451143612070nteger @ A ) @ ring_11222124179247155820nteger ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_minus
% 5.17/5.49 thf(fact_7904_Ints__minus,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( member_rat @ ( uminus_uminus_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_minus
% 5.17/5.49 thf(fact_7905_minus__in__Ints__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( member_real @ ( uminus_uminus_real @ X ) @ ring_1_Ints_real )
% 5.17/5.49 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_in_Ints_iff
% 5.17/5.49 thf(fact_7906_minus__in__Ints__iff,axiom,
% 5.17/5.49 ! [X: int] :
% 5.17/5.49 ( ( member_int @ ( uminus_uminus_int @ X ) @ ring_1_Ints_int )
% 5.17/5.49 = ( member_int @ X @ ring_1_Ints_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_in_Ints_iff
% 5.17/5.49 thf(fact_7907_minus__in__Ints__iff,axiom,
% 5.17/5.49 ! [X: complex] :
% 5.17/5.49 ( ( member_complex @ ( uminus1482373934393186551omplex @ X ) @ ring_1_Ints_complex )
% 5.17/5.49 = ( member_complex @ X @ ring_1_Ints_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_in_Ints_iff
% 5.17/5.49 thf(fact_7908_minus__in__Ints__iff,axiom,
% 5.17/5.49 ! [X: code_integer] :
% 5.17/5.49 ( ( member_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ ring_11222124179247155820nteger )
% 5.17/5.49 = ( member_Code_integer @ X @ ring_11222124179247155820nteger ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_in_Ints_iff
% 5.17/5.49 thf(fact_7909_minus__in__Ints__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( member_rat @ ( uminus_uminus_rat @ X ) @ ring_1_Ints_rat )
% 5.17/5.49 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % minus_in_Ints_iff
% 5.17/5.49 thf(fact_7910_of__nat__gbinomial,axiom,
% 5.17/5.49 ! [N: nat,K: nat] :
% 5.17/5.49 ( ( semiri8010041392384452111omplex @ ( gbinomial_nat @ N @ K ) )
% 5.17/5.49 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_gbinomial
% 5.17/5.49 thf(fact_7911_of__nat__gbinomial,axiom,
% 5.17/5.49 ! [N: nat,K: nat] :
% 5.17/5.49 ( ( semiri5074537144036343181t_real @ ( gbinomial_nat @ N @ K ) )
% 5.17/5.49 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_gbinomial
% 5.17/5.49 thf(fact_7912_of__nat__gbinomial,axiom,
% 5.17/5.49 ! [N: nat,K: nat] :
% 5.17/5.49 ( ( semiri681578069525770553at_rat @ ( gbinomial_nat @ N @ K ) )
% 5.17/5.49 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_gbinomial
% 5.17/5.49 thf(fact_7913_xor_Oleft__commute,axiom,
% 5.17/5.49 ! [B: nat,A: nat,C: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 5.17/5.49 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor.left_commute
% 5.17/5.49 thf(fact_7914_xor_Oleft__commute,axiom,
% 5.17/5.49 ! [B: int,A: int,C: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor.left_commute
% 5.17/5.49 thf(fact_7915_xor_Ocommute,axiom,
% 5.17/5.49 ( bit_se6528837805403552850or_nat
% 5.17/5.49 = ( ^ [A3: nat,B2: nat] : ( bit_se6528837805403552850or_nat @ B2 @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor.commute
% 5.17/5.49 thf(fact_7916_xor_Ocommute,axiom,
% 5.17/5.49 ( bit_se6526347334894502574or_int
% 5.17/5.49 = ( ^ [A3: int,B2: int] : ( bit_se6526347334894502574or_int @ B2 @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor.commute
% 5.17/5.49 thf(fact_7917_xor_Oassoc,axiom,
% 5.17/5.49 ! [A: nat,B: nat,C: nat] :
% 5.17/5.49 ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 5.17/5.49 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor.assoc
% 5.17/5.49 thf(fact_7918_xor_Oassoc,axiom,
% 5.17/5.49 ! [A: int,B: int,C: int] :
% 5.17/5.49 ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % xor.assoc
% 5.17/5.49 thf(fact_7919_inverse__eq__imp__eq,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ( inverse_inverse_real @ A )
% 5.17/5.49 = ( inverse_inverse_real @ B ) )
% 5.17/5.49 => ( A = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_imp_eq
% 5.17/5.49 thf(fact_7920_inverse__eq__imp__eq,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 => ( A = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_imp_eq
% 5.17/5.49 thf(fact_7921_inverse__eq__imp__eq,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = ( inverse_inverse_rat @ B ) )
% 5.17/5.49 => ( A = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_imp_eq
% 5.17/5.49 thf(fact_7922_of__nat__xor__eq,axiom,
% 5.17/5.49 ! [M: nat,N: nat] :
% 5.17/5.49 ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.17/5.49 = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_xor_eq
% 5.17/5.49 thf(fact_7923_of__nat__xor__eq,axiom,
% 5.17/5.49 ! [M: nat,N: nat] :
% 5.17/5.49 ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N ) )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_nat_xor_eq
% 5.17/5.49 thf(fact_7924_nonzero__imp__inverse__nonzero,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( inverse_inverse_real @ A )
% 5.17/5.49 != zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_imp_inverse_nonzero
% 5.17/5.49 thf(fact_7925_nonzero__imp__inverse__nonzero,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 != zero_zero_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_imp_inverse_nonzero
% 5.17/5.49 thf(fact_7926_nonzero__imp__inverse__nonzero,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( inverse_inverse_rat @ A )
% 5.17/5.49 != zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_imp_inverse_nonzero
% 5.17/5.49 thf(fact_7927_nonzero__inverse__inverse__eq,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = A ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_inverse_eq
% 5.17/5.49 thf(fact_7928_nonzero__inverse__inverse__eq,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.17/5.49 = A ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_inverse_eq
% 5.17/5.49 thf(fact_7929_nonzero__inverse__inverse__eq,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = A ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_inverse_eq
% 5.17/5.49 thf(fact_7930_nonzero__inverse__eq__imp__eq,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ( inverse_inverse_real @ A )
% 5.17/5.49 = ( inverse_inverse_real @ B ) )
% 5.17/5.49 => ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( B != zero_zero_real )
% 5.17/5.49 => ( A = B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_eq_imp_eq
% 5.17/5.49 thf(fact_7931_nonzero__inverse__eq__imp__eq,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 => ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( B != zero_zero_complex )
% 5.17/5.49 => ( A = B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_eq_imp_eq
% 5.17/5.49 thf(fact_7932_nonzero__inverse__eq__imp__eq,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = ( inverse_inverse_rat @ B ) )
% 5.17/5.49 => ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( B != zero_zero_rat )
% 5.17/5.49 => ( A = B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_eq_imp_eq
% 5.17/5.49 thf(fact_7933_inverse__zero__imp__zero,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ( inverse_inverse_real @ A )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 => ( A = zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_zero_imp_zero
% 5.17/5.49 thf(fact_7934_inverse__zero__imp__zero,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = zero_zero_complex )
% 5.17/5.49 => ( A = zero_zero_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_zero_imp_zero
% 5.17/5.49 thf(fact_7935_inverse__zero__imp__zero,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = zero_zero_rat )
% 5.17/5.49 => ( A = zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_zero_imp_zero
% 5.17/5.49 thf(fact_7936_field__class_Ofield__inverse__zero,axiom,
% 5.17/5.49 ( ( inverse_inverse_real @ zero_zero_real )
% 5.17/5.49 = zero_zero_real ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_inverse_zero
% 5.17/5.49 thf(fact_7937_field__class_Ofield__inverse__zero,axiom,
% 5.17/5.49 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.17/5.49 = zero_zero_complex ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_inverse_zero
% 5.17/5.49 thf(fact_7938_field__class_Ofield__inverse__zero,axiom,
% 5.17/5.49 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.17/5.49 = zero_zero_rat ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_inverse_zero
% 5.17/5.49 thf(fact_7939_mult__commute__imp__mult__inverse__commute,axiom,
% 5.17/5.49 ! [Y4: real,X: real] :
% 5.17/5.49 ( ( ( times_times_real @ Y4 @ X )
% 5.17/5.49 = ( times_times_real @ X @ Y4 ) )
% 5.17/5.49 => ( ( times_times_real @ ( inverse_inverse_real @ Y4 ) @ X )
% 5.17/5.49 = ( times_times_real @ X @ ( inverse_inverse_real @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_commute_imp_mult_inverse_commute
% 5.17/5.49 thf(fact_7940_mult__commute__imp__mult__inverse__commute,axiom,
% 5.17/5.49 ! [Y4: complex,X: complex] :
% 5.17/5.49 ( ( ( times_times_complex @ Y4 @ X )
% 5.17/5.49 = ( times_times_complex @ X @ Y4 ) )
% 5.17/5.49 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y4 ) @ X )
% 5.17/5.49 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_commute_imp_mult_inverse_commute
% 5.17/5.49 thf(fact_7941_mult__commute__imp__mult__inverse__commute,axiom,
% 5.17/5.49 ! [Y4: rat,X: rat] :
% 5.17/5.49 ( ( ( times_times_rat @ Y4 @ X )
% 5.17/5.49 = ( times_times_rat @ X @ Y4 ) )
% 5.17/5.49 => ( ( times_times_rat @ ( inverse_inverse_rat @ Y4 ) @ X )
% 5.17/5.49 = ( times_times_rat @ X @ ( inverse_inverse_rat @ Y4 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_commute_imp_mult_inverse_commute
% 5.17/5.49 thf(fact_7942_nonzero__norm__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( real_V7735802525324610683m_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_norm_inverse
% 5.17/5.49 thf(fact_7943_nonzero__norm__inverse,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( real_V1022390504157884413omplex @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_norm_inverse
% 5.17/5.49 thf(fact_7944_Ints__of__nat,axiom,
% 5.17/5.49 ! [N: nat] : ( member_complex @ ( semiri8010041392384452111omplex @ N ) @ ring_1_Ints_complex ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_nat
% 5.17/5.49 thf(fact_7945_Ints__of__nat,axiom,
% 5.17/5.49 ! [N: nat] : ( member_real @ ( semiri5074537144036343181t_real @ N ) @ ring_1_Ints_real ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_nat
% 5.17/5.49 thf(fact_7946_Ints__of__nat,axiom,
% 5.17/5.49 ! [N: nat] : ( member_rat @ ( semiri681578069525770553at_rat @ N ) @ ring_1_Ints_rat ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_nat
% 5.17/5.49 thf(fact_7947_Ints__of__nat,axiom,
% 5.17/5.49 ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ring_1_Ints_int ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_nat
% 5.17/5.49 thf(fact_7948_bit_Oconj__xor__distrib2,axiom,
% 5.17/5.49 ! [Y4: int,Z: int,X: int] :
% 5.17/5.49 ( ( bit_se725231765392027082nd_int @ ( bit_se6526347334894502574or_int @ Y4 @ Z ) @ X )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ Y4 @ X ) @ ( bit_se725231765392027082nd_int @ Z @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit.conj_xor_distrib2
% 5.17/5.49 thf(fact_7949_bit_Oconj__xor__distrib,axiom,
% 5.17/5.49 ! [X: int,Y4: int,Z: int] :
% 5.17/5.49 ( ( bit_se725231765392027082nd_int @ X @ ( bit_se6526347334894502574or_int @ Y4 @ Z ) )
% 5.17/5.49 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ ( bit_se725231765392027082nd_int @ X @ Z ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit.conj_xor_distrib
% 5.17/5.49 thf(fact_7950_bit__xor__iff,axiom,
% 5.17/5.49 ! [A: nat,B: nat,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ N )
% 5.17/5.49 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.49 != ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_xor_iff
% 5.17/5.49 thf(fact_7951_bit__xor__iff,axiom,
% 5.17/5.49 ! [A: int,B: int,N: nat] :
% 5.17/5.49 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ N )
% 5.17/5.49 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.49 != ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_xor_iff
% 5.17/5.49 thf(fact_7952_Ints__abs,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( member_int @ ( abs_abs_int @ A ) @ ring_1_Ints_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_abs
% 5.17/5.49 thf(fact_7953_Ints__abs,axiom,
% 5.17/5.49 ! [A: code_integer] :
% 5.17/5.49 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.17/5.49 => ( member_Code_integer @ ( abs_abs_Code_integer @ A ) @ ring_11222124179247155820nteger ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_abs
% 5.17/5.49 thf(fact_7954_Ints__abs,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( member_rat @ ( abs_abs_rat @ A ) @ ring_1_Ints_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_abs
% 5.17/5.49 thf(fact_7955_Ints__abs,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( member_real @ ( abs_abs_real @ A ) @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_abs
% 5.17/5.49 thf(fact_7956_Ints__of__int,axiom,
% 5.17/5.49 ! [Z: int] : ( member_int @ ( ring_1_of_int_int @ Z ) @ ring_1_Ints_int ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_int
% 5.17/5.49 thf(fact_7957_Ints__of__int,axiom,
% 5.17/5.49 ! [Z: int] : ( member_real @ ( ring_1_of_int_real @ Z ) @ ring_1_Ints_real ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_int
% 5.17/5.49 thf(fact_7958_Ints__of__int,axiom,
% 5.17/5.49 ! [Z: int] : ( member_complex @ ( ring_17405671764205052669omplex @ Z ) @ ring_1_Ints_complex ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_int
% 5.17/5.49 thf(fact_7959_Ints__of__int,axiom,
% 5.17/5.49 ! [Z: int] : ( member_rat @ ( ring_1_of_int_rat @ Z ) @ ring_1_Ints_rat ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_of_int
% 5.17/5.49 thf(fact_7960_Ints__induct,axiom,
% 5.17/5.49 ! [Q2: int,P: int > $o] :
% 5.17/5.49 ( ( member_int @ Q2 @ ring_1_Ints_int )
% 5.17/5.49 => ( ! [Z2: int] : ( P @ ( ring_1_of_int_int @ Z2 ) )
% 5.17/5.49 => ( P @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_induct
% 5.17/5.49 thf(fact_7961_Ints__induct,axiom,
% 5.17/5.49 ! [Q2: real,P: real > $o] :
% 5.17/5.49 ( ( member_real @ Q2 @ ring_1_Ints_real )
% 5.17/5.49 => ( ! [Z2: int] : ( P @ ( ring_1_of_int_real @ Z2 ) )
% 5.17/5.49 => ( P @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_induct
% 5.17/5.49 thf(fact_7962_Ints__induct,axiom,
% 5.17/5.49 ! [Q2: complex,P: complex > $o] :
% 5.17/5.49 ( ( member_complex @ Q2 @ ring_1_Ints_complex )
% 5.17/5.49 => ( ! [Z2: int] : ( P @ ( ring_17405671764205052669omplex @ Z2 ) )
% 5.17/5.49 => ( P @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_induct
% 5.17/5.49 thf(fact_7963_Ints__induct,axiom,
% 5.17/5.49 ! [Q2: rat,P: rat > $o] :
% 5.17/5.49 ( ( member_rat @ Q2 @ ring_1_Ints_rat )
% 5.17/5.49 => ( ! [Z2: int] : ( P @ ( ring_1_of_int_rat @ Z2 ) )
% 5.17/5.49 => ( P @ Q2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_induct
% 5.17/5.49 thf(fact_7964_Ints__cases,axiom,
% 5.17/5.49 ! [Q2: int] :
% 5.17/5.49 ( ( member_int @ Q2 @ ring_1_Ints_int )
% 5.17/5.49 => ~ ! [Z2: int] :
% 5.17/5.49 ( Q2
% 5.17/5.49 != ( ring_1_of_int_int @ Z2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_cases
% 5.17/5.49 thf(fact_7965_Ints__cases,axiom,
% 5.17/5.49 ! [Q2: real] :
% 5.17/5.49 ( ( member_real @ Q2 @ ring_1_Ints_real )
% 5.17/5.49 => ~ ! [Z2: int] :
% 5.17/5.49 ( Q2
% 5.17/5.49 != ( ring_1_of_int_real @ Z2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_cases
% 5.17/5.49 thf(fact_7966_Ints__cases,axiom,
% 5.17/5.49 ! [Q2: complex] :
% 5.17/5.49 ( ( member_complex @ Q2 @ ring_1_Ints_complex )
% 5.17/5.49 => ~ ! [Z2: int] :
% 5.17/5.49 ( Q2
% 5.17/5.49 != ( ring_17405671764205052669omplex @ Z2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_cases
% 5.17/5.49 thf(fact_7967_Ints__cases,axiom,
% 5.17/5.49 ! [Q2: rat] :
% 5.17/5.49 ( ( member_rat @ Q2 @ ring_1_Ints_rat )
% 5.17/5.49 => ~ ! [Z2: int] :
% 5.17/5.49 ( Q2
% 5.17/5.49 != ( ring_1_of_int_rat @ Z2 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_cases
% 5.17/5.49 thf(fact_7968_norm__inverse__le__norm,axiom,
% 5.17/5.49 ! [R2: real,X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ R2 @ ( real_V7735802525324610683m_real @ X ) )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.17/5.49 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % norm_inverse_le_norm
% 5.17/5.49 thf(fact_7969_norm__inverse__le__norm,axiom,
% 5.17/5.49 ! [R2: real,X: complex] :
% 5.17/5.49 ( ( ord_less_eq_real @ R2 @ ( real_V1022390504157884413omplex @ X ) )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.17/5.49 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X ) ) @ ( inverse_inverse_real @ R2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % norm_inverse_le_norm
% 5.17/5.49 thf(fact_7970_positive__imp__inverse__positive,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % positive_imp_inverse_positive
% 5.17/5.49 thf(fact_7971_positive__imp__inverse__positive,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % positive_imp_inverse_positive
% 5.17/5.49 thf(fact_7972_negative__imp__inverse__negative,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % negative_imp_inverse_negative
% 5.17/5.49 thf(fact_7973_negative__imp__inverse__negative,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % negative_imp_inverse_negative
% 5.17/5.49 thf(fact_7974_inverse__positive__imp__positive,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 => ( ( A != zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_positive_imp_positive
% 5.17/5.49 thf(fact_7975_inverse__positive__imp__positive,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 => ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_positive_imp_positive
% 5.17/5.49 thf(fact_7976_inverse__negative__imp__negative,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.17/5.49 => ( ( A != zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_negative_imp_negative
% 5.17/5.49 thf(fact_7977_inverse__negative__imp__negative,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.17/5.49 => ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_negative_imp_negative
% 5.17/5.49 thf(fact_7978_less__imp__inverse__less__neg,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ A @ B )
% 5.17/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % less_imp_inverse_less_neg
% 5.17/5.49 thf(fact_7979_less__imp__inverse__less__neg,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ A @ B )
% 5.17/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % less_imp_inverse_less_neg
% 5.17/5.49 thf(fact_7980_inverse__less__imp__less__neg,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_imp_less_neg
% 5.17/5.49 thf(fact_7981_inverse__less__imp__less__neg,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_imp_less_neg
% 5.17/5.49 thf(fact_7982_less__imp__inverse__less,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ A @ B )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % less_imp_inverse_less
% 5.17/5.49 thf(fact_7983_less__imp__inverse__less,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ A @ B )
% 5.17/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % less_imp_inverse_less
% 5.17/5.49 thf(fact_7984_inverse__less__imp__less,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ord_less_real @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_imp_less
% 5.17/5.49 thf(fact_7985_inverse__less__imp__less,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_imp_less
% 5.17/5.49 thf(fact_7986_nonzero__inverse__mult__distrib,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( B != zero_zero_real )
% 5.17/5.49 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.17/5.49 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_mult_distrib
% 5.17/5.49 thf(fact_7987_nonzero__inverse__mult__distrib,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( B != zero_zero_complex )
% 5.17/5.49 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.17/5.49 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_mult_distrib
% 5.17/5.49 thf(fact_7988_nonzero__inverse__mult__distrib,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( B != zero_zero_rat )
% 5.17/5.49 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.49 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_mult_distrib
% 5.17/5.49 thf(fact_7989_bit__Suc__0__iff,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.49 = ( N = zero_zero_nat ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_Suc_0_iff
% 5.17/5.49 thf(fact_7990_not__bit__Suc__0__Suc,axiom,
% 5.17/5.49 ! [N: nat] :
% 5.17/5.49 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % not_bit_Suc_0_Suc
% 5.17/5.49 thf(fact_7991_nonzero__inverse__minus__eq,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_minus_eq
% 5.17/5.49 thf(fact_7992_nonzero__inverse__minus__eq,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_minus_eq
% 5.17/5.49 thf(fact_7993_nonzero__inverse__minus__eq,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.17/5.49 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_minus_eq
% 5.17/5.49 thf(fact_7994_inverse__numeral__1,axiom,
% 5.17/5.49 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.17/5.49 = ( numeral_numeral_real @ one ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_numeral_1
% 5.17/5.49 thf(fact_7995_inverse__numeral__1,axiom,
% 5.17/5.49 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.17/5.49 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_numeral_1
% 5.17/5.49 thf(fact_7996_inverse__numeral__1,axiom,
% 5.17/5.49 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.17/5.49 = ( numeral_numeral_rat @ one ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_numeral_1
% 5.17/5.49 thf(fact_7997_inverse__unique,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ( times_times_real @ A @ B )
% 5.17/5.49 = one_one_real )
% 5.17/5.49 => ( ( inverse_inverse_real @ A )
% 5.17/5.49 = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_unique
% 5.17/5.49 thf(fact_7998_inverse__unique,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( ( times_times_complex @ A @ B )
% 5.17/5.49 = one_one_complex )
% 5.17/5.49 => ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_unique
% 5.17/5.49 thf(fact_7999_inverse__unique,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ( times_times_rat @ A @ B )
% 5.17/5.49 = one_one_rat )
% 5.17/5.49 => ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = B ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_unique
% 5.17/5.49 thf(fact_8000_divide__inverse__commute,axiom,
% 5.17/5.49 ( divide_divide_real
% 5.17/5.49 = ( ^ [A3: real,B2: real] : ( times_times_real @ ( inverse_inverse_real @ B2 ) @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_inverse_commute
% 5.17/5.49 thf(fact_8001_divide__inverse__commute,axiom,
% 5.17/5.49 ( divide1717551699836669952omplex
% 5.17/5.49 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_inverse_commute
% 5.17/5.49 thf(fact_8002_divide__inverse__commute,axiom,
% 5.17/5.49 ( divide_divide_rat
% 5.17/5.49 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B2 ) @ A3 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_inverse_commute
% 5.17/5.49 thf(fact_8003_divide__inverse,axiom,
% 5.17/5.49 ( divide_divide_real
% 5.17/5.49 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_inverse
% 5.17/5.49 thf(fact_8004_divide__inverse,axiom,
% 5.17/5.49 ( divide1717551699836669952omplex
% 5.17/5.49 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_inverse
% 5.17/5.49 thf(fact_8005_divide__inverse,axiom,
% 5.17/5.49 ( divide_divide_rat
% 5.17/5.49 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ A3 @ ( inverse_inverse_rat @ B2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_inverse
% 5.17/5.49 thf(fact_8006_field__class_Ofield__divide__inverse,axiom,
% 5.17/5.49 ( divide_divide_real
% 5.17/5.49 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_divide_inverse
% 5.17/5.49 thf(fact_8007_field__class_Ofield__divide__inverse,axiom,
% 5.17/5.49 ( divide1717551699836669952omplex
% 5.17/5.49 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_divide_inverse
% 5.17/5.49 thf(fact_8008_field__class_Ofield__divide__inverse,axiom,
% 5.17/5.49 ( divide_divide_rat
% 5.17/5.49 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ A3 @ ( inverse_inverse_rat @ B2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_divide_inverse
% 5.17/5.49 thf(fact_8009_inverse__eq__divide,axiom,
% 5.17/5.49 ( inverse_inverse_real
% 5.17/5.49 = ( divide_divide_real @ one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide
% 5.17/5.49 thf(fact_8010_inverse__eq__divide,axiom,
% 5.17/5.49 ( invers8013647133539491842omplex
% 5.17/5.49 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide
% 5.17/5.49 thf(fact_8011_inverse__eq__divide,axiom,
% 5.17/5.49 ( inverse_inverse_rat
% 5.17/5.49 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_eq_divide
% 5.17/5.49 thf(fact_8012_power__mult__inverse__distrib,axiom,
% 5.17/5.49 ! [X: real,M: nat] :
% 5.17/5.49 ( ( times_times_real @ ( power_power_real @ X @ M ) @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( times_times_real @ ( inverse_inverse_real @ X ) @ ( power_power_real @ X @ M ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_mult_inverse_distrib
% 5.17/5.49 thf(fact_8013_power__mult__inverse__distrib,axiom,
% 5.17/5.49 ! [X: complex,M: nat] :
% 5.17/5.49 ( ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( invers8013647133539491842omplex @ X ) )
% 5.17/5.49 = ( times_times_complex @ ( invers8013647133539491842omplex @ X ) @ ( power_power_complex @ X @ M ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_mult_inverse_distrib
% 5.17/5.49 thf(fact_8014_power__mult__inverse__distrib,axiom,
% 5.17/5.49 ! [X: rat,M: nat] :
% 5.17/5.49 ( ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( inverse_inverse_rat @ X ) )
% 5.17/5.49 = ( times_times_rat @ ( inverse_inverse_rat @ X ) @ ( power_power_rat @ X @ M ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_mult_inverse_distrib
% 5.17/5.49 thf(fact_8015_power__mult__power__inverse__commute,axiom,
% 5.17/5.49 ! [X: real,M: nat,N: nat] :
% 5.17/5.49 ( ( times_times_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N ) )
% 5.17/5.49 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X ) @ N ) @ ( power_power_real @ X @ M ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_mult_power_inverse_commute
% 5.17/5.49 thf(fact_8016_power__mult__power__inverse__commute,axiom,
% 5.17/5.49 ! [X: complex,M: nat,N: nat] :
% 5.17/5.49 ( ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N ) )
% 5.17/5.49 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ N ) @ ( power_power_complex @ X @ M ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_mult_power_inverse_commute
% 5.17/5.49 thf(fact_8017_power__mult__power__inverse__commute,axiom,
% 5.17/5.49 ! [X: rat,M: nat,N: nat] :
% 5.17/5.49 ( ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ N ) )
% 5.17/5.49 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ N ) @ ( power_power_rat @ X @ M ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_mult_power_inverse_commute
% 5.17/5.49 thf(fact_8018_mult__inverse__of__nat__commute,axiom,
% 5.17/5.49 ! [Xa: nat,X: real] :
% 5.17/5.49 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X )
% 5.17/5.49 = ( times_times_real @ X @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_inverse_of_nat_commute
% 5.17/5.49 thf(fact_8019_mult__inverse__of__nat__commute,axiom,
% 5.17/5.49 ! [Xa: nat,X: complex] :
% 5.17/5.49 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X )
% 5.17/5.49 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_inverse_of_nat_commute
% 5.17/5.49 thf(fact_8020_mult__inverse__of__nat__commute,axiom,
% 5.17/5.49 ! [Xa: nat,X: rat] :
% 5.17/5.49 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) @ X )
% 5.17/5.49 = ( times_times_rat @ X @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_inverse_of_nat_commute
% 5.17/5.49 thf(fact_8021_nonzero__abs__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.17/5.49 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_abs_inverse
% 5.17/5.49 thf(fact_8022_nonzero__abs__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.17/5.49 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_abs_inverse
% 5.17/5.49 thf(fact_8023_mult__inverse__of__int__commute,axiom,
% 5.17/5.49 ! [Xa: int,X: real] :
% 5.17/5.49 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) @ X )
% 5.17/5.49 = ( times_times_real @ X @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_inverse_of_int_commute
% 5.17/5.49 thf(fact_8024_mult__inverse__of__int__commute,axiom,
% 5.17/5.49 ! [Xa: int,X: complex] :
% 5.17/5.49 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) @ X )
% 5.17/5.49 = ( times_times_complex @ X @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_inverse_of_int_commute
% 5.17/5.49 thf(fact_8025_mult__inverse__of__int__commute,axiom,
% 5.17/5.49 ! [Xa: int,X: rat] :
% 5.17/5.49 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) @ X )
% 5.17/5.49 = ( times_times_rat @ X @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % mult_inverse_of_int_commute
% 5.17/5.49 thf(fact_8026_divide__real__def,axiom,
% 5.17/5.49 ( divide_divide_real
% 5.17/5.49 = ( ^ [X3: real,Y6: real] : ( times_times_real @ X3 @ ( inverse_inverse_real @ Y6 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % divide_real_def
% 5.17/5.49 thf(fact_8027_Ints__double__eq__0__iff,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( ( ( plus_plus_complex @ A @ A )
% 5.17/5.49 = zero_zero_complex )
% 5.17/5.49 = ( A = zero_zero_complex ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_double_eq_0_iff
% 5.17/5.49 thf(fact_8028_Ints__double__eq__0__iff,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( ( ( plus_plus_real @ A @ A )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( A = zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_double_eq_0_iff
% 5.17/5.49 thf(fact_8029_Ints__double__eq__0__iff,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( ( plus_plus_rat @ A @ A )
% 5.17/5.49 = zero_zero_rat )
% 5.17/5.49 = ( A = zero_zero_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_double_eq_0_iff
% 5.17/5.49 thf(fact_8030_Ints__double__eq__0__iff,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( ( ( plus_plus_int @ A @ A )
% 5.17/5.49 = zero_zero_int )
% 5.17/5.49 = ( A = zero_zero_int ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_double_eq_0_iff
% 5.17/5.49 thf(fact_8031_binomial__gbinomial,axiom,
% 5.17/5.49 ! [N: nat,K: nat] :
% 5.17/5.49 ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.17/5.49 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % binomial_gbinomial
% 5.17/5.49 thf(fact_8032_binomial__gbinomial,axiom,
% 5.17/5.49 ! [N: nat,K: nat] :
% 5.17/5.49 ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.17/5.49 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % binomial_gbinomial
% 5.17/5.49 thf(fact_8033_binomial__gbinomial,axiom,
% 5.17/5.49 ! [N: nat,K: nat] :
% 5.17/5.49 ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.17/5.49 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K ) ) ).
% 5.17/5.49
% 5.17/5.49 % binomial_gbinomial
% 5.17/5.49 thf(fact_8034_le__imp__inverse__le__neg,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.49 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_imp_inverse_le_neg
% 5.17/5.49 thf(fact_8035_le__imp__inverse__le__neg,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_imp_inverse_le_neg
% 5.17/5.49 thf(fact_8036_inverse__le__imp__le__neg,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.17/5.49 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_imp_le_neg
% 5.17/5.49 thf(fact_8037_inverse__le__imp__le__neg,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_imp_le_neg
% 5.17/5.49 thf(fact_8038_le__imp__inverse__le,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_imp_inverse_le
% 5.17/5.49 thf(fact_8039_le__imp__inverse__le,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_imp_inverse_le
% 5.17/5.49 thf(fact_8040_inverse__le__imp__le,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_imp_le
% 5.17/5.49 thf(fact_8041_inverse__le__imp__le,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_imp_le
% 5.17/5.49 thf(fact_8042_inverse__le__1__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.17/5.49 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.49 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_1_iff
% 5.17/5.49 thf(fact_8043_inverse__le__1__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 5.17/5.49 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.49 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_1_iff
% 5.17/5.49 thf(fact_8044_one__less__inverse__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_less_inverse_iff
% 5.17/5.49 thf(fact_8045_one__less__inverse__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 5.17/5.49 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.49 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_less_inverse_iff
% 5.17/5.49 thf(fact_8046_one__less__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( ord_less_real @ A @ one_one_real )
% 5.17/5.49 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_less_inverse
% 5.17/5.49 thf(fact_8047_one__less__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.17/5.49 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_less_inverse
% 5.17/5.49 thf(fact_8048_division__ring__inverse__add,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( B != zero_zero_real )
% 5.17/5.49 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % division_ring_inverse_add
% 5.17/5.49 thf(fact_8049_division__ring__inverse__add,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( B != zero_zero_complex )
% 5.17/5.49 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % division_ring_inverse_add
% 5.17/5.49 thf(fact_8050_division__ring__inverse__add,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( B != zero_zero_rat )
% 5.17/5.49 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % division_ring_inverse_add
% 5.17/5.49 thf(fact_8051_inverse__add,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( B != zero_zero_real )
% 5.17/5.49 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_add
% 5.17/5.49 thf(fact_8052_inverse__add,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( B != zero_zero_complex )
% 5.17/5.49 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_add
% 5.17/5.49 thf(fact_8053_inverse__add,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( B != zero_zero_rat )
% 5.17/5.49 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_add
% 5.17/5.49 thf(fact_8054_field__class_Ofield__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.17/5.49 = one_one_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_inverse
% 5.17/5.49 thf(fact_8055_field__class_Ofield__inverse,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.17/5.49 = one_one_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_inverse
% 5.17/5.49 thf(fact_8056_field__class_Ofield__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.17/5.49 = one_one_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % field_class.field_inverse
% 5.17/5.49 thf(fact_8057_division__ring__inverse__diff,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( B != zero_zero_real )
% 5.17/5.49 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % division_ring_inverse_diff
% 5.17/5.49 thf(fact_8058_division__ring__inverse__diff,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( B != zero_zero_complex )
% 5.17/5.49 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % division_ring_inverse_diff
% 5.17/5.49 thf(fact_8059_division__ring__inverse__diff,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( B != zero_zero_rat )
% 5.17/5.49 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % division_ring_inverse_diff
% 5.17/5.49 thf(fact_8060_not__bit__Suc__0__numeral,axiom,
% 5.17/5.49 ! [N: num] :
% 5.17/5.49 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.17/5.49
% 5.17/5.49 % not_bit_Suc_0_numeral
% 5.17/5.49 thf(fact_8061_nonzero__inverse__eq__divide,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( inverse_inverse_real @ A )
% 5.17/5.49 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_eq_divide
% 5.17/5.49 thf(fact_8062_nonzero__inverse__eq__divide,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( invers8013647133539491842omplex @ A )
% 5.17/5.49 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_eq_divide
% 5.17/5.49 thf(fact_8063_nonzero__inverse__eq__divide,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( inverse_inverse_rat @ A )
% 5.17/5.49 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % nonzero_inverse_eq_divide
% 5.17/5.49 thf(fact_8064_gbinomial__Suc__Suc,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.17/5.49 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_Suc_Suc
% 5.17/5.49 thf(fact_8065_gbinomial__Suc__Suc,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.17/5.49 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_Suc_Suc
% 5.17/5.49 thf(fact_8066_gbinomial__Suc__Suc,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.17/5.49 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_Suc_Suc
% 5.17/5.49 thf(fact_8067_gbinomial__of__nat__symmetric,axiom,
% 5.17/5.49 ! [K: nat,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.49 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 5.17/5.49 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_of_nat_symmetric
% 5.17/5.49 thf(fact_8068_gbinomial__of__nat__symmetric,axiom,
% 5.17/5.49 ! [K: nat,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.49 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.17/5.49 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_of_nat_symmetric
% 5.17/5.49 thf(fact_8069_gbinomial__of__nat__symmetric,axiom,
% 5.17/5.49 ! [K: nat,N: nat] :
% 5.17/5.49 ( ( ord_less_eq_nat @ K @ N )
% 5.17/5.49 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ K )
% 5.17/5.49 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_of_nat_symmetric
% 5.17/5.49 thf(fact_8070_inverse__powr,axiom,
% 5.17/5.49 ! [Y4: real,A: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.49 => ( ( powr_real @ ( inverse_inverse_real @ Y4 ) @ A )
% 5.17/5.49 = ( inverse_inverse_real @ ( powr_real @ Y4 @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_powr
% 5.17/5.49 thf(fact_8071_Ints__odd__nonzero,axiom,
% 5.17/5.49 ! [A: complex] :
% 5.17/5.49 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.17/5.49 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 5.17/5.49 != zero_zero_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_nonzero
% 5.17/5.49 thf(fact_8072_Ints__odd__nonzero,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 5.17/5.49 != zero_zero_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_nonzero
% 5.17/5.49 thf(fact_8073_Ints__odd__nonzero,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 5.17/5.49 != zero_zero_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_nonzero
% 5.17/5.49 thf(fact_8074_Ints__odd__nonzero,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 5.17/5.49 != zero_zero_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_nonzero
% 5.17/5.49 thf(fact_8075_of__int__divide__in__Ints,axiom,
% 5.17/5.49 ! [B: int,A: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.49 => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B ) ) @ ring_1_Ints_complex ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_divide_in_Ints
% 5.17/5.49 thf(fact_8076_of__int__divide__in__Ints,axiom,
% 5.17/5.49 ! [B: int,A: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.49 => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_divide_in_Ints
% 5.17/5.49 thf(fact_8077_of__int__divide__in__Ints,axiom,
% 5.17/5.49 ! [B: int,A: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.49 => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) @ ring_1_Ints_rat ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_divide_in_Ints
% 5.17/5.49 thf(fact_8078_of__int__divide__in__Ints,axiom,
% 5.17/5.49 ! [B: int,A: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.17/5.49 => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) @ ring_1_Ints_int ) ) ).
% 5.17/5.49
% 5.17/5.49 % of_int_divide_in_Ints
% 5.17/5.49 thf(fact_8079_inverse__le__iff,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.49 => ( ord_less_eq_real @ B @ A ) )
% 5.17/5.49 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.17/5.49 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_iff
% 5.17/5.49 thf(fact_8080_inverse__le__iff,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.49 => ( ord_less_eq_rat @ B @ A ) )
% 5.17/5.49 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_le_iff
% 5.17/5.49 thf(fact_8081_inverse__less__iff,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.17/5.49 => ( ord_less_real @ B @ A ) )
% 5.17/5.49 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.17/5.49 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_iff
% 5.17/5.49 thf(fact_8082_inverse__less__iff,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.17/5.49 => ( ord_less_rat @ B @ A ) )
% 5.17/5.49 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.17/5.49 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_iff
% 5.17/5.49 thf(fact_8083_one__le__inverse__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 & ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_le_inverse_iff
% 5.17/5.49 thf(fact_8084_one__le__inverse__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X ) )
% 5.17/5.49 = ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.49 & ( ord_less_eq_rat @ X @ one_one_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_le_inverse_iff
% 5.17/5.49 thf(fact_8085_inverse__less__1__iff,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ ( inverse_inverse_real @ X ) @ one_one_real )
% 5.17/5.49 = ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.49 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_1_iff
% 5.17/5.49 thf(fact_8086_inverse__less__1__iff,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ ( inverse_inverse_rat @ X ) @ one_one_rat )
% 5.17/5.49 = ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.17/5.49 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_less_1_iff
% 5.17/5.49 thf(fact_8087_one__le__inverse,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.17/5.49 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_le_inverse
% 5.17/5.49 thf(fact_8088_one__le__inverse,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.17/5.49 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % one_le_inverse
% 5.17/5.49 thf(fact_8089_inverse__diff__inverse,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( A != zero_zero_real )
% 5.17/5.49 => ( ( B != zero_zero_real )
% 5.17/5.49 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_diff_inverse
% 5.17/5.49 thf(fact_8090_inverse__diff__inverse,axiom,
% 5.17/5.49 ! [A: complex,B: complex] :
% 5.17/5.49 ( ( A != zero_zero_complex )
% 5.17/5.49 => ( ( B != zero_zero_complex )
% 5.17/5.49 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.17/5.49 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_diff_inverse
% 5.17/5.49 thf(fact_8091_inverse__diff__inverse,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( A != zero_zero_rat )
% 5.17/5.49 => ( ( B != zero_zero_rat )
% 5.17/5.49 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.17/5.49 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % inverse_diff_inverse
% 5.17/5.49 thf(fact_8092_reals__Archimedean,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ? [N2: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % reals_Archimedean
% 5.17/5.49 thf(fact_8093_reals__Archimedean,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.49 => ? [N2: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) ) @ X ) ) ).
% 5.17/5.49
% 5.17/5.49 % reals_Archimedean
% 5.17/5.49 thf(fact_8094_gbinomial__addition__formula,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.17/5.49 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_addition_formula
% 5.17/5.49 thf(fact_8095_gbinomial__addition__formula,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.17/5.49 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_addition_formula
% 5.17/5.49 thf(fact_8096_gbinomial__addition__formula,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.17/5.49 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_addition_formula
% 5.17/5.49 thf(fact_8097_gbinomial__absorb__comp,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.17/5.49 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorb_comp
% 5.17/5.49 thf(fact_8098_gbinomial__absorb__comp,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.17/5.49 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorb_comp
% 5.17/5.49 thf(fact_8099_gbinomial__absorb__comp,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.17/5.49 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorb_comp
% 5.17/5.49 thf(fact_8100_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.17/5.49 ! [K: nat,A: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.17/5.49 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_ge_n_over_k_pow_k
% 5.17/5.49 thf(fact_8101_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.17/5.49 ! [K: nat,A: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.17/5.49 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_ge_n_over_k_pow_k
% 5.17/5.49 thf(fact_8102_gbinomial__mult__1_H,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.17/5.49 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_mult_1'
% 5.17/5.49 thf(fact_8103_gbinomial__mult__1_H,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.17/5.49 = ( 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 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_mult_1'
% 5.17/5.49 thf(fact_8104_gbinomial__mult__1_H,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.17/5.49 = ( 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 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_mult_1'
% 5.17/5.49 thf(fact_8105_gbinomial__mult__1,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.17/5.49 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_mult_1
% 5.17/5.49 thf(fact_8106_gbinomial__mult__1,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.17/5.49 = ( 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 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_mult_1
% 5.17/5.49 thf(fact_8107_gbinomial__mult__1,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.17/5.49 = ( 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 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_mult_1
% 5.17/5.49 thf(fact_8108_forall__pos__mono__1,axiom,
% 5.17/5.49 ! [P: real > $o,E2: real] :
% 5.17/5.49 ( ! [D2: real,E: real] :
% 5.17/5.49 ( ( ord_less_real @ D2 @ E )
% 5.17/5.49 => ( ( P @ D2 )
% 5.17/5.49 => ( P @ E ) ) )
% 5.17/5.49 => ( ! [N2: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.17/5.49 => ( P @ E2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % forall_pos_mono_1
% 5.17/5.49 thf(fact_8109_real__arch__inverse,axiom,
% 5.17/5.49 ! [E2: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.17/5.49 = ( ? [N4: nat] :
% 5.17/5.49 ( ( N4 != zero_zero_nat )
% 5.17/5.49 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.17/5.49 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % real_arch_inverse
% 5.17/5.49 thf(fact_8110_forall__pos__mono,axiom,
% 5.17/5.49 ! [P: real > $o,E2: real] :
% 5.17/5.49 ( ! [D2: real,E: real] :
% 5.17/5.49 ( ( ord_less_real @ D2 @ E )
% 5.17/5.49 => ( ( P @ D2 )
% 5.17/5.49 => ( P @ E ) ) )
% 5.17/5.49 => ( ! [N2: nat] :
% 5.17/5.49 ( ( N2 != zero_zero_nat )
% 5.17/5.49 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.17/5.49 => ( P @ E2 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % forall_pos_mono
% 5.17/5.49 thf(fact_8111_bit__nat__iff,axiom,
% 5.17/5.49 ! [K: int,N: nat] :
% 5.17/5.49 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.17/5.49 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.49 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_nat_iff
% 5.17/5.49 thf(fact_8112_even__xor__iff,axiom,
% 5.17/5.49 ! [A: code_integer,B: code_integer] :
% 5.17/5.49 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 5.17/5.49 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_xor_iff
% 5.17/5.49 thf(fact_8113_even__xor__iff,axiom,
% 5.17/5.49 ! [A: nat,B: nat] :
% 5.17/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.17/5.49 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_xor_iff
% 5.17/5.49 thf(fact_8114_even__xor__iff,axiom,
% 5.17/5.49 ! [A: int,B: int] :
% 5.17/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.17/5.49 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.49 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % even_xor_iff
% 5.17/5.49 thf(fact_8115_sqrt__divide__self__eq,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.17/5.49 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % sqrt_divide_self_eq
% 5.17/5.49 thf(fact_8116_ln__inverse,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ln_inverse
% 5.17/5.49 thf(fact_8117_Ints__odd__less__0,axiom,
% 5.17/5.49 ! [A: real] :
% 5.17/5.49 ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 5.17/5.49 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_less_0
% 5.17/5.49 thf(fact_8118_Ints__odd__less__0,axiom,
% 5.17/5.49 ! [A: rat] :
% 5.17/5.49 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 5.17/5.49 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_less_0
% 5.17/5.49 thf(fact_8119_Ints__odd__less__0,axiom,
% 5.17/5.49 ! [A: int] :
% 5.17/5.49 ( ( member_int @ A @ ring_1_Ints_int )
% 5.17/5.49 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 5.17/5.49 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_odd_less_0
% 5.17/5.49 thf(fact_8120_Ints__nonzero__abs__ge1,axiom,
% 5.17/5.49 ! [X: code_integer] :
% 5.17/5.49 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.17/5.49 => ( ( X != zero_z3403309356797280102nteger )
% 5.17/5.49 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_ge1
% 5.17/5.49 thf(fact_8121_Ints__nonzero__abs__ge1,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( X != zero_zero_rat )
% 5.17/5.49 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_ge1
% 5.17/5.49 thf(fact_8122_Ints__nonzero__abs__ge1,axiom,
% 5.17/5.49 ! [X: int] :
% 5.17/5.49 ( ( member_int @ X @ ring_1_Ints_int )
% 5.17/5.49 => ( ( X != zero_zero_int )
% 5.17/5.49 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_ge1
% 5.17/5.49 thf(fact_8123_Ints__nonzero__abs__ge1,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( member_real @ X @ ring_1_Ints_real )
% 5.17/5.49 => ( ( X != zero_zero_real )
% 5.17/5.49 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_ge1
% 5.17/5.49 thf(fact_8124_Ints__nonzero__abs__less1,axiom,
% 5.17/5.49 ! [X: code_integer] :
% 5.17/5.49 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.17/5.49 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer )
% 5.17/5.49 => ( X = zero_z3403309356797280102nteger ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_less1
% 5.17/5.49 thf(fact_8125_Ints__nonzero__abs__less1,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( member_real @ X @ ring_1_Ints_real )
% 5.17/5.49 => ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.49 => ( X = zero_zero_real ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_less1
% 5.17/5.49 thf(fact_8126_Ints__nonzero__abs__less1,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 5.17/5.49 => ( X = zero_zero_rat ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_less1
% 5.17/5.49 thf(fact_8127_Ints__nonzero__abs__less1,axiom,
% 5.17/5.49 ! [X: int] :
% 5.17/5.49 ( ( member_int @ X @ ring_1_Ints_int )
% 5.17/5.49 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 5.17/5.49 => ( X = zero_zero_int ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_nonzero_abs_less1
% 5.17/5.49 thf(fact_8128_Ints__eq__abs__less1,axiom,
% 5.17/5.49 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.49 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.17/5.49 => ( ( member_Code_integer @ Y4 @ ring_11222124179247155820nteger )
% 5.17/5.49 => ( ( X = Y4 )
% 5.17/5.49 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ Y4 ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_eq_abs_less1
% 5.17/5.49 thf(fact_8129_Ints__eq__abs__less1,axiom,
% 5.17/5.49 ! [X: real,Y4: real] :
% 5.17/5.49 ( ( member_real @ X @ ring_1_Ints_real )
% 5.17/5.49 => ( ( member_real @ Y4 @ ring_1_Ints_real )
% 5.17/5.49 => ( ( X = Y4 )
% 5.17/5.49 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y4 ) ) @ one_one_real ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_eq_abs_less1
% 5.17/5.49 thf(fact_8130_Ints__eq__abs__less1,axiom,
% 5.17/5.49 ! [X: rat,Y4: rat] :
% 5.17/5.49 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( member_rat @ Y4 @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( X = Y4 )
% 5.17/5.49 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y4 ) ) @ one_one_rat ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_eq_abs_less1
% 5.17/5.49 thf(fact_8131_Ints__eq__abs__less1,axiom,
% 5.17/5.49 ! [X: int,Y4: int] :
% 5.17/5.49 ( ( member_int @ X @ ring_1_Ints_int )
% 5.17/5.49 => ( ( member_int @ Y4 @ ring_1_Ints_int )
% 5.17/5.49 => ( ( X = Y4 )
% 5.17/5.49 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y4 ) ) @ one_one_int ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Ints_eq_abs_less1
% 5.17/5.49 thf(fact_8132_sin__times__pi__eq__0,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.17/5.49 = zero_zero_real )
% 5.17/5.49 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.17/5.49
% 5.17/5.49 % sin_times_pi_eq_0
% 5.17/5.49 thf(fact_8133_ex__inverse__of__nat__less,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ? [N2: nat] :
% 5.17/5.49 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.49 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ex_inverse_of_nat_less
% 5.17/5.49 thf(fact_8134_ex__inverse__of__nat__less,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.17/5.49 => ? [N2: nat] :
% 5.17/5.49 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.17/5.49 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ X ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % ex_inverse_of_nat_less
% 5.17/5.49 thf(fact_8135_power__diff__conv__inverse,axiom,
% 5.17/5.49 ! [X: real,M: nat,N: nat] :
% 5.17/5.49 ( ( X != zero_zero_real )
% 5.17/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.49 => ( ( power_power_real @ X @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.49 = ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ ( inverse_inverse_real @ X ) @ M ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_diff_conv_inverse
% 5.17/5.49 thf(fact_8136_power__diff__conv__inverse,axiom,
% 5.17/5.49 ! [X: complex,M: nat,N: nat] :
% 5.17/5.49 ( ( X != zero_zero_complex )
% 5.17/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.49 => ( ( power_power_complex @ X @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.49 = ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X ) @ M ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_diff_conv_inverse
% 5.17/5.49 thf(fact_8137_power__diff__conv__inverse,axiom,
% 5.17/5.49 ! [X: rat,M: nat,N: nat] :
% 5.17/5.49 ( ( X != zero_zero_rat )
% 5.17/5.49 => ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.49 => ( ( power_power_rat @ X @ ( minus_minus_nat @ N @ M ) )
% 5.17/5.49 = ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ ( inverse_inverse_rat @ X ) @ M ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % power_diff_conv_inverse
% 5.17/5.49 thf(fact_8138_Suc__times__gbinomial,axiom,
% 5.17/5.49 ! [K: nat,A: complex] :
% 5.17/5.49 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.17/5.49 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Suc_times_gbinomial
% 5.17/5.49 thf(fact_8139_Suc__times__gbinomial,axiom,
% 5.17/5.49 ! [K: nat,A: real] :
% 5.17/5.49 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.17/5.49 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Suc_times_gbinomial
% 5.17/5.49 thf(fact_8140_Suc__times__gbinomial,axiom,
% 5.17/5.49 ! [K: nat,A: rat] :
% 5.17/5.49 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.17/5.49 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % Suc_times_gbinomial
% 5.17/5.49 thf(fact_8141_gbinomial__absorption,axiom,
% 5.17/5.49 ! [K: nat,A: complex] :
% 5.17/5.49 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.17/5.49 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorption
% 5.17/5.49 thf(fact_8142_gbinomial__absorption,axiom,
% 5.17/5.49 ! [K: nat,A: real] :
% 5.17/5.49 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.17/5.49 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorption
% 5.17/5.49 thf(fact_8143_gbinomial__absorption,axiom,
% 5.17/5.49 ! [K: nat,A: rat] :
% 5.17/5.49 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.17/5.49 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_absorption
% 5.17/5.49 thf(fact_8144_gbinomial__trinomial__revision,axiom,
% 5.17/5.49 ! [K: nat,M: nat,A: complex] :
% 5.17/5.49 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.49 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.17/5.49 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_trinomial_revision
% 5.17/5.49 thf(fact_8145_gbinomial__trinomial__revision,axiom,
% 5.17/5.49 ! [K: nat,M: nat,A: real] :
% 5.17/5.49 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.49 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.17/5.49 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_trinomial_revision
% 5.17/5.49 thf(fact_8146_gbinomial__trinomial__revision,axiom,
% 5.17/5.49 ! [K: nat,M: nat,A: rat] :
% 5.17/5.49 ( ( ord_less_eq_nat @ K @ M )
% 5.17/5.49 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.17/5.49 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_trinomial_revision
% 5.17/5.49 thf(fact_8147_log__inverse,axiom,
% 5.17/5.49 ! [A: real,X: real] :
% 5.17/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( A != one_one_real )
% 5.17/5.49 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.49 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 5.17/5.49 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % log_inverse
% 5.17/5.49 thf(fact_8148_frac__neg,axiom,
% 5.17/5.49 ! [X: real] :
% 5.17/5.49 ( ( ( member_real @ X @ ring_1_Ints_real )
% 5.17/5.49 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 5.17/5.49 = zero_zero_real ) )
% 5.17/5.49 & ( ~ ( member_real @ X @ ring_1_Ints_real )
% 5.17/5.49 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 5.17/5.49 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_neg
% 5.17/5.49 thf(fact_8149_frac__neg,axiom,
% 5.17/5.49 ! [X: rat] :
% 5.17/5.49 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 5.17/5.49 = zero_zero_rat ) )
% 5.17/5.49 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 5.17/5.49 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 5.17/5.49 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % frac_neg
% 5.17/5.49 thf(fact_8150_bit__nat__def,axiom,
% 5.17/5.49 ( bit_se1148574629649215175it_nat
% 5.17/5.49 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.49 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % bit_nat_def
% 5.17/5.49 thf(fact_8151_gbinomial__factors,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.17/5.49 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_factors
% 5.17/5.49 thf(fact_8152_gbinomial__factors,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.17/5.49 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_factors
% 5.17/5.49 thf(fact_8153_gbinomial__factors,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.17/5.49 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_factors
% 5.17/5.49 thf(fact_8154_gbinomial__rec,axiom,
% 5.17/5.49 ! [A: complex,K: nat] :
% 5.17/5.49 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.17/5.49 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_rec
% 5.17/5.49 thf(fact_8155_gbinomial__rec,axiom,
% 5.17/5.49 ! [A: real,K: nat] :
% 5.17/5.49 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.17/5.49 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_rec
% 5.17/5.49 thf(fact_8156_gbinomial__rec,axiom,
% 5.17/5.49 ! [A: rat,K: nat] :
% 5.17/5.49 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.17/5.49 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_rec
% 5.17/5.49 thf(fact_8157_gbinomial__index__swap,axiom,
% 5.17/5.49 ! [K: nat,N: nat] :
% 5.17/5.49 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.17/5.49 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_index_swap
% 5.17/5.49 thf(fact_8158_gbinomial__index__swap,axiom,
% 5.17/5.49 ! [K: nat,N: nat] :
% 5.17/5.49 ( ( 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 ) )
% 5.17/5.49 = ( 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 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_index_swap
% 5.17/5.49 thf(fact_8159_gbinomial__index__swap,axiom,
% 5.17/5.49 ! [K: nat,N: nat] :
% 5.17/5.49 ( ( 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 ) )
% 5.17/5.49 = ( 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 ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_index_swap
% 5.17/5.49 thf(fact_8160_gbinomial__negated__upper,axiom,
% 5.17/5.49 ( gbinomial_complex
% 5.17/5.49 = ( ^ [A3: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A3 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_negated_upper
% 5.17/5.49 thf(fact_8161_gbinomial__negated__upper,axiom,
% 5.17/5.49 ( gbinomial_real
% 5.17/5.49 = ( ^ [A3: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A3 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_negated_upper
% 5.17/5.49 thf(fact_8162_gbinomial__negated__upper,axiom,
% 5.17/5.49 ( gbinomial_rat
% 5.17/5.49 = ( ^ [A3: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A3 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % gbinomial_negated_upper
% 5.17/5.49 thf(fact_8163_exp__plus__inverse__exp,axiom,
% 5.17/5.49 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % exp_plus_inverse_exp
% 5.17/5.49 thf(fact_8164_le__mult__floor__Ints,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_mult_floor_Ints
% 5.17/5.49 thf(fact_8165_le__mult__floor__Ints,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_mult_floor_Ints
% 5.17/5.49 thf(fact_8166_le__mult__floor__Ints,axiom,
% 5.17/5.49 ! [A: real,B: real] :
% 5.17/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.49 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.49 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.49
% 5.17/5.49 % le_mult_floor_Ints
% 5.17/5.49 thf(fact_8167_le__mult__floor__Ints,axiom,
% 5.17/5.49 ! [A: rat,B: rat] :
% 5.17/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.49 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % le_mult_floor_Ints
% 5.17/5.50 thf(fact_8168_le__mult__floor__Ints,axiom,
% 5.17/5.50 ! [A: rat,B: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.50 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % le_mult_floor_Ints
% 5.17/5.50 thf(fact_8169_le__mult__floor__Ints,axiom,
% 5.17/5.50 ! [A: rat,B: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.50 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % le_mult_floor_Ints
% 5.17/5.50 thf(fact_8170_frac__unique__iff,axiom,
% 5.17/5.50 ! [X: rat,A: rat] :
% 5.17/5.50 ( ( ( archimedean_frac_rat @ X )
% 5.17/5.50 = A )
% 5.17/5.50 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 5.17/5.50 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.50 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % frac_unique_iff
% 5.17/5.50 thf(fact_8171_frac__unique__iff,axiom,
% 5.17/5.50 ! [X: real,A: real] :
% 5.17/5.50 ( ( ( archim2898591450579166408c_real @ X )
% 5.17/5.50 = A )
% 5.17/5.50 = ( ( member_real @ ( minus_minus_real @ X @ A ) @ ring_1_Ints_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % frac_unique_iff
% 5.17/5.50 thf(fact_8172_mult__ceiling__le__Ints,axiom,
% 5.17/5.50 ! [A: rat,B: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.50 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_ceiling_le_Ints
% 5.17/5.50 thf(fact_8173_mult__ceiling__le__Ints,axiom,
% 5.17/5.50 ! [A: rat,B: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.50 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_ceiling_le_Ints
% 5.17/5.50 thf(fact_8174_mult__ceiling__le__Ints,axiom,
% 5.17/5.50 ! [A: rat,B: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.17/5.50 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_ceiling_le_Ints
% 5.17/5.50 thf(fact_8175_mult__ceiling__le__Ints,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_ceiling_le_Ints
% 5.17/5.50 thf(fact_8176_mult__ceiling__le__Ints,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_ceiling_le_Ints
% 5.17/5.50 thf(fact_8177_mult__ceiling__le__Ints,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.17/5.50 => ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_ceiling_le_Ints
% 5.17/5.50 thf(fact_8178_gbinomial__minus,axiom,
% 5.17/5.50 ! [A: complex,K: nat] :
% 5.17/5.50 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.17/5.50 = ( 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 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_minus
% 5.17/5.50 thf(fact_8179_gbinomial__minus,axiom,
% 5.17/5.50 ! [A: real,K: nat] :
% 5.17/5.50 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.17/5.50 = ( 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 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_minus
% 5.17/5.50 thf(fact_8180_gbinomial__minus,axiom,
% 5.17/5.50 ! [A: rat,K: nat] :
% 5.17/5.50 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.17/5.50 = ( 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 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_minus
% 5.17/5.50 thf(fact_8181_plus__inverse__ge__2,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % plus_inverse_ge_2
% 5.17/5.50 thf(fact_8182_real__inv__sqrt__pow2,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( inverse_inverse_real @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_inv_sqrt_pow2
% 5.17/5.50 thf(fact_8183_gbinomial__reduce__nat,axiom,
% 5.17/5.50 ! [K: nat,A: complex] :
% 5.17/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.50 => ( ( gbinomial_complex @ A @ K )
% 5.17/5.50 = ( 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 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_reduce_nat
% 5.17/5.50 thf(fact_8184_gbinomial__reduce__nat,axiom,
% 5.17/5.50 ! [K: nat,A: real] :
% 5.17/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.50 => ( ( gbinomial_real @ A @ K )
% 5.17/5.50 = ( 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 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_reduce_nat
% 5.17/5.50 thf(fact_8185_gbinomial__reduce__nat,axiom,
% 5.17/5.50 ! [K: nat,A: rat] :
% 5.17/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.17/5.50 => ( ( gbinomial_rat @ A @ K )
% 5.17/5.50 = ( 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 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_reduce_nat
% 5.17/5.50 thf(fact_8186_gbinomial__pochhammer,axiom,
% 5.17/5.50 ( gbinomial_rat
% 5.17/5.50 = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_pochhammer
% 5.17/5.50 thf(fact_8187_gbinomial__pochhammer,axiom,
% 5.17/5.50 ( gbinomial_real
% 5.17/5.50 = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A3 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_pochhammer
% 5.17/5.50 thf(fact_8188_gbinomial__pochhammer,axiom,
% 5.17/5.50 ( gbinomial_complex
% 5.17/5.50 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_pochhammer
% 5.17/5.50 thf(fact_8189_gbinomial__pochhammer_H,axiom,
% 5.17/5.50 ( gbinomial_rat
% 5.17/5.50 = ( ^ [A3: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_pochhammer'
% 5.17/5.50 thf(fact_8190_gbinomial__pochhammer_H,axiom,
% 5.17/5.50 ( gbinomial_real
% 5.17/5.50 = ( ^ [A3: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_pochhammer'
% 5.17/5.50 thf(fact_8191_gbinomial__pochhammer_H,axiom,
% 5.17/5.50 ( gbinomial_complex
% 5.17/5.50 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % gbinomial_pochhammer'
% 5.17/5.50 thf(fact_8192_tan__cot,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.17/5.50 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tan_cot
% 5.17/5.50 thf(fact_8193_sin__integer__2pi,axiom,
% 5.17/5.50 ! [N: real] :
% 5.17/5.50 ( ( member_real @ N @ ring_1_Ints_real )
% 5.17/5.50 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % sin_integer_2pi
% 5.17/5.50 thf(fact_8194_cos__integer__2pi,axiom,
% 5.17/5.50 ! [N: real] :
% 5.17/5.50 ( ( member_real @ N @ ring_1_Ints_real )
% 5.17/5.50 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.17/5.50 = one_one_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % cos_integer_2pi
% 5.17/5.50 thf(fact_8195_xor__nat__unfold,axiom,
% 5.17/5.50 ( bit_se6528837805403552850or_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M5 @ ( 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 @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_nat_unfold
% 5.17/5.50 thf(fact_8196_real__le__x__sinh,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_le_x_sinh
% 5.17/5.50 thf(fact_8197_xor__nat__rec,axiom,
% 5.17/5.50 ( bit_se6528837805403552850or_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.50 ( plus_plus_nat
% 5.17/5.50 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.50 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 ) )
% 5.17/5.50 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 5.17/5.50 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_nat_rec
% 5.17/5.50 thf(fact_8198_one__xor__eq,axiom,
% 5.17/5.50 ! [A: code_integer] :
% 5.17/5.50 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 5.17/5.50 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.50 @ ( zero_n356916108424825756nteger
% 5.17/5.50 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % one_xor_eq
% 5.17/5.50 thf(fact_8199_one__xor__eq,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 5.17/5.50 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.50 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.50 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % one_xor_eq
% 5.17/5.50 thf(fact_8200_one__xor__eq,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 5.17/5.50 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.50 @ ( zero_n2684676970156552555ol_int
% 5.17/5.50 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % one_xor_eq
% 5.17/5.50 thf(fact_8201_xor__one__eq,axiom,
% 5.17/5.50 ! [A: code_integer] :
% 5.17/5.50 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 5.17/5.50 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.50 @ ( zero_n356916108424825756nteger
% 5.17/5.50 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_one_eq
% 5.17/5.50 thf(fact_8202_xor__one__eq,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 5.17/5.50 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.50 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.50 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_one_eq
% 5.17/5.50 thf(fact_8203_xor__one__eq,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 5.17/5.50 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.17/5.50 @ ( zero_n2684676970156552555ol_int
% 5.17/5.50 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_one_eq
% 5.17/5.50 thf(fact_8204_real__le__abs__sinh,axiom,
% 5.17/5.50 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_le_abs_sinh
% 5.17/5.50 thf(fact_8205_tan__sec,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ( cos_real @ X )
% 5.17/5.50 != zero_zero_real )
% 5.17/5.50 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tan_sec
% 5.17/5.50 thf(fact_8206_tan__sec,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( ( cos_complex @ X )
% 5.17/5.50 != zero_zero_complex )
% 5.17/5.50 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tan_sec
% 5.17/5.50 thf(fact_8207_sinh__ln__real,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.17/5.50 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_ln_real
% 5.17/5.50 thf(fact_8208_cosh__ln__real,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.17/5.50 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_ln_real
% 5.17/5.50 thf(fact_8209_horner__sum__of__bool__2__less,axiom,
% 5.17/5.50 ! [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 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % horner_sum_of_bool_2_less
% 5.17/5.50 thf(fact_8210_cosh__zero__iff,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ( cosh_real @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 = ( ( power_power_real @ ( exp_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_zero_iff
% 5.17/5.50 thf(fact_8211_cosh__zero__iff,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( ( cosh_complex @ X )
% 5.17/5.50 = zero_zero_complex )
% 5.17/5.50 = ( ( power_power_complex @ ( exp_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_zero_iff
% 5.17/5.50 thf(fact_8212_push__bit__numeral__minus__1,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_numeral_minus_1
% 5.17/5.50 thf(fact_8213_push__bit__numeral__minus__1,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_numeral_minus_1
% 5.17/5.50 thf(fact_8214_push__bit__nonnegative__int__iff,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.17/5.50 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_nonnegative_int_iff
% 5.17/5.50 thf(fact_8215_push__bit__negative__int__iff,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.17/5.50 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_negative_int_iff
% 5.17/5.50 thf(fact_8216_push__bit__of__0,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ zero_zero_int )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_0
% 5.17/5.50 thf(fact_8217_push__bit__of__0,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ zero_zero_nat )
% 5.17/5.50 = zero_zero_nat ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_0
% 5.17/5.50 thf(fact_8218_push__bit__eq__0__iff,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( ( bit_se545348938243370406it_int @ N @ A )
% 5.17/5.50 = zero_zero_int )
% 5.17/5.50 = ( A = zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_eq_0_iff
% 5.17/5.50 thf(fact_8219_push__bit__eq__0__iff,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( ( bit_se547839408752420682it_nat @ N @ A )
% 5.17/5.50 = zero_zero_nat )
% 5.17/5.50 = ( A = zero_zero_nat ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_eq_0_iff
% 5.17/5.50 thf(fact_8220_sinh__0,axiom,
% 5.17/5.50 ( ( sinh_complex @ zero_zero_complex )
% 5.17/5.50 = zero_zero_complex ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_0
% 5.17/5.50 thf(fact_8221_sinh__0,axiom,
% 5.17/5.50 ( ( sinh_real @ zero_zero_real )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_0
% 5.17/5.50 thf(fact_8222_push__bit__push__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_push_bit
% 5.17/5.50 thf(fact_8223_push__bit__push__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.17/5.50 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_push_bit
% 5.17/5.50 thf(fact_8224_push__bit__and,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_and
% 5.17/5.50 thf(fact_8225_push__bit__and,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se727722235901077358nd_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_and
% 5.17/5.50 thf(fact_8226_push__bit__xor,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.17/5.50 = ( bit_se6526347334894502574or_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_xor
% 5.17/5.50 thf(fact_8227_push__bit__xor,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se6528837805403552850or_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_xor
% 5.17/5.50 thf(fact_8228_concat__bit__of__zero__1,axiom,
% 5.17/5.50 ! [N: nat,L: int] :
% 5.17/5.50 ( ( bit_concat_bit @ N @ zero_zero_int @ L )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ N @ L ) ) ).
% 5.17/5.50
% 5.17/5.50 % concat_bit_of_zero_1
% 5.17/5.50 thf(fact_8229_sinh__real__zero__iff,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ( sinh_real @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 = ( X = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_real_zero_iff
% 5.17/5.50 thf(fact_8230_sinh__real__le__iff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y4 ) )
% 5.17/5.50 = ( ord_less_eq_real @ X @ Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_real_le_iff
% 5.17/5.50 thf(fact_8231_cosh__0,axiom,
% 5.17/5.50 ( ( cosh_complex @ zero_zero_complex )
% 5.17/5.50 = one_one_complex ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_0
% 5.17/5.50 thf(fact_8232_cosh__0,axiom,
% 5.17/5.50 ( ( cosh_real @ zero_zero_real )
% 5.17/5.50 = one_one_real ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_0
% 5.17/5.50 thf(fact_8233_sinh__real__neg__iff,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.17/5.50 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_real_neg_iff
% 5.17/5.50 thf(fact_8234_sinh__real__pos__iff,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.17/5.50 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_real_pos_iff
% 5.17/5.50 thf(fact_8235_sinh__real__nonpos__iff,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.17/5.50 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_real_nonpos_iff
% 5.17/5.50 thf(fact_8236_sinh__real__nonneg__iff,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.17/5.50 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_real_nonneg_iff
% 5.17/5.50 thf(fact_8237_xor__nonnegative__int__iff,axiom,
% 5.17/5.50 ! [K: int,L: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.17/5.50 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.50 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_nonnegative_int_iff
% 5.17/5.50 thf(fact_8238_xor__negative__int__iff,axiom,
% 5.17/5.50 ! [K: int,L: int] :
% 5.17/5.50 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.17/5.50 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.50 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_negative_int_iff
% 5.17/5.50 thf(fact_8239_push__bit__Suc__numeral,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( numeral_numeral_int @ K ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ N @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_Suc_numeral
% 5.17/5.50 thf(fact_8240_push__bit__Suc__numeral,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.50 = ( bit_se547839408752420682it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_Suc_numeral
% 5.17/5.50 thf(fact_8241_push__bit__Suc__minus__numeral,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.17/5.50 = ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_Suc_minus_numeral
% 5.17/5.50 thf(fact_8242_push__bit__Suc__minus__numeral,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_Suc_minus_numeral
% 5.17/5.50 thf(fact_8243_push__bit__numeral,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ K ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_numeral
% 5.17/5.50 thf(fact_8244_push__bit__numeral,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.50 = ( bit_se547839408752420682it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_numeral
% 5.17/5.50 thf(fact_8245_push__bit__Suc,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_Suc
% 5.17/5.50 thf(fact_8246_push__bit__Suc,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 5.17/5.50 = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_Suc
% 5.17/5.50 thf(fact_8247_push__bit__of__Suc__0,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_Suc_0
% 5.17/5.50 thf(fact_8248_push__bit__of__1,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 5.17/5.50 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_1
% 5.17/5.50 thf(fact_8249_push__bit__of__1,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 5.17/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_1
% 5.17/5.50 thf(fact_8250_even__push__bit__iff,axiom,
% 5.17/5.50 ! [N: nat,A: code_integer] :
% 5.17/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N @ A ) )
% 5.17/5.50 = ( ( N != zero_zero_nat )
% 5.17/5.50 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_push_bit_iff
% 5.17/5.50 thf(fact_8251_even__push__bit__iff,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.17/5.50 = ( ( N != zero_zero_nat )
% 5.17/5.50 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_push_bit_iff
% 5.17/5.50 thf(fact_8252_even__push__bit__iff,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.17/5.50 = ( ( N != zero_zero_nat )
% 5.17/5.50 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_push_bit_iff
% 5.17/5.50 thf(fact_8253_push__bit__minus__numeral,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.17/5.50 = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus_numeral
% 5.17/5.50 thf(fact_8254_push__bit__minus__numeral,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus_numeral
% 5.17/5.50 thf(fact_8255_flip__bit__int__def,axiom,
% 5.17/5.50 ( bit_se2159334234014336723it_int
% 5.17/5.50 = ( ^ [N4: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % flip_bit_int_def
% 5.17/5.50 thf(fact_8256_bit__xor__int__iff,axiom,
% 5.17/5.50 ! [K: int,L: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N )
% 5.17/5.50 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.17/5.50 != ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_xor_int_iff
% 5.17/5.50 thf(fact_8257_sinh__add,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( sinh_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.50 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_add
% 5.17/5.50 thf(fact_8258_cosh__add,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( cosh_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.50 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_add
% 5.17/5.50 thf(fact_8259_cosh__diff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( cosh_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_real @ ( times_times_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( sinh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_diff
% 5.17/5.50 thf(fact_8260_sinh__diff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( sinh_real @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_real @ ( times_times_real @ ( sinh_real @ X ) @ ( cosh_real @ Y4 ) ) @ ( times_times_real @ ( cosh_real @ X ) @ ( sinh_real @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_diff
% 5.17/5.50 thf(fact_8261_cosh__real__nonzero,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( cosh_real @ X )
% 5.17/5.50 != zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_nonzero
% 5.17/5.50 thf(fact_8262_push__bit__nat__eq,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.17/5.50 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_nat_eq
% 5.17/5.50 thf(fact_8263_sinh__le__cosh__real,axiom,
% 5.17/5.50 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_le_cosh_real
% 5.17/5.50 thf(fact_8264_push__bit__of__nat,axiom,
% 5.17/5.50 ! [N: nat,M: nat] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.17/5.50 = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_nat
% 5.17/5.50 thf(fact_8265_push__bit__of__nat,axiom,
% 5.17/5.50 ! [N: nat,M: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.17/5.50 = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_nat
% 5.17/5.50 thf(fact_8266_of__nat__push__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ M @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_push_bit
% 5.17/5.50 thf(fact_8267_of__nat__push__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M @ N ) )
% 5.17/5.50 = ( bit_se547839408752420682it_nat @ M @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_push_bit
% 5.17/5.50 thf(fact_8268_push__bit__minus,axiom,
% 5.17/5.50 ! [N: nat,A: code_integer] :
% 5.17/5.50 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ A ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus
% 5.17/5.50 thf(fact_8269_push__bit__minus,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ A ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus
% 5.17/5.50 thf(fact_8270_push__bit__add,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( plus_plus_int @ A @ B ) )
% 5.17/5.50 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_add
% 5.17/5.50 thf(fact_8271_push__bit__add,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( plus_plus_nat @ A @ B ) )
% 5.17/5.50 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_add
% 5.17/5.50 thf(fact_8272_push__bit__of__int,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.17/5.50 = ( ring_1_of_int_int @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_of_int
% 5.17/5.50 thf(fact_8273_tanh__def,axiom,
% 5.17/5.50 ( tanh_complex
% 5.17/5.50 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X3 ) @ ( cosh_complex @ X3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tanh_def
% 5.17/5.50 thf(fact_8274_tanh__def,axiom,
% 5.17/5.50 ( tanh_real
% 5.17/5.50 = ( ^ [X3: real] : ( divide_divide_real @ ( sinh_real @ X3 ) @ ( cosh_real @ X3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tanh_def
% 5.17/5.50 thf(fact_8275_sinh__minus__cosh,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( minus_minus_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) )
% 5.17/5.50 = ( uminus_uminus_real @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_minus_cosh
% 5.17/5.50 thf(fact_8276_sinh__minus__cosh,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( minus_minus_complex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) )
% 5.17/5.50 = ( uminus1482373934393186551omplex @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_minus_cosh
% 5.17/5.50 thf(fact_8277_cosh__minus__sinh,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( minus_minus_real @ ( cosh_real @ X ) @ ( sinh_real @ X ) )
% 5.17/5.50 = ( exp_real @ ( uminus_uminus_real @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_minus_sinh
% 5.17/5.50 thf(fact_8278_cosh__minus__sinh,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( minus_minus_complex @ ( cosh_complex @ X ) @ ( sinh_complex @ X ) )
% 5.17/5.50 = ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_minus_sinh
% 5.17/5.50 thf(fact_8279_XOR__lower,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % XOR_lower
% 5.17/5.50 thf(fact_8280_cosh__real__pos,axiom,
% 5.17/5.50 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_pos
% 5.17/5.50 thf(fact_8281_cosh__real__nonpos__le__iff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) )
% 5.17/5.50 = ( ord_less_eq_real @ Y4 @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_nonpos_le_iff
% 5.17/5.50 thf(fact_8282_cosh__real__nonneg__le__iff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) )
% 5.17/5.50 = ( ord_less_eq_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_nonneg_le_iff
% 5.17/5.50 thf(fact_8283_cosh__real__nonneg,axiom,
% 5.17/5.50 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_nonneg
% 5.17/5.50 thf(fact_8284_cosh__real__ge__1,axiom,
% 5.17/5.50 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_ge_1
% 5.17/5.50 thf(fact_8285_sinh__double,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.50 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X ) ) @ ( cosh_complex @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_double
% 5.17/5.50 thf(fact_8286_sinh__double,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.50 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X ) ) @ ( cosh_real @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_double
% 5.17/5.50 thf(fact_8287_push__bit__take__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.17/5.50 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_take_bit
% 5.17/5.50 thf(fact_8288_push__bit__take__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.17/5.50 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_take_bit
% 5.17/5.50 thf(fact_8289_take__bit__push__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: int] :
% 5.17/5.50 ( ( bit_se2923211474154528505it_int @ M @ ( bit_se545348938243370406it_int @ N @ A ) )
% 5.17/5.50 = ( bit_se545348938243370406it_int @ N @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_push_bit
% 5.17/5.50 thf(fact_8290_take__bit__push__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se547839408752420682it_nat @ N @ A ) )
% 5.17/5.50 = ( bit_se547839408752420682it_nat @ N @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M @ N ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_push_bit
% 5.17/5.50 thf(fact_8291_flip__bit__nat__def,axiom,
% 5.17/5.50 ( bit_se2161824704523386999it_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] : ( bit_se6528837805403552850or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M5 @ one_one_nat ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % flip_bit_nat_def
% 5.17/5.50 thf(fact_8292_cosh__real__nonpos__less__iff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) )
% 5.17/5.50 = ( ord_less_real @ Y4 @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_nonpos_less_iff
% 5.17/5.50 thf(fact_8293_cosh__real__nonneg__less__iff,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.50 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) )
% 5.17/5.50 = ( ord_less_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_nonneg_less_iff
% 5.17/5.50 thf(fact_8294_cosh__real__strict__mono,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.50 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_real_strict_mono
% 5.17/5.50 thf(fact_8295_bit__push__bit__iff__int,axiom,
% 5.17/5.50 ! [M: nat,K: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.17/5.50 = ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.50 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_push_bit_iff_int
% 5.17/5.50 thf(fact_8296_cosh__square__eq,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_square_eq
% 5.17/5.50 thf(fact_8297_cosh__square__eq,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_square_eq
% 5.17/5.50 thf(fact_8298_sinh__square__eq,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_square_eq
% 5.17/5.50 thf(fact_8299_sinh__square__eq,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_square_eq
% 5.17/5.50 thf(fact_8300_hyperbolic__pythagoras,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = one_one_complex ) ).
% 5.17/5.50
% 5.17/5.50 % hyperbolic_pythagoras
% 5.17/5.50 thf(fact_8301_hyperbolic__pythagoras,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = one_one_real ) ).
% 5.17/5.50
% 5.17/5.50 % hyperbolic_pythagoras
% 5.17/5.50 thf(fact_8302_xor__nat__def,axiom,
% 5.17/5.50 ( bit_se6528837805403552850or_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_nat_def
% 5.17/5.50 thf(fact_8303_bit__push__bit__iff__nat,axiom,
% 5.17/5.50 ! [M: nat,Q2: nat,N: nat] :
% 5.17/5.50 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.17/5.50 = ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.50 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_push_bit_iff_nat
% 5.17/5.50 thf(fact_8304_arcosh__cosh__real,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % arcosh_cosh_real
% 5.17/5.50 thf(fact_8305_concat__bit__eq,axiom,
% 5.17/5.50 ( bit_concat_bit
% 5.17/5.50 = ( ^ [N4: nat,K3: int,L3: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N4 @ K3 ) @ ( bit_se545348938243370406it_int @ N4 @ L3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % concat_bit_eq
% 5.17/5.50 thf(fact_8306_flip__bit__eq__xor,axiom,
% 5.17/5.50 ( bit_se1345352211410354436nteger
% 5.17/5.50 = ( ^ [N4: nat,A3: code_integer] : ( bit_se3222712562003087583nteger @ A3 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % flip_bit_eq_xor
% 5.17/5.50 thf(fact_8307_flip__bit__eq__xor,axiom,
% 5.17/5.50 ( bit_se2159334234014336723it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % flip_bit_eq_xor
% 5.17/5.50 thf(fact_8308_flip__bit__eq__xor,axiom,
% 5.17/5.50 ( bit_se2161824704523386999it_nat
% 5.17/5.50 = ( ^ [N4: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % flip_bit_eq_xor
% 5.17/5.50 thf(fact_8309_cosh__double,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.50 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_double
% 5.17/5.50 thf(fact_8310_cosh__double,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 5.17/5.50 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_double
% 5.17/5.50 thf(fact_8311_push__bit__double,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( times_times_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_double
% 5.17/5.50 thf(fact_8312_push__bit__double,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_double
% 5.17/5.50 thf(fact_8313_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.17/5.50 ( bit_se1146084159140164899it_int
% 5.17/5.50 = ( ^ [A3: int,N4: nat] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ A3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) )
% 5.17/5.50 != zero_zero_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_and_push_bit_not_eq_0
% 5.17/5.50 thf(fact_8314_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.17/5.50 ( bit_se1148574629649215175it_nat
% 5.17/5.50 = ( ^ [A3: nat,N4: nat] :
% 5.17/5.50 ( ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) )
% 5.17/5.50 != zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_and_push_bit_not_eq_0
% 5.17/5.50 thf(fact_8315_push__bit__int__def,axiom,
% 5.17/5.50 ( bit_se545348938243370406it_int
% 5.17/5.50 = ( ^ [N4: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_int_def
% 5.17/5.50 thf(fact_8316_push__bit__nat__def,axiom,
% 5.17/5.50 ( bit_se547839408752420682it_nat
% 5.17/5.50 = ( ^ [N4: nat,M5: nat] : ( times_times_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_nat_def
% 5.17/5.50 thf(fact_8317_push__bit__eq__mult,axiom,
% 5.17/5.50 ( bit_se545348938243370406it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( times_times_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_eq_mult
% 5.17/5.50 thf(fact_8318_push__bit__eq__mult,axiom,
% 5.17/5.50 ( bit_se547839408752420682it_nat
% 5.17/5.50 = ( ^ [N4: nat,A3: nat] : ( times_times_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_eq_mult
% 5.17/5.50 thf(fact_8319_exp__dvdE,axiom,
% 5.17/5.50 ! [N: nat,A: code_integer] :
% 5.17/5.50 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A )
% 5.17/5.50 => ~ ! [B3: code_integer] :
% 5.17/5.50 ( A
% 5.17/5.50 != ( bit_se7788150548672797655nteger @ N @ B3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % exp_dvdE
% 5.17/5.50 thf(fact_8320_exp__dvdE,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A )
% 5.17/5.50 => ~ ! [B3: int] :
% 5.17/5.50 ( A
% 5.17/5.50 != ( bit_se545348938243370406it_int @ N @ B3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % exp_dvdE
% 5.17/5.50 thf(fact_8321_exp__dvdE,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A )
% 5.17/5.50 => ~ ! [B3: nat] :
% 5.17/5.50 ( A
% 5.17/5.50 != ( bit_se547839408752420682it_nat @ N @ B3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % exp_dvdE
% 5.17/5.50 thf(fact_8322_push__bit__minus__one,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus_one
% 5.17/5.50 thf(fact_8323_tanh__add,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( ( cosh_complex @ X )
% 5.17/5.50 != zero_zero_complex )
% 5.17/5.50 => ( ( ( cosh_complex @ Y4 )
% 5.17/5.50 != zero_zero_complex )
% 5.17/5.50 => ( ( tanh_complex @ ( plus_plus_complex @ X @ Y4 ) )
% 5.17/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y4 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X ) @ ( tanh_complex @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tanh_add
% 5.17/5.50 thf(fact_8324_tanh__add,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ( cosh_real @ X )
% 5.17/5.50 != zero_zero_real )
% 5.17/5.50 => ( ( ( cosh_real @ Y4 )
% 5.17/5.50 != zero_zero_real )
% 5.17/5.50 => ( ( tanh_real @ ( plus_plus_real @ X @ Y4 ) )
% 5.17/5.50 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X ) @ ( tanh_real @ Y4 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X ) @ ( tanh_real @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % tanh_add
% 5.17/5.50 thf(fact_8325_XOR__upper,axiom,
% 5.17/5.50 ! [X: int,N: nat,Y4: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.50 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.50 => ( ( ord_less_int @ Y4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.50 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y4 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % XOR_upper
% 5.17/5.50 thf(fact_8326_cosh__field__def,axiom,
% 5.17/5.50 ( cosh_real
% 5.17/5.50 = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_field_def
% 5.17/5.50 thf(fact_8327_cosh__field__def,axiom,
% 5.17/5.50 ( cosh_complex
% 5.17/5.50 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_field_def
% 5.17/5.50 thf(fact_8328_complex__inverse,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_inverse
% 5.17/5.50 thf(fact_8329_xor__int__rec,axiom,
% 5.17/5.50 ( bit_se6526347334894502574or_int
% 5.17/5.50 = ( ^ [K3: int,L3: int] :
% 5.17/5.50 ( plus_plus_int
% 5.17/5.50 @ ( zero_n2684676970156552555ol_int
% 5.17/5.50 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.17/5.50 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 5.17/5.50 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_int_rec
% 5.17/5.50 thf(fact_8330_sinh__field__def,axiom,
% 5.17/5.50 ( sinh_real
% 5.17/5.50 = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_field_def
% 5.17/5.50 thf(fact_8331_sinh__field__def,axiom,
% 5.17/5.50 ( sinh_complex
% 5.17/5.50 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_field_def
% 5.17/5.50 thf(fact_8332_xor__int__unfold,axiom,
% 5.17/5.50 ( bit_se6526347334894502574or_int
% 5.17/5.50 = ( ^ [K3: int,L3: int] :
% 5.17/5.50 ( if_int
% 5.17/5.50 @ ( K3
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 @ ( bit_ri7919022796975470100ot_int @ L3 )
% 5.17/5.50 @ ( if_int
% 5.17/5.50 @ ( L3
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.17/5.50 @ ( if_int @ ( K3 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_int_unfold
% 5.17/5.50 thf(fact_8333_bit__horner__sum__bit__iff,axiom,
% 5.17/5.50 ! [Bs: list_o,N: nat] :
% 5.17/5.50 ( ( bit_se9216721137139052372nteger @ ( groups3417619833198082522nteger @ zero_n356916108424825756nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.17/5.50 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.17/5.50 & ( nth_o @ Bs @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_horner_sum_bit_iff
% 5.17/5.50 thf(fact_8334_bit__horner__sum__bit__iff,axiom,
% 5.17/5.50 ! [Bs: list_o,N: nat] :
% 5.17/5.50 ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.17/5.50 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.17/5.50 & ( nth_o @ Bs @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_horner_sum_bit_iff
% 5.17/5.50 thf(fact_8335_bit__horner__sum__bit__iff,axiom,
% 5.17/5.50 ! [Bs: list_o,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N )
% 5.17/5.50 = ( ( ord_less_nat @ N @ ( size_size_list_o @ Bs ) )
% 5.17/5.50 & ( nth_o @ Bs @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_horner_sum_bit_iff
% 5.17/5.50 thf(fact_8336_valid__eq2,axiom,
% 5.17/5.50 ! [T: vEBT_VEBT,D: nat] :
% 5.17/5.50 ( ( vEBT_VEBT_valid @ T @ D )
% 5.17/5.50 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.17/5.50
% 5.17/5.50 % valid_eq2
% 5.17/5.50 thf(fact_8337_valid__eq1,axiom,
% 5.17/5.50 ! [T: vEBT_VEBT,D: nat] :
% 5.17/5.50 ( ( vEBT_invar_vebt @ T @ D )
% 5.17/5.50 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.17/5.50
% 5.17/5.50 % valid_eq1
% 5.17/5.50 thf(fact_8338_valid__eq,axiom,
% 5.17/5.50 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.17/5.50
% 5.17/5.50 % valid_eq
% 5.17/5.50 thf(fact_8339_intind,axiom,
% 5.17/5.50 ! [I: nat,N: nat,P: nat > $o,X: nat] :
% 5.17/5.50 ( ( ord_less_nat @ I @ N )
% 5.17/5.50 => ( ( P @ X )
% 5.17/5.50 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % intind
% 5.17/5.50 thf(fact_8340_intind,axiom,
% 5.17/5.50 ! [I: nat,N: nat,P: int > $o,X: int] :
% 5.17/5.50 ( ( ord_less_nat @ I @ N )
% 5.17/5.50 => ( ( P @ X )
% 5.17/5.50 => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % intind
% 5.17/5.50 thf(fact_8341_intind,axiom,
% 5.17/5.50 ! [I: nat,N: nat,P: real > $o,X: real] :
% 5.17/5.50 ( ( ord_less_nat @ I @ N )
% 5.17/5.50 => ( ( P @ X )
% 5.17/5.50 => ( P @ ( nth_real @ ( replicate_real @ N @ X ) @ I ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % intind
% 5.17/5.50 thf(fact_8342_intind,axiom,
% 5.17/5.50 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.17/5.50 ( ( ord_less_nat @ I @ N )
% 5.17/5.50 => ( ( P @ X )
% 5.17/5.50 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % intind
% 5.17/5.50 thf(fact_8343_inthall,axiom,
% 5.17/5.50 ! [Xs: list_complex,P: complex > $o,N: nat] :
% 5.17/5.50 ( ! [X4: complex] :
% 5.17/5.50 ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8344_inthall,axiom,
% 5.17/5.50 ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 5.17/5.50 ( ! [X4: set_nat] :
% 5.17/5.50 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8345_inthall,axiom,
% 5.17/5.50 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.17/5.50 ( ! [X4: vEBT_VEBT] :
% 5.17/5.50 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8346_inthall,axiom,
% 5.17/5.50 ! [Xs: list_real,P: real > $o,N: nat] :
% 5.17/5.50 ( ! [X4: real] :
% 5.17/5.50 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8347_inthall,axiom,
% 5.17/5.50 ! [Xs: list_o,P: $o > $o,N: nat] :
% 5.17/5.50 ( ! [X4: $o] :
% 5.17/5.50 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8348_inthall,axiom,
% 5.17/5.50 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 5.17/5.50 ( ! [X4: nat] :
% 5.17/5.50 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8349_inthall,axiom,
% 5.17/5.50 ! [Xs: list_int,P: int > $o,N: nat] :
% 5.17/5.50 ( ! [X4: int] :
% 5.17/5.50 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.17/5.50 => ( P @ X4 ) )
% 5.17/5.50 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.17/5.50 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inthall
% 5.17/5.50 thf(fact_8350_bit_Ocompl__eq__compl__iff,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( ( bit_ri7919022796975470100ot_int @ X )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ Y4 ) )
% 5.17/5.50 = ( X = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_eq_compl_iff
% 5.17/5.50 thf(fact_8351_bit_Odouble__compl,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X ) )
% 5.17/5.50 = X ) ).
% 5.17/5.50
% 5.17/5.50 % bit.double_compl
% 5.17/5.50 thf(fact_8352_bit_Oxor__compl__right,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ Y4 ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_compl_right
% 5.17/5.50 thf(fact_8353_bit_Oxor__compl__left,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ Y4 )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_compl_left
% 5.17/5.50 thf(fact_8354_bit_Oconj__cancel__left,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % bit.conj_cancel_left
% 5.17/5.50 thf(fact_8355_bit_Oconj__cancel__right,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % bit.conj_cancel_right
% 5.17/5.50 thf(fact_8356_bit_Ocompl__zero,axiom,
% 5.17/5.50 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_zero
% 5.17/5.50 thf(fact_8357_bit_Ocompl__zero,axiom,
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_zero
% 5.17/5.50 thf(fact_8358_bit_Ocompl__one,axiom,
% 5.17/5.50 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 = zero_z3403309356797280102nteger ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_one
% 5.17/5.50 thf(fact_8359_bit_Ocompl__one,axiom,
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_one
% 5.17/5.50 thf(fact_8360_bit_Oxor__one__left,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.17/5.50 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_one_left
% 5.17/5.50 thf(fact_8361_bit_Oxor__one__left,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_one_left
% 5.17/5.50 thf(fact_8362_bit_Oxor__one__right,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_one_right
% 5.17/5.50 thf(fact_8363_bit_Oxor__one__right,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_one_right
% 5.17/5.50 thf(fact_8364_bit_Oxor__cancel__left,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_cancel_left
% 5.17/5.50 thf(fact_8365_bit_Oxor__cancel__left,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_cancel_left
% 5.17/5.50 thf(fact_8366_bit_Oxor__cancel__right,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_cancel_right
% 5.17/5.50 thf(fact_8367_bit_Oxor__cancel__right,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_cancel_right
% 5.17/5.50 thf(fact_8368_not__negative__int__iff,axiom,
% 5.17/5.50 ! [K: int] :
% 5.17/5.50 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.17/5.50 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_negative_int_iff
% 5.17/5.50 thf(fact_8369_not__nonnegative__int__iff,axiom,
% 5.17/5.50 ! [K: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.17/5.50 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_nonnegative_int_iff
% 5.17/5.50 thf(fact_8370_minus__not__numeral__eq,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_not_numeral_eq
% 5.17/5.50 thf(fact_8371_minus__not__numeral__eq,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.50 = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_not_numeral_eq
% 5.17/5.50 thf(fact_8372_even__not__iff,axiom,
% 5.17/5.50 ! [A: code_integer] :
% 5.17/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 5.17/5.50 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_not_iff
% 5.17/5.50 thf(fact_8373_even__not__iff,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.17/5.50 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_not_iff
% 5.17/5.50 thf(fact_8374_push__bit__minus__one__eq__not__mask,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus_one_eq_not_mask
% 5.17/5.50 thf(fact_8375_push__bit__minus__one__eq__not__mask,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_minus_one_eq_not_mask
% 5.17/5.50 thf(fact_8376_not__one__eq,axiom,
% 5.17/5.50 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_one_eq
% 5.17/5.50 thf(fact_8377_not__one__eq,axiom,
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_one_eq
% 5.17/5.50 thf(fact_8378_of__int__not__eq,axiom,
% 5.17/5.50 ! [K: int] :
% 5.17/5.50 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_int_not_eq
% 5.17/5.50 thf(fact_8379_take__bit__not__iff,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.17/5.50 = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 5.17/5.50 = ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.17/5.50 = ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_not_iff
% 5.17/5.50 thf(fact_8380_take__bit__not__take__bit,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.17/5.50 = ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_not_take_bit
% 5.17/5.50 thf(fact_8381_bit__not__int__iff,axiom,
% 5.17/5.50 ! [K: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.17/5.50 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_not_int_iff
% 5.17/5.50 thf(fact_8382_of__int__not__numeral,axiom,
% 5.17/5.50 ! [K: num] :
% 5.17/5.50 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_int_not_numeral
% 5.17/5.50 thf(fact_8383_not__add__distrib,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 5.17/5.50 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_add_distrib
% 5.17/5.50 thf(fact_8384_not__diff__distrib,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 5.17/5.50 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_diff_distrib
% 5.17/5.50 thf(fact_8385_minus__eq__not__plus__1,axiom,
% 5.17/5.50 ( uminus1351360451143612070nteger
% 5.17/5.50 = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_eq_not_plus_1
% 5.17/5.50 thf(fact_8386_minus__eq__not__plus__1,axiom,
% 5.17/5.50 ( uminus_uminus_int
% 5.17/5.50 = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_eq_not_plus_1
% 5.17/5.50 thf(fact_8387_not__eq__complement,axiom,
% 5.17/5.50 ( bit_ri7632146776885996613nteger
% 5.17/5.50 = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_eq_complement
% 5.17/5.50 thf(fact_8388_not__eq__complement,axiom,
% 5.17/5.50 ( bit_ri7919022796975470100ot_int
% 5.17/5.50 = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_eq_complement
% 5.17/5.50 thf(fact_8389_minus__eq__not__minus__1,axiom,
% 5.17/5.50 ( uminus1351360451143612070nteger
% 5.17/5.50 = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_eq_not_minus_1
% 5.17/5.50 thf(fact_8390_minus__eq__not__minus__1,axiom,
% 5.17/5.50 ( uminus_uminus_int
% 5.17/5.50 = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_eq_not_minus_1
% 5.17/5.50 thf(fact_8391_not__int__def,axiom,
% 5.17/5.50 ( bit_ri7919022796975470100ot_int
% 5.17/5.50 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_int_def
% 5.17/5.50 thf(fact_8392_and__not__numerals_I1_J,axiom,
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(1)
% 5.17/5.50 thf(fact_8393_disjunctive__diff,axiom,
% 5.17/5.50 ! [B: int,A: int] :
% 5.17/5.50 ( ! [N2: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ B @ N2 )
% 5.17/5.50 => ( bit_se1146084159140164899it_int @ A @ N2 ) )
% 5.17/5.50 => ( ( minus_minus_int @ A @ B )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % disjunctive_diff
% 5.17/5.50 thf(fact_8394_take__bit__not__eq__mask__diff,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se2923211474154528505it_int @ N @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.17/5.50 = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_not_eq_mask_diff
% 5.17/5.50 thf(fact_8395_minus__numeral__inc__eq,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 5.17/5.50 = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_numeral_inc_eq
% 5.17/5.50 thf(fact_8396_minus__numeral__inc__eq,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_numeral_inc_eq
% 5.17/5.50 thf(fact_8397_unset__bit__int__def,axiom,
% 5.17/5.50 ( bit_se4203085406695923979it_int
% 5.17/5.50 = ( ^ [N4: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % unset_bit_int_def
% 5.17/5.50 thf(fact_8398_not__int__div__2,axiom,
% 5.17/5.50 ! [K: int] :
% 5.17/5.50 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_int_div_2
% 5.17/5.50 thf(fact_8399_even__not__iff__int,axiom,
% 5.17/5.50 ! [K: int] :
% 5.17/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.17/5.50 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_not_iff_int
% 5.17/5.50 thf(fact_8400_not__numeral__Bit0__eq,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_numeral_Bit0_eq
% 5.17/5.50 thf(fact_8401_not__numeral__Bit0__eq,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_numeral_Bit0_eq
% 5.17/5.50 thf(fact_8402_and__not__numerals_I4_J,axiom,
% 5.17/5.50 ! [M: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.17/5.50 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(4)
% 5.17/5.50 thf(fact_8403_and__not__numerals_I2_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = one_one_int ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(2)
% 5.17/5.50 thf(fact_8404_bit__minus__int__iff,axiom,
% 5.17/5.50 ! [K: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.17/5.50 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_minus_int_iff
% 5.17/5.50 thf(fact_8405_take__bit__not__mask__eq__0,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.50 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) )
% 5.17/5.50 = zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_not_mask_eq_0
% 5.17/5.50 thf(fact_8406_push__bit__mask__eq,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_mask_eq
% 5.17/5.50 thf(fact_8407_unset__bit__eq__and__not,axiom,
% 5.17/5.50 ( bit_se4203085406695923979it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % unset_bit_eq_and_not
% 5.17/5.50 thf(fact_8408_unset__bit__eq__and__not,axiom,
% 5.17/5.50 ( bit_se8260200283734997820nteger
% 5.17/5.50 = ( ^ [N4: nat,A3: code_integer] : ( bit_se3949692690581998587nteger @ A3 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % unset_bit_eq_and_not
% 5.17/5.50 thf(fact_8409_and__not__numerals_I5_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(5)
% 5.17/5.50 thf(fact_8410_and__not__numerals_I7_J,axiom,
% 5.17/5.50 ! [M: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.17/5.50 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(7)
% 5.17/5.50 thf(fact_8411_and__not__numerals_I3_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(3)
% 5.17/5.50 thf(fact_8412_and__not__numerals_I6_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(6)
% 5.17/5.50 thf(fact_8413_and__not__numerals_I9_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(9)
% 5.17/5.50 thf(fact_8414_bit__not__iff__eq,axiom,
% 5.17/5.50 ! [A: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N )
% 5.17/5.50 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.17/5.50 != zero_zero_int )
% 5.17/5.50 & ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_not_iff_eq
% 5.17/5.50 thf(fact_8415_minus__exp__eq__not__mask,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.50 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_exp_eq_not_mask
% 5.17/5.50 thf(fact_8416_minus__exp__eq__not__mask,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_exp_eq_not_mask
% 5.17/5.50 thf(fact_8417_and__not__numerals_I8_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_not_numerals(8)
% 5.17/5.50 thf(fact_8418_not__int__rec,axiom,
% 5.17/5.50 ( bit_ri7919022796975470100ot_int
% 5.17/5.50 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % not_int_rec
% 5.17/5.50 thf(fact_8419_Cauchy__iff2,axiom,
% 5.17/5.50 ( topolo4055970368930404560y_real
% 5.17/5.50 = ( ^ [X8: nat > real] :
% 5.17/5.50 ! [J3: nat] :
% 5.17/5.50 ? [M7: nat] :
% 5.17/5.50 ! [M5: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M7 @ M5 )
% 5.17/5.50 => ! [N4: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M7 @ N4 )
% 5.17/5.50 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Cauchy_iff2
% 5.17/5.50 thf(fact_8420_length__subseqs,axiom,
% 5.17/5.50 ! [Xs: list_real] :
% 5.17/5.50 ( ( size_s6660260683639930848t_real @ ( subseqs_real @ Xs ) )
% 5.17/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_real @ Xs ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_subseqs
% 5.17/5.50 thf(fact_8421_length__subseqs,axiom,
% 5.17/5.50 ! [Xs: list_o] :
% 5.17/5.50 ( ( size_s2710708370519433104list_o @ ( subseqs_o @ Xs ) )
% 5.17/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_subseqs
% 5.17/5.50 thf(fact_8422_length__subseqs,axiom,
% 5.17/5.50 ! [Xs: list_nat] :
% 5.17/5.50 ( ( size_s3023201423986296836st_nat @ ( subseqs_nat @ Xs ) )
% 5.17/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_subseqs
% 5.17/5.50 thf(fact_8423_length__subseqs,axiom,
% 5.17/5.50 ! [Xs: list_int] :
% 5.17/5.50 ( ( size_s533118279054570080st_int @ ( subseqs_int @ Xs ) )
% 5.17/5.50 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_subseqs
% 5.17/5.50 thf(fact_8424_csqrt_Osimps_I1_J,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( re @ ( csqrt @ Z ) )
% 5.17/5.50 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt.simps(1)
% 5.17/5.50 thf(fact_8425_sinh__def,axiom,
% 5.17/5.50 ( sinh_complex
% 5.17/5.50 = ( ^ [X3: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_def
% 5.17/5.50 thf(fact_8426_sinh__def,axiom,
% 5.17/5.50 ( sinh_real
% 5.17/5.50 = ( ^ [X3: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sinh_def
% 5.17/5.50 thf(fact_8427_scaleR__cancel__right,axiom,
% 5.17/5.50 ! [A: real,X: complex,B: real] :
% 5.17/5.50 ( ( ( real_V2046097035970521341omplex @ A @ X )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ B @ X ) )
% 5.17/5.50 = ( ( A = B )
% 5.17/5.50 | ( X = zero_zero_complex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_cancel_right
% 5.17/5.50 thf(fact_8428_scaleR__cancel__right,axiom,
% 5.17/5.50 ! [A: real,X: real,B: real] :
% 5.17/5.50 ( ( ( real_V1485227260804924795R_real @ A @ X )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ B @ X ) )
% 5.17/5.50 = ( ( A = B )
% 5.17/5.50 | ( X = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_cancel_right
% 5.17/5.50 thf(fact_8429_scaleR__zero__right,axiom,
% 5.17/5.50 ! [A: real] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ A @ zero_zero_complex )
% 5.17/5.50 = zero_zero_complex ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_zero_right
% 5.17/5.50 thf(fact_8430_scaleR__zero__right,axiom,
% 5.17/5.50 ! [A: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ A @ zero_zero_real )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_zero_right
% 5.17/5.50 thf(fact_8431_mult__scaleR__right,axiom,
% 5.17/5.50 ! [X: complex,A: real,Y4: complex] :
% 5.17/5.50 ( ( times_times_complex @ X @ ( real_V2046097035970521341omplex @ A @ Y4 ) )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_scaleR_right
% 5.17/5.50 thf(fact_8432_mult__scaleR__right,axiom,
% 5.17/5.50 ! [X: real,A: real,Y4: real] :
% 5.17/5.50 ( ( times_times_real @ X @ ( real_V1485227260804924795R_real @ A @ Y4 ) )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_scaleR_right
% 5.17/5.50 thf(fact_8433_mult__scaleR__left,axiom,
% 5.17/5.50 ! [A: real,X: complex,Y4: complex] :
% 5.17/5.50 ( ( times_times_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ Y4 )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ A @ ( times_times_complex @ X @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_scaleR_left
% 5.17/5.50 thf(fact_8434_mult__scaleR__left,axiom,
% 5.17/5.50 ! [A: real,X: real,Y4: real] :
% 5.17/5.50 ( ( times_times_real @ ( real_V1485227260804924795R_real @ A @ X ) @ Y4 )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ A @ ( times_times_real @ X @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mult_scaleR_left
% 5.17/5.50 thf(fact_8435_scaleR__cancel__left,axiom,
% 5.17/5.50 ! [A: real,X: complex,Y4: complex] :
% 5.17/5.50 ( ( ( real_V2046097035970521341omplex @ A @ X )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ A @ Y4 ) )
% 5.17/5.50 = ( ( X = Y4 )
% 5.17/5.50 | ( A = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_cancel_left
% 5.17/5.50 thf(fact_8436_scaleR__cancel__left,axiom,
% 5.17/5.50 ! [A: real,X: real,Y4: real] :
% 5.17/5.50 ( ( ( real_V1485227260804924795R_real @ A @ X )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ A @ Y4 ) )
% 5.17/5.50 = ( ( X = Y4 )
% 5.17/5.50 | ( A = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_cancel_left
% 5.17/5.50 thf(fact_8437_scaleR__scaleR,axiom,
% 5.17/5.50 ! [A: real,B: real,X: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ A @ ( real_V2046097035970521341omplex @ B @ X ) )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_scaleR
% 5.17/5.50 thf(fact_8438_scaleR__scaleR,axiom,
% 5.17/5.50 ! [A: real,B: real,X: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ A @ ( real_V1485227260804924795R_real @ B @ X ) )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ ( times_times_real @ A @ B ) @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_scaleR
% 5.17/5.50 thf(fact_8439_complex__Re__of__nat,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( re @ ( semiri8010041392384452111omplex @ N ) )
% 5.17/5.50 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Re_of_nat
% 5.17/5.50 thf(fact_8440_scaleR__zero__left,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ zero_zero_real @ X )
% 5.17/5.50 = zero_zero_complex ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_zero_left
% 5.17/5.50 thf(fact_8441_scaleR__zero__left,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ zero_zero_real @ X )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_zero_left
% 5.17/5.50 thf(fact_8442_scaleR__eq__0__iff,axiom,
% 5.17/5.50 ! [A: real,X: complex] :
% 5.17/5.50 ( ( ( real_V2046097035970521341omplex @ A @ X )
% 5.17/5.50 = zero_zero_complex )
% 5.17/5.50 = ( ( A = zero_zero_real )
% 5.17/5.50 | ( X = zero_zero_complex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_eq_0_iff
% 5.17/5.50 thf(fact_8443_scaleR__eq__0__iff,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( ( real_V1485227260804924795R_real @ A @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 = ( ( A = zero_zero_real )
% 5.17/5.50 | ( X = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_eq_0_iff
% 5.17/5.50 thf(fact_8444_complex__Re__numeral,axiom,
% 5.17/5.50 ! [V: num] :
% 5.17/5.50 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.17/5.50 = ( numeral_numeral_real @ V ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Re_numeral
% 5.17/5.50 thf(fact_8445_scaleR__collapse,axiom,
% 5.17/5.50 ! [U: real,A: complex] :
% 5.17/5.50 ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V2046097035970521341omplex @ U @ A ) )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_collapse
% 5.17/5.50 thf(fact_8446_scaleR__collapse,axiom,
% 5.17/5.50 ! [U: real,A: real] :
% 5.17/5.50 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_collapse
% 5.17/5.50 thf(fact_8447_norm__scaleR,axiom,
% 5.17/5.50 ! [A: real,X: complex] :
% 5.17/5.50 ( ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ A @ X ) )
% 5.17/5.50 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % norm_scaleR
% 5.17/5.50 thf(fact_8448_norm__scaleR,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ A @ X ) )
% 5.17/5.50 = ( times_times_real @ ( abs_abs_real @ A ) @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % norm_scaleR
% 5.17/5.50 thf(fact_8449_Re__divide__of__nat,axiom,
% 5.17/5.50 ! [Z: complex,N: nat] :
% 5.17/5.50 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.17/5.50 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_divide_of_nat
% 5.17/5.50 thf(fact_8450_Re__divide__of__real,axiom,
% 5.17/5.50 ! [Z: complex,R2: real] :
% 5.17/5.50 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.17/5.50 = ( divide_divide_real @ ( re @ Z ) @ R2 ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_divide_of_real
% 5.17/5.50 thf(fact_8451_Re__sgn,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.17/5.50 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_sgn
% 5.17/5.50 thf(fact_8452_scaleR__times,axiom,
% 5.17/5.50 ! [U: num,W: num,A: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_times
% 5.17/5.50 thf(fact_8453_scaleR__times,axiom,
% 5.17/5.50 ! [U: num,W: num,A: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_times
% 5.17/5.50 thf(fact_8454_Re__divide__numeral,axiom,
% 5.17/5.50 ! [Z: complex,W: num] :
% 5.17/5.50 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.50 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_divide_numeral
% 5.17/5.50 thf(fact_8455_cos__Arg__i__mult__zero,axiom,
% 5.17/5.50 ! [Y4: complex] :
% 5.17/5.50 ( ( Y4 != zero_zero_complex )
% 5.17/5.50 => ( ( ( re @ Y4 )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( cos_real @ ( arg @ Y4 ) )
% 5.17/5.50 = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cos_Arg_i_mult_zero
% 5.17/5.50 thf(fact_8456_inverse__scaleR__times,axiom,
% 5.17/5.50 ! [V: num,W: num,A: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % inverse_scaleR_times
% 5.17/5.50 thf(fact_8457_inverse__scaleR__times,axiom,
% 5.17/5.50 ! [V: num,W: num,A: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % inverse_scaleR_times
% 5.17/5.50 thf(fact_8458_fraction__scaleR__times,axiom,
% 5.17/5.50 ! [U: num,V: num,W: num,A: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % fraction_scaleR_times
% 5.17/5.50 thf(fact_8459_fraction__scaleR__times,axiom,
% 5.17/5.50 ! [U: num,V: num,W: num,A: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % fraction_scaleR_times
% 5.17/5.50 thf(fact_8460_scaleR__half__double,axiom,
% 5.17/5.50 ! [A: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ A @ A ) )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_half_double
% 5.17/5.50 thf(fact_8461_scaleR__half__double,axiom,
% 5.17/5.50 ! [A: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_half_double
% 5.17/5.50 thf(fact_8462_scaleR__right__imp__eq,axiom,
% 5.17/5.50 ! [X: complex,A: real,B: real] :
% 5.17/5.50 ( ( X != zero_zero_complex )
% 5.17/5.50 => ( ( ( real_V2046097035970521341omplex @ A @ X )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ B @ X ) )
% 5.17/5.50 => ( A = B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_right_imp_eq
% 5.17/5.50 thf(fact_8463_scaleR__right__imp__eq,axiom,
% 5.17/5.50 ! [X: real,A: real,B: real] :
% 5.17/5.50 ( ( X != zero_zero_real )
% 5.17/5.50 => ( ( ( real_V1485227260804924795R_real @ A @ X )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ B @ X ) )
% 5.17/5.50 => ( A = B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_right_imp_eq
% 5.17/5.50 thf(fact_8464_scaleR__right__diff__distrib,axiom,
% 5.17/5.50 ! [A: real,X: complex,Y4: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ A @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ A @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_right_diff_distrib
% 5.17/5.50 thf(fact_8465_scaleR__right__diff__distrib,axiom,
% 5.17/5.50 ! [A: real,X: real,Y4: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ A @ ( minus_minus_real @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_right_diff_distrib
% 5.17/5.50 thf(fact_8466_scaleR__complex_Osimps_I1_J,axiom,
% 5.17/5.50 ! [R2: real,X: complex] :
% 5.17/5.50 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.17/5.50 = ( times_times_real @ R2 @ ( re @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_complex.simps(1)
% 5.17/5.50 thf(fact_8467_scaleR__left__imp__eq,axiom,
% 5.17/5.50 ! [A: real,X: complex,Y4: complex] :
% 5.17/5.50 ( ( A != zero_zero_real )
% 5.17/5.50 => ( ( ( real_V2046097035970521341omplex @ A @ X )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ A @ Y4 ) )
% 5.17/5.50 => ( X = Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_imp_eq
% 5.17/5.50 thf(fact_8468_scaleR__left__imp__eq,axiom,
% 5.17/5.50 ! [A: real,X: real,Y4: real] :
% 5.17/5.50 ( ( A != zero_zero_real )
% 5.17/5.50 => ( ( ( real_V1485227260804924795R_real @ A @ X )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ A @ Y4 ) )
% 5.17/5.50 => ( X = Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_imp_eq
% 5.17/5.50 thf(fact_8469_real__scaleR__def,axiom,
% 5.17/5.50 real_V1485227260804924795R_real = times_times_real ).
% 5.17/5.50
% 5.17/5.50 % real_scaleR_def
% 5.17/5.50 thf(fact_8470_scaleR__conv__of__real,axiom,
% 5.17/5.50 ( real_V2046097035970521341omplex
% 5.17/5.50 = ( ^ [R5: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R5 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_conv_of_real
% 5.17/5.50 thf(fact_8471_scaleR__conv__of__real,axiom,
% 5.17/5.50 ( real_V1485227260804924795R_real
% 5.17/5.50 = ( ^ [R5: real] : ( times_times_real @ ( real_V1803761363581548252l_real @ R5 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_conv_of_real
% 5.17/5.50 thf(fact_8472_scaleR__left__diff__distrib,axiom,
% 5.17/5.50 ! [A: real,B: real,X: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( minus_minus_real @ A @ B ) @ X )
% 5.17/5.50 = ( minus_minus_complex @ ( real_V2046097035970521341omplex @ A @ X ) @ ( real_V2046097035970521341omplex @ B @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_diff_distrib
% 5.17/5.50 thf(fact_8473_scaleR__left__diff__distrib,axiom,
% 5.17/5.50 ! [A: real,B: real,X: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ X )
% 5.17/5.50 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_diff_distrib
% 5.17/5.50 thf(fact_8474_scaleR__left_Odiff,axiom,
% 5.17/5.50 ! [X: real,Y4: real,Xa: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( minus_minus_real @ X @ Y4 ) @ Xa )
% 5.17/5.50 = ( minus_minus_complex @ ( real_V2046097035970521341omplex @ X @ Xa ) @ ( real_V2046097035970521341omplex @ Y4 @ Xa ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left.diff
% 5.17/5.50 thf(fact_8475_scaleR__left_Odiff,axiom,
% 5.17/5.50 ! [X: real,Y4: real,Xa: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( minus_minus_real @ X @ Y4 ) @ Xa )
% 5.17/5.50 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ X @ Xa ) @ ( real_V1485227260804924795R_real @ Y4 @ Xa ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left.diff
% 5.17/5.50 thf(fact_8476_imaginary__unit_Osimps_I1_J,axiom,
% 5.17/5.50 ( ( re @ imaginary_unit )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % imaginary_unit.simps(1)
% 5.17/5.50 thf(fact_8477_complex__Re__le__cmod,axiom,
% 5.17/5.50 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Re_le_cmod
% 5.17/5.50 thf(fact_8478_zero__complex_Osimps_I1_J,axiom,
% 5.17/5.50 ( ( re @ zero_zero_complex )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % zero_complex.simps(1)
% 5.17/5.50 thf(fact_8479_complex__scaleR,axiom,
% 5.17/5.50 ! [R2: real,A: real,B: real] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.17/5.50 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_scaleR
% 5.17/5.50 thf(fact_8480_minus__complex_Osimps_I1_J,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( re @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_real @ ( re @ X ) @ ( re @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_complex.simps(1)
% 5.17/5.50 thf(fact_8481_scaleR__right__mono,axiom,
% 5.17/5.50 ! [A: real,B: real,X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_right_mono
% 5.17/5.50 thf(fact_8482_scaleR__right__mono__neg,axiom,
% 5.17/5.50 ! [B: real,A: real,C: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.50 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_right_mono_neg
% 5.17/5.50 thf(fact_8483_scaleR__le__cancel__left__pos,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.17/5.50 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_le_cancel_left_pos
% 5.17/5.50 thf(fact_8484_scaleR__le__cancel__left__neg,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.17/5.50 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_le_cancel_left_neg
% 5.17/5.50 thf(fact_8485_scaleR__le__cancel__left,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) )
% 5.17/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.17/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_le_cancel_left
% 5.17/5.50 thf(fact_8486_scaleR__left__mono,axiom,
% 5.17/5.50 ! [X: real,Y4: real,A: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ A @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_mono
% 5.17/5.50 thf(fact_8487_scaleR__left__mono__neg,axiom,
% 5.17/5.50 ! [B: real,A: real,C: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.50 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( real_V1485227260804924795R_real @ C @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_mono_neg
% 5.17/5.50 thf(fact_8488_vector__fraction__eq__iff,axiom,
% 5.17/5.50 ! [U: real,V: real,A: complex,X: complex] :
% 5.17/5.50 ( ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ U @ V ) @ A )
% 5.17/5.50 = X )
% 5.17/5.50 = ( ( ( V = zero_zero_real )
% 5.17/5.50 => ( X = zero_zero_complex ) )
% 5.17/5.50 & ( ( V != zero_zero_real )
% 5.17/5.50 => ( ( real_V2046097035970521341omplex @ U @ A )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ V @ X ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % vector_fraction_eq_iff
% 5.17/5.50 thf(fact_8489_vector__fraction__eq__iff,axiom,
% 5.17/5.50 ! [U: real,V: real,A: real,X: real] :
% 5.17/5.50 ( ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ U @ V ) @ A )
% 5.17/5.50 = X )
% 5.17/5.50 = ( ( ( V = zero_zero_real )
% 5.17/5.50 => ( X = zero_zero_real ) )
% 5.17/5.50 & ( ( V != zero_zero_real )
% 5.17/5.50 => ( ( real_V1485227260804924795R_real @ U @ A )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ V @ X ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % vector_fraction_eq_iff
% 5.17/5.50 thf(fact_8490_eq__vector__fraction__iff,axiom,
% 5.17/5.50 ! [X: complex,U: real,V: real,A: complex] :
% 5.17/5.50 ( ( X
% 5.17/5.50 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ U @ V ) @ A ) )
% 5.17/5.50 = ( ( ( V = zero_zero_real )
% 5.17/5.50 => ( X = zero_zero_complex ) )
% 5.17/5.50 & ( ( V != zero_zero_real )
% 5.17/5.50 => ( ( real_V2046097035970521341omplex @ V @ X )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ U @ A ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % eq_vector_fraction_iff
% 5.17/5.50 thf(fact_8491_eq__vector__fraction__iff,axiom,
% 5.17/5.50 ! [X: real,U: real,V: real,A: real] :
% 5.17/5.50 ( ( X
% 5.17/5.50 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ U @ V ) @ A ) )
% 5.17/5.50 = ( ( ( V = zero_zero_real )
% 5.17/5.50 => ( X = zero_zero_real ) )
% 5.17/5.50 & ( ( V != zero_zero_real )
% 5.17/5.50 => ( ( real_V1485227260804924795R_real @ V @ X )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ U @ A ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % eq_vector_fraction_iff
% 5.17/5.50 thf(fact_8492_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 5.17/5.50 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 5.17/5.50 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.17/5.50
% 5.17/5.50 % Real_Vector_Spaces.le_add_iff1
% 5.17/5.50 thf(fact_8493_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 5.17/5.50 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 5.17/5.50 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Real_Vector_Spaces.le_add_iff2
% 5.17/5.50 thf(fact_8494_abs__Re__le__cmod,axiom,
% 5.17/5.50 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % abs_Re_le_cmod
% 5.17/5.50 thf(fact_8495_Re__csqrt,axiom,
% 5.17/5.50 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_csqrt
% 5.17/5.50 thf(fact_8496_zero__le__scaleR__iff,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 5.17/5.50 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.17/5.50 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.17/5.50 | ( A = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % zero_le_scaleR_iff
% 5.17/5.50 thf(fact_8497_scaleR__le__0__iff,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 5.17/5.50 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.50 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.17/5.50 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.17/5.50 | ( A = zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_le_0_iff
% 5.17/5.50 thf(fact_8498_scaleR__mono,axiom,
% 5.17/5.50 ! [A: real,B: real,X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.50 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ ( real_V1485227260804924795R_real @ B @ Y4 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_mono
% 5.17/5.50 thf(fact_8499_scaleR__mono_H,axiom,
% 5.17/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.50 => ( ( ord_less_eq_real @ C @ D )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_mono'
% 5.17/5.50 thf(fact_8500_split__scaleR__neg__le,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 & ( ord_less_eq_real @ X @ zero_zero_real ) )
% 5.17/5.50 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ X ) ) )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % split_scaleR_neg_le
% 5.17/5.50 thf(fact_8501_split__scaleR__pos__le,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.17/5.50 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.17/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % split_scaleR_pos_le
% 5.17/5.50 thf(fact_8502_scaleR__nonneg__nonneg,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_nonneg_nonneg
% 5.17/5.50 thf(fact_8503_scaleR__nonneg__nonpos,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.17/5.50 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_nonneg_nonpos
% 5.17/5.50 thf(fact_8504_scaleR__nonpos__nonneg,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ zero_zero_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_nonpos_nonneg
% 5.17/5.50 thf(fact_8505_scaleR__nonpos__nonpos,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.17/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_nonpos_nonpos
% 5.17/5.50 thf(fact_8506_scaleR__left__le__one__le,axiom,
% 5.17/5.50 ! [X: real,A: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.50 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.17/5.50 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X ) @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_left_le_one_le
% 5.17/5.50 thf(fact_8507_scaleR__2,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.17/5.50 = ( plus_plus_complex @ X @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_2
% 5.17/5.50 thf(fact_8508_scaleR__2,axiom,
% 5.17/5.50 ! [X: real] :
% 5.17/5.50 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X )
% 5.17/5.50 = ( plus_plus_real @ X @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_2
% 5.17/5.50 thf(fact_8509_real__vector__eq__affinity,axiom,
% 5.17/5.50 ! [M: real,Y4: complex,X: complex,C: complex] :
% 5.17/5.50 ( ( M != zero_zero_real )
% 5.17/5.50 => ( ( Y4
% 5.17/5.50 = ( plus_plus_complex @ ( real_V2046097035970521341omplex @ M @ X ) @ C ) )
% 5.17/5.50 = ( ( minus_minus_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ C ) )
% 5.17/5.50 = X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_vector_eq_affinity
% 5.17/5.50 thf(fact_8510_real__vector__eq__affinity,axiom,
% 5.17/5.50 ! [M: real,Y4: real,X: real,C: real] :
% 5.17/5.50 ( ( M != zero_zero_real )
% 5.17/5.50 => ( ( Y4
% 5.17/5.50 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X ) @ C ) )
% 5.17/5.50 = ( ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) )
% 5.17/5.50 = X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_vector_eq_affinity
% 5.17/5.50 thf(fact_8511_real__vector__affinity__eq,axiom,
% 5.17/5.50 ! [M: real,X: complex,C: complex,Y4: complex] :
% 5.17/5.50 ( ( M != zero_zero_real )
% 5.17/5.50 => ( ( ( plus_plus_complex @ ( real_V2046097035970521341omplex @ M @ X ) @ C )
% 5.17/5.50 = Y4 )
% 5.17/5.50 = ( X
% 5.17/5.50 = ( minus_minus_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_vector_affinity_eq
% 5.17/5.50 thf(fact_8512_real__vector__affinity__eq,axiom,
% 5.17/5.50 ! [M: real,X: real,C: real,Y4: real] :
% 5.17/5.50 ( ( M != zero_zero_real )
% 5.17/5.50 => ( ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X ) @ C )
% 5.17/5.50 = Y4 )
% 5.17/5.50 = ( X
% 5.17/5.50 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y4 ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_vector_affinity_eq
% 5.17/5.50 thf(fact_8513_pos__divideR__le__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.17/5.50 = ( ord_less_eq_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_divideR_le_eq
% 5.17/5.50 thf(fact_8514_pos__le__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_eq_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.17/5.50 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_le_divideR_eq
% 5.17/5.50 thf(fact_8515_neg__divideR__le__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.17/5.50 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_divideR_le_eq
% 5.17/5.50 thf(fact_8516_neg__le__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.17/5.50 = ( ord_less_eq_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_le_divideR_eq
% 5.17/5.50 thf(fact_8517_neg__less__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.17/5.50 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_less_divideR_eq
% 5.17/5.50 thf(fact_8518_neg__divideR__less__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.17/5.50 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_divideR_less_eq
% 5.17/5.50 thf(fact_8519_pos__less__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.17/5.50 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_less_divideR_eq
% 5.17/5.50 thf(fact_8520_pos__divideR__less__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.17/5.50 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_divideR_less_eq
% 5.17/5.50 thf(fact_8521_nonzero__inverse__scaleR__distrib,axiom,
% 5.17/5.50 ! [A: real,X: complex] :
% 5.17/5.50 ( ( A != zero_zero_real )
% 5.17/5.50 => ( ( X != zero_zero_complex )
% 5.17/5.50 => ( ( invers8013647133539491842omplex @ ( real_V2046097035970521341omplex @ A @ X ) )
% 5.17/5.50 = ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ A ) @ ( invers8013647133539491842omplex @ X ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % nonzero_inverse_scaleR_distrib
% 5.17/5.50 thf(fact_8522_nonzero__inverse__scaleR__distrib,axiom,
% 5.17/5.50 ! [A: real,X: real] :
% 5.17/5.50 ( ( A != zero_zero_real )
% 5.17/5.50 => ( ( X != zero_zero_real )
% 5.17/5.50 => ( ( inverse_inverse_real @ ( real_V1485227260804924795R_real @ A @ X ) )
% 5.17/5.50 = ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ X ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % nonzero_inverse_scaleR_distrib
% 5.17/5.50 thf(fact_8523_pos__le__minus__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.17/5.50 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_le_minus_divideR_eq
% 5.17/5.50 thf(fact_8524_pos__minus__divideR__le__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.17/5.50 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_minus_divideR_le_eq
% 5.17/5.50 thf(fact_8525_neg__le__minus__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.17/5.50 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_le_minus_divideR_eq
% 5.17/5.50 thf(fact_8526_neg__minus__divideR__le__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.17/5.50 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_minus_divideR_le_eq
% 5.17/5.50 thf(fact_8527_pos__less__minus__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.17/5.50 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_less_minus_divideR_eq
% 5.17/5.50 thf(fact_8528_pos__minus__divideR__less__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.50 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.17/5.50 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % pos_minus_divideR_less_eq
% 5.17/5.50 thf(fact_8529_neg__less__minus__divideR__eq,axiom,
% 5.17/5.50 ! [C: real,A: real,B: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.17/5.50 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_less_minus_divideR_eq
% 5.17/5.50 thf(fact_8530_neg__minus__divideR__less__eq,axiom,
% 5.17/5.50 ! [C: real,B: real,A: real] :
% 5.17/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.17/5.50 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.17/5.50 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % neg_minus_divideR_less_eq
% 5.17/5.50 thf(fact_8531_cmod__plus__Re__le__0__iff,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.17/5.50 = ( ( re @ Z )
% 5.17/5.50 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_plus_Re_le_0_iff
% 5.17/5.50 thf(fact_8532_cos__n__Re__cis__pow__n,axiom,
% 5.17/5.50 ! [N: nat,A: real] :
% 5.17/5.50 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.17/5.50 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cos_n_Re_cis_pow_n
% 5.17/5.50 thf(fact_8533_CauchyD,axiom,
% 5.17/5.50 ! [X9: nat > complex,E2: real] :
% 5.17/5.50 ( ( topolo6517432010174082258omplex @ X9 )
% 5.17/5.50 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.17/5.50 => ? [M8: nat] :
% 5.17/5.50 ! [M2: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M8 @ M2 )
% 5.17/5.50 => ! [N6: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M8 @ N6 )
% 5.17/5.50 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X9 @ M2 ) @ ( X9 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % CauchyD
% 5.17/5.50 thf(fact_8534_CauchyD,axiom,
% 5.17/5.50 ! [X9: nat > real,E2: real] :
% 5.17/5.50 ( ( topolo4055970368930404560y_real @ X9 )
% 5.17/5.50 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.17/5.50 => ? [M8: nat] :
% 5.17/5.50 ! [M2: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M8 @ M2 )
% 5.17/5.50 => ! [N6: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M8 @ N6 )
% 5.17/5.50 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X9 @ M2 ) @ ( X9 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % CauchyD
% 5.17/5.50 thf(fact_8535_CauchyI,axiom,
% 5.17/5.50 ! [X9: nat > complex] :
% 5.17/5.50 ( ! [E: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ E )
% 5.17/5.50 => ? [M9: nat] :
% 5.17/5.50 ! [M4: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M9 @ M4 )
% 5.17/5.50 => ! [N2: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M9 @ N2 )
% 5.17/5.50 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) ) @ E ) ) ) )
% 5.17/5.50 => ( topolo6517432010174082258omplex @ X9 ) ) ).
% 5.17/5.50
% 5.17/5.50 % CauchyI
% 5.17/5.50 thf(fact_8536_CauchyI,axiom,
% 5.17/5.50 ! [X9: nat > real] :
% 5.17/5.50 ( ! [E: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ E )
% 5.17/5.50 => ? [M9: nat] :
% 5.17/5.50 ! [M4: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M9 @ M4 )
% 5.17/5.50 => ! [N2: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M9 @ N2 )
% 5.17/5.50 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) ) @ E ) ) ) )
% 5.17/5.50 => ( topolo4055970368930404560y_real @ X9 ) ) ).
% 5.17/5.50
% 5.17/5.50 % CauchyI
% 5.17/5.50 thf(fact_8537_Cauchy__iff,axiom,
% 5.17/5.50 ( topolo6517432010174082258omplex
% 5.17/5.50 = ( ^ [X8: nat > complex] :
% 5.17/5.50 ! [E3: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.17/5.50 => ? [M7: nat] :
% 5.17/5.50 ! [M5: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M7 @ M5 )
% 5.17/5.50 => ! [N4: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M7 @ N4 )
% 5.17/5.50 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Cauchy_iff
% 5.17/5.50 thf(fact_8538_Cauchy__iff,axiom,
% 5.17/5.50 ( topolo4055970368930404560y_real
% 5.17/5.50 = ( ^ [X8: nat > real] :
% 5.17/5.50 ! [E3: real] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.17/5.50 => ? [M7: nat] :
% 5.17/5.50 ! [M5: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M7 @ M5 )
% 5.17/5.50 => ! [N4: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ M7 @ N4 )
% 5.17/5.50 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Cauchy_iff
% 5.17/5.50 thf(fact_8539_cosh__def,axiom,
% 5.17/5.50 ( cosh_complex
% 5.17/5.50 = ( ^ [X3: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_def
% 5.17/5.50 thf(fact_8540_cosh__def,axiom,
% 5.17/5.50 ( cosh_real
% 5.17/5.50 = ( ^ [X3: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cosh_def
% 5.17/5.50 thf(fact_8541_csqrt_Ocode,axiom,
% 5.17/5.50 ( csqrt
% 5.17/5.50 = ( ^ [Z5: complex] :
% 5.17/5.50 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.50 @ ( times_times_real
% 5.17/5.50 @ ( if_real
% 5.17/5.50 @ ( ( im @ Z5 )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 @ one_one_real
% 5.17/5.50 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 5.17/5.50 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt.code
% 5.17/5.50 thf(fact_8542_csqrt_Osimps_I2_J,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( im @ ( csqrt @ Z ) )
% 5.17/5.50 = ( times_times_real
% 5.17/5.50 @ ( if_real
% 5.17/5.50 @ ( ( im @ Z )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 @ one_one_real
% 5.17/5.50 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.17/5.50 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt.simps(2)
% 5.17/5.50 thf(fact_8543_csqrt__of__real__nonpos,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( ( im @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.17/5.50 => ( ( csqrt @ X )
% 5.17/5.50 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt_of_real_nonpos
% 5.17/5.50 thf(fact_8544_Complex__divide,axiom,
% 5.17/5.50 ( divide1717551699836669952omplex
% 5.17/5.50 = ( ^ [X3: complex,Y6: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Complex_divide
% 5.17/5.50 thf(fact_8545_complex__Im__of__int,axiom,
% 5.17/5.50 ! [Z: int] :
% 5.17/5.50 ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Im_of_int
% 5.17/5.50 thf(fact_8546_complex__Im__fact,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Im_fact
% 5.17/5.50 thf(fact_8547_Im__complex__of__real,axiom,
% 5.17/5.50 ! [Z: real] :
% 5.17/5.50 ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % Im_complex_of_real
% 5.17/5.50 thf(fact_8548_Im__power__real,axiom,
% 5.17/5.50 ! [X: complex,N: nat] :
% 5.17/5.50 ( ( ( im @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( im @ ( power_power_complex @ X @ N ) )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_power_real
% 5.17/5.50 thf(fact_8549_complex__Im__numeral,axiom,
% 5.17/5.50 ! [V: num] :
% 5.17/5.50 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Im_numeral
% 5.17/5.50 thf(fact_8550_complex__Im__of__nat,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % complex_Im_of_nat
% 5.17/5.50 thf(fact_8551_Im__divide__of__real,axiom,
% 5.17/5.50 ! [Z: complex,R2: real] :
% 5.17/5.50 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.17/5.50 = ( divide_divide_real @ ( im @ Z ) @ R2 ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_divide_of_real
% 5.17/5.50 thf(fact_8552_Im__sgn,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.17/5.50 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_sgn
% 5.17/5.50 thf(fact_8553_Re__power__real,axiom,
% 5.17/5.50 ! [X: complex,N: nat] :
% 5.17/5.50 ( ( ( im @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( re @ ( power_power_complex @ X @ N ) )
% 5.17/5.50 = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_power_real
% 5.17/5.50 thf(fact_8554_Im__divide__numeral,axiom,
% 5.17/5.50 ! [Z: complex,W: num] :
% 5.17/5.50 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.17/5.50 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_divide_numeral
% 5.17/5.50 thf(fact_8555_Im__divide__of__nat,axiom,
% 5.17/5.50 ! [Z: complex,N: nat] :
% 5.17/5.50 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.17/5.50 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_divide_of_nat
% 5.17/5.50 thf(fact_8556_csqrt__of__real__nonneg,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( ( im @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 5.17/5.50 => ( ( csqrt @ X )
% 5.17/5.50 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt_of_real_nonneg
% 5.17/5.50 thf(fact_8557_csqrt__minus,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.17/5.50 | ( ( ( im @ X )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.17/5.50 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.17/5.50 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt_minus
% 5.17/5.50 thf(fact_8558_scaleR__complex_Osimps_I2_J,axiom,
% 5.17/5.50 ! [R2: real,X: complex] :
% 5.17/5.50 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X ) )
% 5.17/5.50 = ( times_times_real @ R2 @ ( im @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_complex.simps(2)
% 5.17/5.50 thf(fact_8559_zero__complex_Osimps_I2_J,axiom,
% 5.17/5.50 ( ( im @ zero_zero_complex )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % zero_complex.simps(2)
% 5.17/5.50 thf(fact_8560_one__complex_Osimps_I2_J,axiom,
% 5.17/5.50 ( ( im @ one_one_complex )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % one_complex.simps(2)
% 5.17/5.50 thf(fact_8561_minus__complex_Osimps_I2_J,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( im @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_real @ ( im @ X ) @ ( im @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_complex.simps(2)
% 5.17/5.50 thf(fact_8562_complex__is__Int__iff,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( member_complex @ Z @ ring_1_Ints_complex )
% 5.17/5.50 = ( ( ( im @ Z )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 & ? [I2: int] :
% 5.17/5.50 ( ( re @ Z )
% 5.17/5.50 = ( ring_1_of_int_real @ I2 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_is_Int_iff
% 5.17/5.50 thf(fact_8563_scaleR__complex_Ocode,axiom,
% 5.17/5.50 ( real_V2046097035970521341omplex
% 5.17/5.50 = ( ^ [R5: real,X3: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X3 ) ) @ ( times_times_real @ R5 @ ( im @ X3 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % scaleR_complex.code
% 5.17/5.50 thf(fact_8564_abs__Im__le__cmod,axiom,
% 5.17/5.50 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % abs_Im_le_cmod
% 5.17/5.50 thf(fact_8565_times__complex_Osimps_I2_J,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( im @ ( times_times_complex @ X @ Y4 ) )
% 5.17/5.50 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % times_complex.simps(2)
% 5.17/5.50 thf(fact_8566_cmod__eq__Re,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( ( im @ Z )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( real_V1022390504157884413omplex @ Z )
% 5.17/5.50 = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_eq_Re
% 5.17/5.50 thf(fact_8567_cmod__eq__Im,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( ( re @ Z )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 => ( ( real_V1022390504157884413omplex @ Z )
% 5.17/5.50 = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_eq_Im
% 5.17/5.50 thf(fact_8568_Im__eq__0,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( ( abs_abs_real @ ( re @ Z ) )
% 5.17/5.50 = ( real_V1022390504157884413omplex @ Z ) )
% 5.17/5.50 => ( ( im @ Z )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_eq_0
% 5.17/5.50 thf(fact_8569_cmod__Im__le__iff,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( ( re @ X )
% 5.17/5.50 = ( re @ Y4 ) )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) )
% 5.17/5.50 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_Im_le_iff
% 5.17/5.50 thf(fact_8570_cmod__Re__le__iff,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( ( im @ X )
% 5.17/5.50 = ( im @ Y4 ) )
% 5.17/5.50 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y4 ) )
% 5.17/5.50 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_Re_le_iff
% 5.17/5.50 thf(fact_8571_times__complex_Osimps_I1_J,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( re @ ( times_times_complex @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % times_complex.simps(1)
% 5.17/5.50 thf(fact_8572_minus__complex_Ocode,axiom,
% 5.17/5.50 ( minus_minus_complex
% 5.17/5.50 = ( ^ [X3: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X3 ) @ ( re @ Y6 ) ) @ ( minus_minus_real @ ( im @ X3 ) @ ( im @ Y6 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % minus_complex.code
% 5.17/5.50 thf(fact_8573_csqrt__principal,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.17/5.50 | ( ( ( re @ ( csqrt @ Z ) )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt_principal
% 5.17/5.50 thf(fact_8574_cmod__le,axiom,
% 5.17/5.50 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_le
% 5.17/5.50 thf(fact_8575_sin__n__Im__cis__pow__n,axiom,
% 5.17/5.50 ! [N: nat,A: real] :
% 5.17/5.50 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.17/5.50 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % sin_n_Im_cis_pow_n
% 5.17/5.50 thf(fact_8576_Re__exp,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( re @ ( exp_complex @ Z ) )
% 5.17/5.50 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_exp
% 5.17/5.50 thf(fact_8577_Im__exp,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( im @ ( exp_complex @ Z ) )
% 5.17/5.50 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_exp
% 5.17/5.50 thf(fact_8578_times__complex_Ocode,axiom,
% 5.17/5.50 ( times_times_complex
% 5.17/5.50 = ( ^ [X3: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y6 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y6 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % times_complex.code
% 5.17/5.50 thf(fact_8579_cmod__power2,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cmod_power2
% 5.17/5.50 thf(fact_8580_Im__power2,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_power2
% 5.17/5.50 thf(fact_8581_Re__power2,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_power2
% 5.17/5.50 thf(fact_8582_complex__eq__0,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( Z = zero_zero_complex )
% 5.17/5.50 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_eq_0
% 5.17/5.50 thf(fact_8583_norm__complex__def,axiom,
% 5.17/5.50 ( real_V1022390504157884413omplex
% 5.17/5.50 = ( ^ [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 ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % norm_complex_def
% 5.17/5.50 thf(fact_8584_inverse__complex_Osimps_I1_J,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.17/5.50 = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inverse_complex.simps(1)
% 5.17/5.50 thf(fact_8585_complex__neq__0,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( Z != zero_zero_complex )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_neq_0
% 5.17/5.50 thf(fact_8586_Re__divide,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( re @ ( divide1717551699836669952omplex @ X @ Y4 ) )
% 5.17/5.50 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_divide
% 5.17/5.50 thf(fact_8587_csqrt__unique,axiom,
% 5.17/5.50 ! [W: complex,Z: complex] :
% 5.17/5.50 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = Z )
% 5.17/5.50 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.17/5.50 | ( ( ( re @ W )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.17/5.50 => ( ( csqrt @ Z )
% 5.17/5.50 = W ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt_unique
% 5.17/5.50 thf(fact_8588_csqrt__square,axiom,
% 5.17/5.50 ! [B: complex] :
% 5.17/5.50 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.17/5.50 | ( ( ( re @ B )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.17/5.50 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % csqrt_square
% 5.17/5.50 thf(fact_8589_inverse__complex_Osimps_I2_J,axiom,
% 5.17/5.50 ! [X: complex] :
% 5.17/5.50 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.17/5.50 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inverse_complex.simps(2)
% 5.17/5.50 thf(fact_8590_Im__divide,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( im @ ( divide1717551699836669952omplex @ X @ Y4 ) )
% 5.17/5.50 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_divide
% 5.17/5.50 thf(fact_8591_complex__abs__le__norm,axiom,
% 5.17/5.50 ! [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 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_abs_le_norm
% 5.17/5.50 thf(fact_8592_complex__unit__circle,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( Z != zero_zero_complex )
% 5.17/5.50 => ( ( 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 ) ) ) )
% 5.17/5.50 = one_one_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_unit_circle
% 5.17/5.50 thf(fact_8593_inverse__complex_Ocode,axiom,
% 5.17/5.50 ( invers8013647133539491842omplex
% 5.17/5.50 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % inverse_complex.code
% 5.17/5.50 thf(fact_8594_Im__Reals__divide,axiom,
% 5.17/5.50 ! [R2: complex,Z: complex] :
% 5.17/5.50 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.17/5.50 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_Reals_divide
% 5.17/5.50 thf(fact_8595_length__mul__elem,axiom,
% 5.17/5.50 ! [Xs: list_list_real,N: nat] :
% 5.17/5.50 ( ! [X4: list_real] :
% 5.17/5.50 ( ( member_list_real @ X4 @ ( set_list_real2 @ Xs ) )
% 5.17/5.50 => ( ( size_size_list_real @ X4 )
% 5.17/5.50 = N ) )
% 5.17/5.50 => ( ( size_size_list_real @ ( concat_real @ Xs ) )
% 5.17/5.50 = ( times_times_nat @ ( size_s6660260683639930848t_real @ Xs ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_mul_elem
% 5.17/5.50 thf(fact_8596_length__mul__elem,axiom,
% 5.17/5.50 ! [Xs: list_list_o,N: nat] :
% 5.17/5.50 ( ! [X4: list_o] :
% 5.17/5.50 ( ( member_list_o @ X4 @ ( set_list_o2 @ Xs ) )
% 5.17/5.50 => ( ( size_size_list_o @ X4 )
% 5.17/5.50 = N ) )
% 5.17/5.50 => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 5.17/5.50 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_mul_elem
% 5.17/5.50 thf(fact_8597_length__mul__elem,axiom,
% 5.17/5.50 ! [Xs: list_list_nat,N: nat] :
% 5.17/5.50 ( ! [X4: list_nat] :
% 5.17/5.50 ( ( member_list_nat @ X4 @ ( set_list_nat2 @ Xs ) )
% 5.17/5.50 => ( ( size_size_list_nat @ X4 )
% 5.17/5.50 = N ) )
% 5.17/5.50 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 5.17/5.50 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_mul_elem
% 5.17/5.50 thf(fact_8598_length__mul__elem,axiom,
% 5.17/5.50 ! [Xs: list_list_int,N: nat] :
% 5.17/5.50 ( ! [X4: list_int] :
% 5.17/5.50 ( ( member_list_int @ X4 @ ( set_list_int2 @ Xs ) )
% 5.17/5.50 => ( ( size_size_list_int @ X4 )
% 5.17/5.50 = N ) )
% 5.17/5.50 => ( ( size_size_list_int @ ( concat_int @ Xs ) )
% 5.17/5.50 = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs ) @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % length_mul_elem
% 5.17/5.50 thf(fact_8599_Re__Reals__divide,axiom,
% 5.17/5.50 ! [R2: complex,Z: complex] :
% 5.17/5.50 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.17/5.50 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_Reals_divide
% 5.17/5.50 thf(fact_8600_complex__diff__cnj,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.17/5.50 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_diff_cnj
% 5.17/5.50 thf(fact_8601_complex__cnj__zero__iff,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( ( cnj @ Z )
% 5.17/5.50 = zero_zero_complex )
% 5.17/5.50 = ( Z = zero_zero_complex ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_cnj_zero_iff
% 5.17/5.50 thf(fact_8602_complex__cnj__zero,axiom,
% 5.17/5.50 ( ( cnj @ zero_zero_complex )
% 5.17/5.50 = zero_zero_complex ) ).
% 5.17/5.50
% 5.17/5.50 % complex_cnj_zero
% 5.17/5.50 thf(fact_8603_complex__cnj__diff,axiom,
% 5.17/5.50 ! [X: complex,Y4: complex] :
% 5.17/5.50 ( ( cnj @ ( minus_minus_complex @ X @ Y4 ) )
% 5.17/5.50 = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_cnj_diff
% 5.17/5.50 thf(fact_8604_complex__In__mult__cnj__zero,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.17/5.50 = zero_zero_real ) ).
% 5.17/5.50
% 5.17/5.50 % complex_In_mult_cnj_zero
% 5.17/5.50 thf(fact_8605_Re__divide__Reals,axiom,
% 5.17/5.50 ! [R2: complex,Z: complex] :
% 5.17/5.50 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.17/5.50 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_divide_Reals
% 5.17/5.50 thf(fact_8606_imaginary__eq__real__iff,axiom,
% 5.17/5.50 ! [Y4: complex,X: complex] :
% 5.17/5.50 ( ( member_complex @ Y4 @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( ( times_times_complex @ imaginary_unit @ Y4 )
% 5.17/5.50 = X )
% 5.17/5.50 = ( ( X = zero_zero_complex )
% 5.17/5.50 & ( Y4 = zero_zero_complex ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % imaginary_eq_real_iff
% 5.17/5.50 thf(fact_8607_real__eq__imaginary__iff,axiom,
% 5.17/5.50 ! [Y4: complex,X: complex] :
% 5.17/5.50 ( ( member_complex @ Y4 @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( X
% 5.17/5.50 = ( times_times_complex @ imaginary_unit @ Y4 ) )
% 5.17/5.50 = ( ( X = zero_zero_complex )
% 5.17/5.50 & ( Y4 = zero_zero_complex ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % real_eq_imaginary_iff
% 5.17/5.50 thf(fact_8608_Im__divide__Reals,axiom,
% 5.17/5.50 ! [R2: complex,Z: complex] :
% 5.17/5.50 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.17/5.50 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_divide_Reals
% 5.17/5.50 thf(fact_8609_Reals__of__nat,axiom,
% 5.17/5.50 ! [N: nat] : ( member_complex @ ( semiri8010041392384452111omplex @ N ) @ real_V2521375963428798218omplex ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_of_nat
% 5.17/5.50 thf(fact_8610_Reals__of__nat,axiom,
% 5.17/5.50 ! [N: nat] : ( member_real @ ( semiri5074537144036343181t_real @ N ) @ real_V470468836141973256s_real ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_of_nat
% 5.17/5.50 thf(fact_8611_Reals__divide,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_divide
% 5.17/5.50 thf(fact_8612_Reals__divide,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.17/5.50 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.17/5.50 => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_divide
% 5.17/5.50 thf(fact_8613_Reals__diff,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.17/5.50 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.17/5.50 => ( member_real @ ( minus_minus_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_diff
% 5.17/5.50 thf(fact_8614_Reals__diff,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( member_complex @ ( minus_minus_complex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_diff
% 5.17/5.50 thf(fact_8615_Reals__mult,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.17/5.50 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.17/5.50 => ( member_real @ ( times_times_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_mult
% 5.17/5.50 thf(fact_8616_Reals__mult,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( member_complex @ ( times_times_complex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_mult
% 5.17/5.50 thf(fact_8617_Reals__numeral,axiom,
% 5.17/5.50 ! [W: num] : ( member_complex @ ( numera6690914467698888265omplex @ W ) @ real_V2521375963428798218omplex ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_numeral
% 5.17/5.50 thf(fact_8618_Reals__numeral,axiom,
% 5.17/5.50 ! [W: num] : ( member_real @ ( numeral_numeral_real @ W ) @ real_V470468836141973256s_real ) ).
% 5.17/5.50
% 5.17/5.50 % Reals_numeral
% 5.17/5.50 thf(fact_8619_Reals__0,axiom,
% 5.17/5.50 member_real @ zero_zero_real @ real_V470468836141973256s_real ).
% 5.17/5.50
% 5.17/5.50 % Reals_0
% 5.17/5.50 thf(fact_8620_Reals__0,axiom,
% 5.17/5.50 member_complex @ zero_zero_complex @ real_V2521375963428798218omplex ).
% 5.17/5.50
% 5.17/5.50 % Reals_0
% 5.17/5.50 thf(fact_8621_complex__is__Real__iff,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 5.17/5.50 = ( ( im @ Z )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_is_Real_iff
% 5.17/5.50 thf(fact_8622_nonzero__Reals__divide,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( B != zero_zero_complex )
% 5.17/5.50 => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % nonzero_Reals_divide
% 5.17/5.50 thf(fact_8623_nonzero__Reals__divide,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.17/5.50 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.17/5.50 => ( ( B != zero_zero_real )
% 5.17/5.50 => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % nonzero_Reals_divide
% 5.17/5.50 thf(fact_8624_Complex__in__Reals,axiom,
% 5.17/5.50 ! [X: real] : ( member_complex @ ( complex2 @ X @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 5.17/5.50
% 5.17/5.50 % Complex_in_Reals
% 5.17/5.50 thf(fact_8625_nonzero__Reals__inverse,axiom,
% 5.17/5.50 ! [A: real] :
% 5.17/5.50 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.17/5.50 => ( ( A != zero_zero_real )
% 5.17/5.50 => ( member_real @ ( inverse_inverse_real @ A ) @ real_V470468836141973256s_real ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % nonzero_Reals_inverse
% 5.17/5.50 thf(fact_8626_nonzero__Reals__inverse,axiom,
% 5.17/5.50 ! [A: complex] :
% 5.17/5.50 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.17/5.50 => ( ( A != zero_zero_complex )
% 5.17/5.50 => ( member_complex @ ( invers8013647133539491842omplex @ A ) @ real_V2521375963428798218omplex ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % nonzero_Reals_inverse
% 5.17/5.50 thf(fact_8627_Re__complex__div__eq__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_complex_div_eq_0
% 5.17/5.50 thf(fact_8628_Im__complex__div__eq__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.17/5.50 = zero_zero_real )
% 5.17/5.50 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.17/5.50 = zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_complex_div_eq_0
% 5.17/5.50 thf(fact_8629_Re__complex__div__gt__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.50 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_complex_div_gt_0
% 5.17/5.50 thf(fact_8630_Re__complex__div__lt__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.17/5.50 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_complex_div_lt_0
% 5.17/5.50 thf(fact_8631_Re__complex__div__ge__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.50 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_complex_div_ge_0
% 5.17/5.50 thf(fact_8632_Re__complex__div__le__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.17/5.50 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Re_complex_div_le_0
% 5.17/5.50 thf(fact_8633_Im__complex__div__gt__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.50 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_complex_div_gt_0
% 5.17/5.50 thf(fact_8634_Im__complex__div__lt__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.17/5.50 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_complex_div_lt_0
% 5.17/5.50 thf(fact_8635_Im__complex__div__ge__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.50 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_complex_div_ge_0
% 5.17/5.50 thf(fact_8636_Im__complex__div__le__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.17/5.50 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.17/5.50
% 5.17/5.50 % Im_complex_div_le_0
% 5.17/5.50 thf(fact_8637_complex__mod__mult__cnj,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.17/5.50 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_mod_mult_cnj
% 5.17/5.50 thf(fact_8638_complex__div__gt__0,axiom,
% 5.17/5.50 ! [A: complex,B: complex] :
% 5.17/5.50 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.50 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.17/5.50 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.17/5.50 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_div_gt_0
% 5.17/5.50 thf(fact_8639_complex__norm__square,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_norm_square
% 5.17/5.50 thf(fact_8640_complex__add__cnj,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.17/5.50 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_add_cnj
% 5.17/5.50 thf(fact_8641_complex__div__cnj,axiom,
% 5.17/5.50 ( divide1717551699836669952omplex
% 5.17/5.50 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_div_cnj
% 5.17/5.50 thf(fact_8642_cnj__add__mult__eq__Re,axiom,
% 5.17/5.50 ! [Z: complex,W: complex] :
% 5.17/5.50 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.17/5.50 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % cnj_add_mult_eq_Re
% 5.17/5.50 thf(fact_8643_complex__mult__cnj,axiom,
% 5.17/5.50 ! [Z: complex] :
% 5.17/5.50 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % complex_mult_cnj
% 5.17/5.50 thf(fact_8644_or__int__rec,axiom,
% 5.17/5.50 ( bit_se1409905431419307370or_int
% 5.17/5.50 = ( ^ [K3: int,L3: int] :
% 5.17/5.50 ( plus_plus_int
% 5.17/5.50 @ ( zero_n2684676970156552555ol_int
% 5.17/5.50 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.17/5.50 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 5.17/5.50 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_int_rec
% 5.17/5.50 thf(fact_8645_drop__bit__numeral__minus__bit1,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_numeral_minus_bit1
% 5.17/5.50 thf(fact_8646_or__numerals_I7_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(7)
% 5.17/5.50 thf(fact_8647_or__numerals_I7_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(7)
% 5.17/5.50 thf(fact_8648_or__numerals_I6_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(6)
% 5.17/5.50 thf(fact_8649_or__numerals_I6_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(6)
% 5.17/5.50 thf(fact_8650_or_Oright__idem,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.right_idem
% 5.17/5.50 thf(fact_8651_or_Oright__idem,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.right_idem
% 5.17/5.50 thf(fact_8652_or_Oleft__idem,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.left_idem
% 5.17/5.50 thf(fact_8653_or_Oleft__idem,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.left_idem
% 5.17/5.50 thf(fact_8654_or_Oidem,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ A @ A )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % or.idem
% 5.17/5.50 thf(fact_8655_or_Oidem,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ A @ A )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % or.idem
% 5.17/5.50 thf(fact_8656_or_Oleft__neutral,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % or.left_neutral
% 5.17/5.50 thf(fact_8657_or_Oleft__neutral,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % or.left_neutral
% 5.17/5.50 thf(fact_8658_or_Oright__neutral,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % or.right_neutral
% 5.17/5.50 thf(fact_8659_or_Oright__neutral,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % or.right_neutral
% 5.17/5.50 thf(fact_8660_drop__bit__of__0,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ zero_zero_int )
% 5.17/5.50 = zero_zero_int ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_0
% 5.17/5.50 thf(fact_8661_drop__bit__of__0,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ zero_zero_nat )
% 5.17/5.50 = zero_zero_nat ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_0
% 5.17/5.50 thf(fact_8662_drop__bit__drop__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se8568078237143864401it_int @ N @ A ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_drop_bit
% 5.17/5.50 thf(fact_8663_drop__bit__drop__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ M @ ( bit_se8570568707652914677it_nat @ N @ A ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ ( plus_plus_nat @ M @ N ) @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_drop_bit
% 5.17/5.50 thf(fact_8664_take__bit__or,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_or
% 5.17/5.50 thf(fact_8665_take__bit__or,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_or
% 5.17/5.50 thf(fact_8666_push__bit__or,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( bit_se545348938243370406it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_or
% 5.17/5.50 thf(fact_8667_push__bit__or,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se547839408752420682it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( bit_se547839408752420682it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % push_bit_or
% 5.17/5.50 thf(fact_8668_drop__bit__and,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ ( bit_se8568078237143864401it_int @ N @ A ) @ ( bit_se8568078237143864401it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_and
% 5.17/5.50 thf(fact_8669_drop__bit__and,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se727722235901077358nd_nat @ ( bit_se8570568707652914677it_nat @ N @ A ) @ ( bit_se8570568707652914677it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_and
% 5.17/5.50 thf(fact_8670_drop__bit__or,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_se8568078237143864401it_int @ N @ A ) @ ( bit_se8568078237143864401it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_or
% 5.17/5.50 thf(fact_8671_drop__bit__or,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ ( bit_se8570568707652914677it_nat @ N @ A ) @ ( bit_se8570568707652914677it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_or
% 5.17/5.50 thf(fact_8672_drop__bit__xor,axiom,
% 5.17/5.50 ! [N: nat,A: int,B: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.17/5.50 = ( bit_se6526347334894502574or_int @ ( bit_se8568078237143864401it_int @ N @ A ) @ ( bit_se8568078237143864401it_int @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_xor
% 5.17/5.50 thf(fact_8673_drop__bit__xor,axiom,
% 5.17/5.50 ! [N: nat,A: nat,B: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.17/5.50 = ( bit_se6528837805403552850or_nat @ ( bit_se8570568707652914677it_nat @ N @ A ) @ ( bit_se8570568707652914677it_nat @ N @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_xor
% 5.17/5.50 thf(fact_8674_bit_Odisj__one__right,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se1080825931792720795nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_one_right
% 5.17/5.50 thf(fact_8675_bit_Odisj__one__right,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_one_right
% 5.17/5.50 thf(fact_8676_bit_Odisj__one__left,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_one_left
% 5.17/5.50 thf(fact_8677_bit_Odisj__one__left,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_one_left
% 5.17/5.50 thf(fact_8678_drop__bit__of__bool,axiom,
% 5.17/5.50 ! [N: nat,B: $o] :
% 5.17/5.50 ( ( bit_se3928097537394005634nteger @ N @ ( zero_n356916108424825756nteger @ B ) )
% 5.17/5.50 = ( zero_n356916108424825756nteger
% 5.17/5.50 @ ( ( N = zero_zero_nat )
% 5.17/5.50 & B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_bool
% 5.17/5.50 thf(fact_8679_drop__bit__of__bool,axiom,
% 5.17/5.50 ! [N: nat,B: $o] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( zero_n2684676970156552555ol_int @ B ) )
% 5.17/5.50 = ( zero_n2684676970156552555ol_int
% 5.17/5.50 @ ( ( N = zero_zero_nat )
% 5.17/5.50 & B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_bool
% 5.17/5.50 thf(fact_8680_drop__bit__of__bool,axiom,
% 5.17/5.50 ! [N: nat,B: $o] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( zero_n2687167440665602831ol_nat @ B ) )
% 5.17/5.50 = ( zero_n2687167440665602831ol_nat
% 5.17/5.50 @ ( ( N = zero_zero_nat )
% 5.17/5.50 & B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_bool
% 5.17/5.50 thf(fact_8681_or__nonnegative__int__iff,axiom,
% 5.17/5.50 ! [K: int,L: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.17/5.50 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.17/5.50 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nonnegative_int_iff
% 5.17/5.50 thf(fact_8682_or__negative__int__iff,axiom,
% 5.17/5.50 ! [K: int,L: int] :
% 5.17/5.50 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.17/5.50 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.17/5.50 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_negative_int_iff
% 5.17/5.50 thf(fact_8683_bit_Ode__Morgan__disj,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ X @ Y4 ) )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X ) @ ( bit_ri7919022796975470100ot_int @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.de_Morgan_disj
% 5.17/5.50 thf(fact_8684_bit_Ode__Morgan__conj,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ ( bit_ri7919022796975470100ot_int @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.de_Morgan_conj
% 5.17/5.50 thf(fact_8685_drop__bit__nonnegative__int__iff,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.17/5.50 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_nonnegative_int_iff
% 5.17/5.50 thf(fact_8686_drop__bit__negative__int__iff,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.17/5.50 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_negative_int_iff
% 5.17/5.50 thf(fact_8687_drop__bit__minus__one,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_minus_one
% 5.17/5.50 thf(fact_8688_or__nat__numerals_I2_J,axiom,
% 5.17/5.50 ! [Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_numerals(2)
% 5.17/5.50 thf(fact_8689_or__nat__numerals_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_numerals(4)
% 5.17/5.50 thf(fact_8690_or__numerals_I2_J,axiom,
% 5.17/5.50 ! [Y4: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( numeral_numeral_int @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(2)
% 5.17/5.50 thf(fact_8691_or__numerals_I2_J,axiom,
% 5.17/5.50 ! [Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(2)
% 5.17/5.50 thf(fact_8692_or__numerals_I8_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.17/5.50 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(8)
% 5.17/5.50 thf(fact_8693_or__numerals_I8_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(8)
% 5.17/5.50 thf(fact_8694_drop__bit__Suc__bit0,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ ( numeral_numeral_int @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc_bit0
% 5.17/5.50 thf(fact_8695_drop__bit__Suc__bit0,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ N @ ( numeral_numeral_nat @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc_bit0
% 5.17/5.50 thf(fact_8696_drop__bit__Suc__bit1,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ ( numeral_numeral_int @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc_bit1
% 5.17/5.50 thf(fact_8697_drop__bit__Suc__bit1,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ N @ ( numeral_numeral_nat @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc_bit1
% 5.17/5.50 thf(fact_8698_bit_Odisj__cancel__left,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se1080825931792720795nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_cancel_left
% 5.17/5.50 thf(fact_8699_bit_Odisj__cancel__left,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_cancel_left
% 5.17/5.50 thf(fact_8700_bit_Odisj__cancel__right,axiom,
% 5.17/5.50 ! [X: code_integer] :
% 5.17/5.50 ( ( bit_se1080825931792720795nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_cancel_right
% 5.17/5.50 thf(fact_8701_bit_Odisj__cancel__right,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_cancel_right
% 5.17/5.50 thf(fact_8702_drop__bit__of__1,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se3928097537394005634nteger @ N @ one_one_Code_integer )
% 5.17/5.50 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_1
% 5.17/5.50 thf(fact_8703_drop__bit__of__1,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ one_one_int )
% 5.17/5.50 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_1
% 5.17/5.50 thf(fact_8704_drop__bit__of__1,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ one_one_nat )
% 5.17/5.50 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_1
% 5.17/5.50 thf(fact_8705_or__nat__numerals_I1_J,axiom,
% 5.17/5.50 ! [Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_numerals(1)
% 5.17/5.50 thf(fact_8706_or__nat__numerals_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_numerals(3)
% 5.17/5.50 thf(fact_8707_or__numerals_I3_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(3)
% 5.17/5.50 thf(fact_8708_or__numerals_I3_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(3)
% 5.17/5.50 thf(fact_8709_or__numerals_I1_J,axiom,
% 5.17/5.50 ! [Y4: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( numeral_numeral_int @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(1)
% 5.17/5.50 thf(fact_8710_or__numerals_I1_J,axiom,
% 5.17/5.50 ! [Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(1)
% 5.17/5.50 thf(fact_8711_or__numerals_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.17/5.50 = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(5)
% 5.17/5.50 thf(fact_8712_or__numerals_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.17/5.50 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(5)
% 5.17/5.50 thf(fact_8713_drop__bit__numeral__bit0,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_numeral_bit0
% 5.17/5.50 thf(fact_8714_drop__bit__numeral__bit0,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_numeral_bit0
% 5.17/5.50 thf(fact_8715_drop__bit__numeral__bit1,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_numeral_bit1
% 5.17/5.50 thf(fact_8716_drop__bit__numeral__bit1,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_numeral_bit1
% 5.17/5.50 thf(fact_8717_or__minus__numerals_I6_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(6)
% 5.17/5.50 thf(fact_8718_or__minus__numerals_I2_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(2)
% 5.17/5.50 thf(fact_8719_drop__bit__Suc__minus__bit0,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc_minus_bit0
% 5.17/5.50 thf(fact_8720_drop__bit__numeral__minus__bit0,axiom,
% 5.17/5.50 ! [L: num,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_numeral_minus_bit0
% 5.17/5.50 thf(fact_8721_drop__bit__Suc__minus__bit1,axiom,
% 5.17/5.50 ! [N: nat,K: num] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc_minus_bit1
% 5.17/5.50 thf(fact_8722_and__minus__minus__numerals,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.50 = ( 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 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_minus_minus_numerals
% 5.17/5.50 thf(fact_8723_or__minus__minus__numerals,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.50 = ( 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 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_minus_numerals
% 5.17/5.50 thf(fact_8724_or__numerals_I4_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(4)
% 5.17/5.50 thf(fact_8725_or__numerals_I4_J,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.17/5.50 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_numerals(4)
% 5.17/5.50 thf(fact_8726_of__int__or__eq,axiom,
% 5.17/5.50 ! [K: int,L: int] :
% 5.17/5.50 ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_int_or_eq
% 5.17/5.50 thf(fact_8727_or_Oleft__commute,axiom,
% 5.17/5.50 ! [B: int,A: int,C: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.left_commute
% 5.17/5.50 thf(fact_8728_or_Oleft__commute,axiom,
% 5.17/5.50 ! [B: nat,A: nat,C: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.left_commute
% 5.17/5.50 thf(fact_8729_or_Ocommute,axiom,
% 5.17/5.50 ( bit_se1409905431419307370or_int
% 5.17/5.50 = ( ^ [A3: int,B2: int] : ( bit_se1409905431419307370or_int @ B2 @ A3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.commute
% 5.17/5.50 thf(fact_8730_or_Ocommute,axiom,
% 5.17/5.50 ( bit_se1412395901928357646or_nat
% 5.17/5.50 = ( ^ [A3: nat,B2: nat] : ( bit_se1412395901928357646or_nat @ B2 @ A3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.commute
% 5.17/5.50 thf(fact_8731_or_Oassoc,axiom,
% 5.17/5.50 ! [A: int,B: int,C: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.assoc
% 5.17/5.50 thf(fact_8732_or_Oassoc,axiom,
% 5.17/5.50 ! [A: nat,B: nat,C: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or.assoc
% 5.17/5.50 thf(fact_8733_bit_Oconj__disj__distrib,axiom,
% 5.17/5.50 ! [X: int,Y4: int,Z: int] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ X @ ( bit_se1409905431419307370or_int @ Y4 @ Z ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ ( bit_se725231765392027082nd_int @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.conj_disj_distrib
% 5.17/5.50 thf(fact_8734_bit_Odisj__conj__distrib,axiom,
% 5.17/5.50 ! [X: int,Y4: int,Z: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ X @ ( bit_se725231765392027082nd_int @ Y4 @ Z ) )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X @ Y4 ) @ ( bit_se1409905431419307370or_int @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_conj_distrib
% 5.17/5.50 thf(fact_8735_bit_Oconj__disj__distrib2,axiom,
% 5.17/5.50 ! [Y4: int,Z: int,X: int] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y4 @ Z ) @ X )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y4 @ X ) @ ( bit_se725231765392027082nd_int @ Z @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.conj_disj_distrib2
% 5.17/5.50 thf(fact_8736_bit_Odisj__conj__distrib2,axiom,
% 5.17/5.50 ! [Y4: int,Z: int,X: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y4 @ Z ) @ X )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y4 @ X ) @ ( bit_se1409905431419307370or_int @ Z @ X ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_conj_distrib2
% 5.17/5.50 thf(fact_8737_bit_Odisj__zero__right,axiom,
% 5.17/5.50 ! [X: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ X @ zero_zero_int )
% 5.17/5.50 = X ) ).
% 5.17/5.50
% 5.17/5.50 % bit.disj_zero_right
% 5.17/5.50 thf(fact_8738_or__eq__0__iff,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 5.17/5.50 = zero_zero_int )
% 5.17/5.50 = ( ( A = zero_zero_int )
% 5.17/5.50 & ( B = zero_zero_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_eq_0_iff
% 5.17/5.50 thf(fact_8739_or__eq__0__iff,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 5.17/5.50 = zero_zero_nat )
% 5.17/5.50 = ( ( A = zero_zero_nat )
% 5.17/5.50 & ( B = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_eq_0_iff
% 5.17/5.50 thf(fact_8740_bit__or__int__iff,axiom,
% 5.17/5.50 ! [K: int,L: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N )
% 5.17/5.50 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.17/5.50 | ( bit_se1146084159140164899it_int @ L @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_or_int_iff
% 5.17/5.50 thf(fact_8741_bit__or__iff,axiom,
% 5.17/5.50 ! [A: int,B: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ N )
% 5.17/5.50 = ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.50 | ( bit_se1146084159140164899it_int @ B @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_or_iff
% 5.17/5.50 thf(fact_8742_bit__or__iff,axiom,
% 5.17/5.50 ! [A: nat,B: nat,N: nat] :
% 5.17/5.50 ( ( bit_se1148574629649215175it_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ N )
% 5.17/5.50 = ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.17/5.50 | ( bit_se1148574629649215175it_nat @ B @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_or_iff
% 5.17/5.50 thf(fact_8743_or__nat__def,axiom,
% 5.17/5.50 ( bit_se1412395901928357646or_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M5 ) @ ( semiri1314217659103216013at_int @ N4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_def
% 5.17/5.50 thf(fact_8744_of__nat__drop__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( semiri1314217659103216013at_int @ ( bit_se8570568707652914677it_nat @ M @ N ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ M @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_drop_bit
% 5.17/5.50 thf(fact_8745_of__nat__drop__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( semiri1316708129612266289at_nat @ ( bit_se8570568707652914677it_nat @ M @ N ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ M @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_drop_bit
% 5.17/5.50 thf(fact_8746_drop__bit__of__nat,axiom,
% 5.17/5.50 ! [N: nat,M: nat] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.17/5.50 = ( semiri1314217659103216013at_int @ ( bit_se8570568707652914677it_nat @ N @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_nat
% 5.17/5.50 thf(fact_8747_drop__bit__of__nat,axiom,
% 5.17/5.50 ! [N: nat,M: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.17/5.50 = ( semiri1316708129612266289at_nat @ ( bit_se8570568707652914677it_nat @ N @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_nat
% 5.17/5.50 thf(fact_8748_of__nat__or__eq,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_or_eq
% 5.17/5.50 thf(fact_8749_of__nat__or__eq,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_or_eq
% 5.17/5.50 thf(fact_8750_or__greater__eq,axiom,
% 5.17/5.50 ! [L: int,K: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.17/5.50 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_greater_eq
% 5.17/5.50 thf(fact_8751_OR__lower,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % OR_lower
% 5.17/5.50 thf(fact_8752_disjunctive__add,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ! [N2: nat] :
% 5.17/5.50 ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.17/5.50 | ~ ( bit_se1146084159140164899it_int @ B @ N2 ) )
% 5.17/5.50 => ( ( plus_plus_int @ A @ B )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ A @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % disjunctive_add
% 5.17/5.50 thf(fact_8753_disjunctive__add,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ! [N2: nat] :
% 5.17/5.50 ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.17/5.50 | ~ ( bit_se1148574629649215175it_nat @ B @ N2 ) )
% 5.17/5.50 => ( ( plus_plus_nat @ A @ B )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % disjunctive_add
% 5.17/5.50 thf(fact_8754_plus__and__or,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y4 ) @ ( bit_se1409905431419307370or_int @ X @ Y4 ) )
% 5.17/5.50 = ( plus_plus_int @ X @ Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % plus_and_or
% 5.17/5.50 thf(fact_8755_or__eq__not__not__and,axiom,
% 5.17/5.50 ( bit_se1409905431419307370or_int
% 5.17/5.50 = ( ^ [A3: int,B2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ ( bit_ri7919022796975470100ot_int @ B2 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_eq_not_not_and
% 5.17/5.50 thf(fact_8756_and__eq__not__not__or,axiom,
% 5.17/5.50 ( bit_se725231765392027082nd_int
% 5.17/5.50 = ( ^ [A3: int,B2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ ( bit_ri7919022796975470100ot_int @ B2 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % and_eq_not_not_or
% 5.17/5.50 thf(fact_8757_or__int__def,axiom,
% 5.17/5.50 ( bit_se1409905431419307370or_int
% 5.17/5.50 = ( ^ [K3: int,L3: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L3 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_int_def
% 5.17/5.50 thf(fact_8758_set__bit__nat__def,axiom,
% 5.17/5.50 ( bit_se7882103937844011126it_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] : ( bit_se1412395901928357646or_nat @ N4 @ ( bit_se547839408752420682it_nat @ M5 @ one_one_nat ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % set_bit_nat_def
% 5.17/5.50 thf(fact_8759_take__bit__eq__self__iff__drop__bit__eq__0,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.17/5.50 = A )
% 5.17/5.50 = ( ( bit_se8568078237143864401it_int @ N @ A )
% 5.17/5.50 = zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_eq_self_iff_drop_bit_eq_0
% 5.17/5.50 thf(fact_8760_take__bit__eq__self__iff__drop__bit__eq__0,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.17/5.50 = A )
% 5.17/5.50 = ( ( bit_se8570568707652914677it_nat @ N @ A )
% 5.17/5.50 = zero_zero_nat ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_eq_self_iff_drop_bit_eq_0
% 5.17/5.50 thf(fact_8761_drop__bit__push__bit__int,axiom,
% 5.17/5.50 ! [M: nat,N: nat,K: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_push_bit_int
% 5.17/5.50 thf(fact_8762_take__bit__drop__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: int] :
% 5.17/5.50 ( ( bit_se2923211474154528505it_int @ M @ ( bit_se8568078237143864401it_int @ N @ A ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_drop_bit
% 5.17/5.50 thf(fact_8763_take__bit__drop__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se8570568707652914677it_nat @ N @ A ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ N @ ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N ) @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % take_bit_drop_bit
% 5.17/5.50 thf(fact_8764_drop__bit__take__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.17/5.50 = ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ M ) @ ( bit_se8568078237143864401it_int @ M @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_take_bit
% 5.17/5.50 thf(fact_8765_drop__bit__take__bit,axiom,
% 5.17/5.50 ! [M: nat,N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.17/5.50 = ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ M ) @ ( bit_se8570568707652914677it_nat @ M @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_take_bit
% 5.17/5.50 thf(fact_8766_or__not__numerals_I1_J,axiom,
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(1)
% 5.17/5.50 thf(fact_8767_bit_Oxor__def2,axiom,
% 5.17/5.50 ( bit_se6526347334894502574or_int
% 5.17/5.50 = ( ^ [X3: int,Y6: int] : ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X3 @ Y6 ) @ ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ ( bit_ri7919022796975470100ot_int @ Y6 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_def2
% 5.17/5.50 thf(fact_8768_bit_Oxor__def,axiom,
% 5.17/5.50 ( bit_se6526347334894502574or_int
% 5.17/5.50 = ( ^ [X3: int,Y6: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X3 @ ( bit_ri7919022796975470100ot_int @ Y6 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X3 ) @ Y6 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.xor_def
% 5.17/5.50 thf(fact_8769_set__bit__eq__or,axiom,
% 5.17/5.50 ( bit_se2793503036327961859nteger
% 5.17/5.50 = ( ^ [N4: nat,A3: code_integer] : ( bit_se1080825931792720795nteger @ A3 @ ( bit_se7788150548672797655nteger @ N4 @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % set_bit_eq_or
% 5.17/5.50 thf(fact_8770_set__bit__eq__or,axiom,
% 5.17/5.50 ( bit_se7879613467334960850it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( bit_se1409905431419307370or_int @ A3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % set_bit_eq_or
% 5.17/5.50 thf(fact_8771_set__bit__eq__or,axiom,
% 5.17/5.50 ( bit_se7882103937844011126it_nat
% 5.17/5.50 = ( ^ [N4: nat,A3: nat] : ( bit_se1412395901928357646or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N4 @ one_one_nat ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % set_bit_eq_or
% 5.17/5.50 thf(fact_8772_xor__int__def,axiom,
% 5.17/5.50 ( bit_se6526347334894502574or_int
% 5.17/5.50 = ( ^ [K3: int,L3: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L3 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % xor_int_def
% 5.17/5.50 thf(fact_8773_div__push__bit__of__1__eq__drop__bit,axiom,
% 5.17/5.50 ! [A: int,N: nat] :
% 5.17/5.50 ( ( divide_divide_int @ A @ ( bit_se545348938243370406it_int @ N @ one_one_int ) )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % div_push_bit_of_1_eq_drop_bit
% 5.17/5.50 thf(fact_8774_div__push__bit__of__1__eq__drop__bit,axiom,
% 5.17/5.50 ! [A: nat,N: nat] :
% 5.17/5.50 ( ( divide_divide_nat @ A @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ N @ A ) ) ).
% 5.17/5.50
% 5.17/5.50 % div_push_bit_of_1_eq_drop_bit
% 5.17/5.50 thf(fact_8775_concat__bit__def,axiom,
% 5.17/5.50 ( bit_concat_bit
% 5.17/5.50 = ( ^ [N4: nat,K3: int,L3: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N4 @ K3 ) @ ( bit_se545348938243370406it_int @ N4 @ L3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % concat_bit_def
% 5.17/5.50 thf(fact_8776_bit__iff__and__drop__bit__eq__1,axiom,
% 5.17/5.50 ( bit_se1146084159140164899it_int
% 5.17/5.50 = ( ^ [A3: int,N4: nat] :
% 5.17/5.50 ( ( bit_se725231765392027082nd_int @ ( bit_se8568078237143864401it_int @ N4 @ A3 ) @ one_one_int )
% 5.17/5.50 = one_one_int ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_and_drop_bit_eq_1
% 5.17/5.50 thf(fact_8777_bit__iff__and__drop__bit__eq__1,axiom,
% 5.17/5.50 ( bit_se1148574629649215175it_nat
% 5.17/5.50 = ( ^ [A3: nat,N4: nat] :
% 5.17/5.50 ( ( bit_se727722235901077358nd_nat @ ( bit_se8570568707652914677it_nat @ N4 @ A3 ) @ one_one_nat )
% 5.17/5.50 = one_one_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_and_drop_bit_eq_1
% 5.17/5.50 thf(fact_8778_set__bit__int__def,axiom,
% 5.17/5.50 ( bit_se7879613467334960850it_int
% 5.17/5.50 = ( ^ [N4: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N4 @ one_one_int ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % set_bit_int_def
% 5.17/5.50 thf(fact_8779_bits__ident,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( plus_plus_int @ ( bit_se545348938243370406it_int @ N @ ( bit_se8568078237143864401it_int @ N @ A ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % bits_ident
% 5.17/5.50 thf(fact_8780_bits__ident,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N @ ( bit_se8570568707652914677it_nat @ N @ A ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % bits_ident
% 5.17/5.50 thf(fact_8781_even__or__iff,axiom,
% 5.17/5.50 ! [A: code_integer,B: code_integer] :
% 5.17/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 5.17/5.50 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.17/5.50 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_or_iff
% 5.17/5.50 thf(fact_8782_even__or__iff,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.17/5.50 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.17/5.50 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_or_iff
% 5.17/5.50 thf(fact_8783_even__or__iff,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.17/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.17/5.50 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_or_iff
% 5.17/5.50 thf(fact_8784_bit_Ocomplement__unique,axiom,
% 5.17/5.50 ! [A: code_integer,X: code_integer,Y4: code_integer] :
% 5.17/5.50 ( ( ( bit_se3949692690581998587nteger @ A @ X )
% 5.17/5.50 = zero_z3403309356797280102nteger )
% 5.17/5.50 => ( ( ( bit_se1080825931792720795nteger @ A @ X )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 => ( ( ( bit_se3949692690581998587nteger @ A @ Y4 )
% 5.17/5.50 = zero_z3403309356797280102nteger )
% 5.17/5.50 => ( ( ( bit_se1080825931792720795nteger @ A @ Y4 )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 => ( X = Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.complement_unique
% 5.17/5.50 thf(fact_8785_bit_Ocomplement__unique,axiom,
% 5.17/5.50 ! [A: int,X: int,Y4: int] :
% 5.17/5.50 ( ( ( bit_se725231765392027082nd_int @ A @ X )
% 5.17/5.50 = zero_zero_int )
% 5.17/5.50 => ( ( ( bit_se1409905431419307370or_int @ A @ X )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 => ( ( ( bit_se725231765392027082nd_int @ A @ Y4 )
% 5.17/5.50 = zero_zero_int )
% 5.17/5.50 => ( ( ( bit_se1409905431419307370or_int @ A @ Y4 )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 => ( X = Y4 ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.complement_unique
% 5.17/5.50 thf(fact_8786_or__not__numerals_I4_J,axiom,
% 5.17/5.50 ! [M: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(4)
% 5.17/5.50 thf(fact_8787_or__not__numerals_I2_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(2)
% 5.17/5.50 thf(fact_8788_stable__imp__drop__bit__eq,axiom,
% 5.17/5.50 ! [A: int,N: nat] :
% 5.17/5.50 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.50 = A )
% 5.17/5.50 => ( ( bit_se8568078237143864401it_int @ N @ A )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % stable_imp_drop_bit_eq
% 5.17/5.50 thf(fact_8789_stable__imp__drop__bit__eq,axiom,
% 5.17/5.50 ! [A: nat,N: nat] :
% 5.17/5.50 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.50 = A )
% 5.17/5.50 => ( ( bit_se8570568707652914677it_nat @ N @ A )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % stable_imp_drop_bit_eq
% 5.17/5.50 thf(fact_8790_drop__bit__half,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( divide_divide_int @ ( bit_se8568078237143864401it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_half
% 5.17/5.50 thf(fact_8791_drop__bit__half,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.50 = ( divide_divide_nat @ ( bit_se8570568707652914677it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_half
% 5.17/5.50 thf(fact_8792_bit_Ocompl__unique,axiom,
% 5.17/5.50 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.50 ( ( ( bit_se3949692690581998587nteger @ X @ Y4 )
% 5.17/5.50 = zero_z3403309356797280102nteger )
% 5.17/5.50 => ( ( ( bit_se1080825931792720795nteger @ X @ Y4 )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.17/5.50 => ( ( bit_ri7632146776885996613nteger @ X )
% 5.17/5.50 = Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_unique
% 5.17/5.50 thf(fact_8793_bit_Ocompl__unique,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( ( bit_se725231765392027082nd_int @ X @ Y4 )
% 5.17/5.50 = zero_zero_int )
% 5.17/5.50 => ( ( ( bit_se1409905431419307370or_int @ X @ Y4 )
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 => ( ( bit_ri7919022796975470100ot_int @ X )
% 5.17/5.50 = Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit.compl_unique
% 5.17/5.50 thf(fact_8794_or__not__numerals_I3_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(3)
% 5.17/5.50 thf(fact_8795_or__not__numerals_I7_J,axiom,
% 5.17/5.50 ! [M: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.17/5.50 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(7)
% 5.17/5.50 thf(fact_8796_drop__bit__int__def,axiom,
% 5.17/5.50 ( bit_se8568078237143864401it_int
% 5.17/5.50 = ( ^ [N4: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_int_def
% 5.17/5.50 thf(fact_8797_signed__take__bit__eq__if__negative,axiom,
% 5.17/5.50 ! [A: int,N: nat] :
% 5.17/5.50 ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.17/5.50 => ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % signed_take_bit_eq_if_negative
% 5.17/5.50 thf(fact_8798_drop__bit__Suc,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ A )
% 5.17/5.50 = ( bit_se8568078237143864401it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc
% 5.17/5.50 thf(fact_8799_drop__bit__Suc,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ ( suc @ N ) @ A )
% 5.17/5.50 = ( bit_se8570568707652914677it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_Suc
% 5.17/5.50 thf(fact_8800_drop__bit__eq__div,axiom,
% 5.17/5.50 ( bit_se8568078237143864401it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_eq_div
% 5.17/5.50 thf(fact_8801_drop__bit__eq__div,axiom,
% 5.17/5.50 ( bit_se8570568707652914677it_nat
% 5.17/5.50 = ( ^ [N4: nat,A3: nat] : ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_eq_div
% 5.17/5.50 thf(fact_8802_even__drop__bit__iff__not__bit,axiom,
% 5.17/5.50 ! [N: nat,A: code_integer] :
% 5.17/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3928097537394005634nteger @ N @ A ) )
% 5.17/5.50 = ( ~ ( bit_se9216721137139052372nteger @ A @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_drop_bit_iff_not_bit
% 5.17/5.50 thf(fact_8803_even__drop__bit__iff__not__bit,axiom,
% 5.17/5.50 ! [N: nat,A: int] :
% 5.17/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se8568078237143864401it_int @ N @ A ) )
% 5.17/5.50 = ( ~ ( bit_se1146084159140164899it_int @ A @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_drop_bit_iff_not_bit
% 5.17/5.50 thf(fact_8804_even__drop__bit__iff__not__bit,axiom,
% 5.17/5.50 ! [N: nat,A: nat] :
% 5.17/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se8570568707652914677it_nat @ N @ A ) )
% 5.17/5.50 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % even_drop_bit_iff_not_bit
% 5.17/5.50 thf(fact_8805_bit__iff__odd__drop__bit,axiom,
% 5.17/5.50 ( bit_se9216721137139052372nteger
% 5.17/5.50 = ( ^ [A3: code_integer,N4: nat] :
% 5.17/5.50 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3928097537394005634nteger @ N4 @ A3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_odd_drop_bit
% 5.17/5.50 thf(fact_8806_bit__iff__odd__drop__bit,axiom,
% 5.17/5.50 ( bit_se1146084159140164899it_int
% 5.17/5.50 = ( ^ [A3: int,N4: nat] :
% 5.17/5.50 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se8568078237143864401it_int @ N4 @ A3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_odd_drop_bit
% 5.17/5.50 thf(fact_8807_bit__iff__odd__drop__bit,axiom,
% 5.17/5.50 ( bit_se1148574629649215175it_nat
% 5.17/5.50 = ( ^ [A3: nat,N4: nat] :
% 5.17/5.50 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se8570568707652914677it_nat @ N4 @ A3 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % bit_iff_odd_drop_bit
% 5.17/5.50 thf(fact_8808_mask__Suc__exp,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mask_Suc_exp
% 5.17/5.50 thf(fact_8809_mask__Suc__exp,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mask_Suc_exp
% 5.17/5.50 thf(fact_8810_or__not__numerals_I6_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(6)
% 5.17/5.50 thf(fact_8811_or__one__eq,axiom,
% 5.17/5.50 ! [A: code_integer] :
% 5.17/5.50 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 5.17/5.50 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_one_eq
% 5.17/5.50 thf(fact_8812_or__one__eq,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 5.17/5.50 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_one_eq
% 5.17/5.50 thf(fact_8813_or__one__eq,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 5.17/5.50 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_one_eq
% 5.17/5.50 thf(fact_8814_one__or__eq,axiom,
% 5.17/5.50 ! [A: code_integer] :
% 5.17/5.50 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 5.17/5.50 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % one_or_eq
% 5.17/5.50 thf(fact_8815_one__or__eq,axiom,
% 5.17/5.50 ! [A: int] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 5.17/5.50 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % one_or_eq
% 5.17/5.50 thf(fact_8816_one__or__eq,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 5.17/5.50 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % one_or_eq
% 5.17/5.50 thf(fact_8817_mask__Suc__double,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 5.17/5.50 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mask_Suc_double
% 5.17/5.50 thf(fact_8818_mask__Suc__double,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 5.17/5.50 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % mask_Suc_double
% 5.17/5.50 thf(fact_8819_OR__upper,axiom,
% 5.17/5.50 ! [X: int,N: nat,Y4: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.50 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.50 => ( ( ord_less_int @ Y4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.17/5.50 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y4 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % OR_upper
% 5.17/5.50 thf(fact_8820_or__not__numerals_I5_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(5)
% 5.17/5.50 thf(fact_8821_slice__eq__mask,axiom,
% 5.17/5.50 ! [N: nat,M: nat,A: int] :
% 5.17/5.50 ( ( bit_se545348938243370406it_int @ N @ ( bit_se2923211474154528505it_int @ M @ ( bit_se8568078237143864401it_int @ N @ A ) ) )
% 5.17/5.50 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ M @ N ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % slice_eq_mask
% 5.17/5.50 thf(fact_8822_signed__take__bit__def,axiom,
% 5.17/5.50 ( bit_ri6519982836138164636nteger
% 5.17/5.50 = ( ^ [N4: nat,A3: code_integer] : ( bit_se1080825931792720795nteger @ ( bit_se1745604003318907178nteger @ N4 @ A3 ) @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( bit_se9216721137139052372nteger @ A3 @ N4 ) ) @ ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N4 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % signed_take_bit_def
% 5.17/5.50 thf(fact_8823_signed__take__bit__def,axiom,
% 5.17/5.50 ( bit_ri631733984087533419it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N4 @ A3 ) @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ A3 @ N4 ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N4 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % signed_take_bit_def
% 5.17/5.50 thf(fact_8824_or__Suc__0__eq,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.50 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_Suc_0_eq
% 5.17/5.50 thf(fact_8825_Suc__0__or__eq,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.50 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % Suc_0_or_eq
% 5.17/5.50 thf(fact_8826_drop__bit__rec,axiom,
% 5.17/5.50 ( bit_se8568078237143864401it_int
% 5.17/5.50 = ( ^ [N4: nat,A3: int] : ( if_int @ ( N4 = zero_zero_nat ) @ A3 @ ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_rec
% 5.17/5.50 thf(fact_8827_drop__bit__rec,axiom,
% 5.17/5.50 ( bit_se8570568707652914677it_nat
% 5.17/5.50 = ( ^ [N4: nat,A3: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ A3 @ ( bit_se8570568707652914677it_nat @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_rec
% 5.17/5.50 thf(fact_8828_or__not__numerals_I9_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(9)
% 5.17/5.50 thf(fact_8829_or__not__numerals_I8_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = ( 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 ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_numerals(8)
% 5.17/5.50 thf(fact_8830_or__nat__rec,axiom,
% 5.17/5.50 ( bit_se1412395901928357646or_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.50 ( plus_plus_nat
% 5.17/5.50 @ ( zero_n2687167440665602831ol_nat
% 5.17/5.50 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M5 )
% 5.17/5.50 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.17/5.50 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_rec
% 5.17/5.50 thf(fact_8831_or__int__unfold,axiom,
% 5.17/5.50 ( bit_se1409905431419307370or_int
% 5.17/5.50 = ( ^ [K3: int,L3: int] :
% 5.17/5.50 ( if_int
% 5.17/5.50 @ ( ( K3
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) )
% 5.17/5.50 | ( L3
% 5.17/5.50 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.17/5.50 @ ( uminus_uminus_int @ one_one_int )
% 5.17/5.50 @ ( if_int @ ( K3 = zero_zero_int ) @ L3 @ ( if_int @ ( L3 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_int_unfold
% 5.17/5.50 thf(fact_8832_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 5.17/5.50 boolea2445317508997433345nteger @ bit_se3949692690581998587nteger @ bit_se1080825931792720795nteger @ bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ bit_se3222712562003087583nteger ).
% 5.17/5.50
% 5.17/5.50 % bit.abstract_boolean_algebra_sym_diff_axioms
% 5.17/5.50 thf(fact_8833_bit_Oabstract__boolean__algebra__sym__diff__axioms,axiom,
% 5.17/5.50 boolea8527374999097803216ff_int @ bit_se725231765392027082nd_int @ bit_se1409905431419307370or_int @ bit_ri7919022796975470100ot_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) @ bit_se6526347334894502574or_int ).
% 5.17/5.50
% 5.17/5.50 % bit.abstract_boolean_algebra_sym_diff_axioms
% 5.17/5.50 thf(fact_8834_or__minus__numerals_I8_J,axiom,
% 5.17/5.50 ! [N: num,M: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(8)
% 5.17/5.50 thf(fact_8835_or__minus__numerals_I4_J,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(4)
% 5.17/5.50 thf(fact_8836_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.17/5.50 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.17/5.50 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8837_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.17/5.50 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.17/5.50 & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8838_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: rat,C: rat,A: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.50 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8839_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: num,C: num,A: num] :
% 5.17/5.50 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_less_eq_num @ B @ A )
% 5.17/5.50 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8840_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: nat,C: nat,A: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.50 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8841_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: int,C: int,A: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_less_eq_int @ B @ A )
% 5.17/5.50 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8842_max_Obounded__iff,axiom,
% 5.17/5.50 ! [B: real,C: real,A: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A )
% 5.17/5.50 = ( ( ord_less_eq_real @ B @ A )
% 5.17/5.50 & ( ord_less_eq_real @ C @ A ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.bounded_iff
% 5.17/5.50 thf(fact_8843_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: extended_enat,B: extended_enat] :
% 5.17/5.50 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.17/5.50 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8844_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: code_integer,B: code_integer] :
% 5.17/5.50 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.17/5.50 => ( ( ord_max_Code_integer @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8845_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: rat,B: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.17/5.50 => ( ( ord_max_rat @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8846_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: num,B: num] :
% 5.17/5.50 ( ( ord_less_eq_num @ A @ B )
% 5.17/5.50 => ( ( ord_max_num @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8847_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.50 => ( ( ord_max_nat @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8848_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: int,B: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.17/5.50 => ( ( ord_max_int @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8849_max_Oabsorb2,axiom,
% 5.17/5.50 ! [A: real,B: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.50 => ( ( ord_max_real @ A @ B )
% 5.17/5.50 = B ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb2
% 5.17/5.50 thf(fact_8850_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: extended_enat,A: extended_enat] :
% 5.17/5.50 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.17/5.50 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8851_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: code_integer,A: code_integer] :
% 5.17/5.50 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.17/5.50 => ( ( ord_max_Code_integer @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8852_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: rat,A: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ B @ A )
% 5.17/5.50 => ( ( ord_max_rat @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8853_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: num,A: num] :
% 5.17/5.50 ( ( ord_less_eq_num @ B @ A )
% 5.17/5.50 => ( ( ord_max_num @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8854_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: nat,A: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ B @ A )
% 5.17/5.50 => ( ( ord_max_nat @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8855_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: int,A: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ B @ A )
% 5.17/5.50 => ( ( ord_max_int @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8856_max_Oabsorb1,axiom,
% 5.17/5.50 ! [B: real,A: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ B @ A )
% 5.17/5.50 => ( ( ord_max_real @ A @ B )
% 5.17/5.50 = A ) ) ).
% 5.17/5.50
% 5.17/5.50 % max.absorb1
% 5.17/5.50 thf(fact_8857_of__bool__or__iff,axiom,
% 5.17/5.50 ! [P: $o,Q: $o] :
% 5.17/5.50 ( ( zero_n2687167440665602831ol_nat
% 5.17/5.50 @ ( P
% 5.17/5.50 | Q ) )
% 5.17/5.50 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_bool_or_iff
% 5.17/5.50 thf(fact_8858_of__bool__or__iff,axiom,
% 5.17/5.50 ! [P: $o,Q: $o] :
% 5.17/5.50 ( ( zero_n2684676970156552555ol_int
% 5.17/5.50 @ ( P
% 5.17/5.50 | Q ) )
% 5.17/5.50 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_bool_or_iff
% 5.17/5.50 thf(fact_8859_of__bool__or__iff,axiom,
% 5.17/5.50 ! [P: $o,Q: $o] :
% 5.17/5.50 ( ( zero_n356916108424825756nteger
% 5.17/5.50 @ ( P
% 5.17/5.50 | Q ) )
% 5.17/5.50 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_bool_or_iff
% 5.17/5.50 thf(fact_8860_max__number__of_I1_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.17/5.50 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.17/5.50 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.17/5.50 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.17/5.50 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(1)
% 5.17/5.50 thf(fact_8861_max__number__of_I1_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(1)
% 5.17/5.50 thf(fact_8862_max__number__of_I1_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 = ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(1)
% 5.17/5.50 thf(fact_8863_max__number__of_I1_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.50 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.50 = ( numeral_numeral_nat @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.50 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.17/5.50 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(1)
% 5.17/5.50 thf(fact_8864_max__number__of_I1_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 = ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(1)
% 5.17/5.50 thf(fact_8865_max__number__of_I1_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 = ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(1)
% 5.17/5.50 thf(fact_8866_max__0__1_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.17/5.50 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(3)
% 5.17/5.50 thf(fact_8867_max__0__1_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(3)
% 5.17/5.50 thf(fact_8868_max__0__1_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.17/5.50 = ( numeral_numeral_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(3)
% 5.17/5.50 thf(fact_8869_max__0__1_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.17/5.50 = ( numeral_numeral_rat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(3)
% 5.17/5.50 thf(fact_8870_max__0__1_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.17/5.50 = ( numeral_numeral_nat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(3)
% 5.17/5.50 thf(fact_8871_max__0__1_I3_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.17/5.50 = ( numeral_numeral_int @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(3)
% 5.17/5.50 thf(fact_8872_max__0__1_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.17/5.50 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(4)
% 5.17/5.50 thf(fact_8873_max__0__1_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 5.17/5.50 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(4)
% 5.17/5.50 thf(fact_8874_max__0__1_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.17/5.50 = ( numeral_numeral_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(4)
% 5.17/5.50 thf(fact_8875_max__0__1_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.17/5.50 = ( numeral_numeral_rat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(4)
% 5.17/5.50 thf(fact_8876_max__0__1_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.17/5.50 = ( numeral_numeral_nat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(4)
% 5.17/5.50 thf(fact_8877_max__0__1_I4_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.17/5.50 = ( numeral_numeral_int @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(4)
% 5.17/5.50 thf(fact_8878_max__0__1_I2_J,axiom,
% 5.17/5.50 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.17/5.50 = one_one_real ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(2)
% 5.17/5.50 thf(fact_8879_max__0__1_I2_J,axiom,
% 5.17/5.50 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.17/5.50 = one_one_rat ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(2)
% 5.17/5.50 thf(fact_8880_max__0__1_I2_J,axiom,
% 5.17/5.50 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.17/5.50 = one_one_int ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(2)
% 5.17/5.50 thf(fact_8881_max__0__1_I2_J,axiom,
% 5.17/5.50 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.17/5.50 = one_one_nat ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(2)
% 5.17/5.50 thf(fact_8882_max__0__1_I2_J,axiom,
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.17/5.50 = one_on7984719198319812577d_enat ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(2)
% 5.17/5.50 thf(fact_8883_max__0__1_I2_J,axiom,
% 5.17/5.50 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 5.17/5.50 = one_one_Code_integer ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(2)
% 5.17/5.50 thf(fact_8884_max__0__1_I1_J,axiom,
% 5.17/5.50 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.17/5.50 = one_one_real ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(1)
% 5.17/5.50 thf(fact_8885_max__0__1_I1_J,axiom,
% 5.17/5.50 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.17/5.50 = one_one_rat ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(1)
% 5.17/5.50 thf(fact_8886_max__0__1_I1_J,axiom,
% 5.17/5.50 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.17/5.50 = one_one_int ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(1)
% 5.17/5.50 thf(fact_8887_max__0__1_I1_J,axiom,
% 5.17/5.50 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.17/5.50 = one_one_nat ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(1)
% 5.17/5.50 thf(fact_8888_max__0__1_I1_J,axiom,
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.17/5.50 = one_on7984719198319812577d_enat ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(1)
% 5.17/5.50 thf(fact_8889_max__0__1_I1_J,axiom,
% 5.17/5.50 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 5.17/5.50 = one_one_Code_integer ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(1)
% 5.17/5.50 thf(fact_8890_max__0__1_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.17/5.50 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(5)
% 5.17/5.50 thf(fact_8891_max__0__1_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(5)
% 5.17/5.50 thf(fact_8892_max__0__1_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.17/5.50 = ( numeral_numeral_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(5)
% 5.17/5.50 thf(fact_8893_max__0__1_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.17/5.50 = ( numeral_numeral_rat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(5)
% 5.17/5.50 thf(fact_8894_max__0__1_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.17/5.50 = ( numeral_numeral_nat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(5)
% 5.17/5.50 thf(fact_8895_max__0__1_I5_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.17/5.50 = ( numeral_numeral_int @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(5)
% 5.17/5.50 thf(fact_8896_max__0__1_I6_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.17/5.50 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(6)
% 5.17/5.50 thf(fact_8897_max__0__1_I6_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 5.17/5.50 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(6)
% 5.17/5.50 thf(fact_8898_max__0__1_I6_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.17/5.50 = ( numeral_numeral_real @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(6)
% 5.17/5.50 thf(fact_8899_max__0__1_I6_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 5.17/5.50 = ( numeral_numeral_rat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(6)
% 5.17/5.50 thf(fact_8900_max__0__1_I6_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.17/5.50 = ( numeral_numeral_nat @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(6)
% 5.17/5.50 thf(fact_8901_max__0__1_I6_J,axiom,
% 5.17/5.50 ! [X: num] :
% 5.17/5.50 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.17/5.50 = ( numeral_numeral_int @ X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_0_1(6)
% 5.17/5.50 thf(fact_8902_max__number__of_I4_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(4)
% 5.17/5.50 thf(fact_8903_max__number__of_I4_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(4)
% 5.17/5.50 thf(fact_8904_max__number__of_I4_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(4)
% 5.17/5.50 thf(fact_8905_max__number__of_I4_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(4)
% 5.17/5.50 thf(fact_8906_max__number__of_I3_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(3)
% 5.17/5.50 thf(fact_8907_max__number__of_I3_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 = ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.17/5.50 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(3)
% 5.17/5.50 thf(fact_8908_max__number__of_I3_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 = ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(3)
% 5.17/5.50 thf(fact_8909_max__number__of_I3_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 = ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.17/5.50 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(3)
% 5.17/5.50 thf(fact_8910_max__number__of_I2_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.17/5.50 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(2)
% 5.17/5.50 thf(fact_8911_max__number__of_I2_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.17/5.50 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(2)
% 5.17/5.50 thf(fact_8912_max__number__of_I2_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.17/5.50 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(2)
% 5.17/5.50 thf(fact_8913_max__number__of_I2_J,axiom,
% 5.17/5.50 ! [U: num,V: num] :
% 5.17/5.50 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.17/5.50 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.17/5.50 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_number_of(2)
% 5.17/5.50 thf(fact_8914_drop__bit__of__Suc__0,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.17/5.50 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_of_Suc_0
% 5.17/5.50 thf(fact_8915_of__nat__max,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y4 ) )
% 5.17/5.50 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_max
% 5.17/5.50 thf(fact_8916_of__nat__max,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y4 ) )
% 5.17/5.50 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_max
% 5.17/5.50 thf(fact_8917_of__nat__max,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y4 ) )
% 5.17/5.50 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_max
% 5.17/5.50 thf(fact_8918_of__nat__max,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X @ Y4 ) )
% 5.17/5.50 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X ) @ ( semiri681578069525770553at_rat @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_max
% 5.17/5.50 thf(fact_8919_of__nat__max,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y4 ) )
% 5.17/5.50 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_max
% 5.17/5.50 thf(fact_8920_of__nat__max,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y4 ) )
% 5.17/5.50 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % of_nat_max
% 5.17/5.50 thf(fact_8921_max__diff__distrib__left,axiom,
% 5.17/5.50 ! [X: code_integer,Y4: code_integer,Z: code_integer] :
% 5.17/5.50 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_diff_distrib_left
% 5.17/5.50 thf(fact_8922_max__diff__distrib__left,axiom,
% 5.17/5.50 ! [X: real,Y4: real,Z: real] :
% 5.17/5.50 ( ( minus_minus_real @ ( ord_max_real @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_diff_distrib_left
% 5.17/5.50 thf(fact_8923_max__diff__distrib__left,axiom,
% 5.17/5.50 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.50 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_diff_distrib_left
% 5.17/5.50 thf(fact_8924_max__diff__distrib__left,axiom,
% 5.17/5.50 ! [X: int,Y4: int,Z: int] :
% 5.17/5.50 ( ( minus_minus_int @ ( ord_max_int @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_diff_distrib_left
% 5.17/5.50 thf(fact_8925_max__add__distrib__right,axiom,
% 5.17/5.50 ! [X: real,Y4: real,Z: real] :
% 5.17/5.50 ( ( plus_plus_real @ X @ ( ord_max_real @ Y4 @ Z ) )
% 5.17/5.50 = ( ord_max_real @ ( plus_plus_real @ X @ Y4 ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_right
% 5.17/5.50 thf(fact_8926_max__add__distrib__right,axiom,
% 5.17/5.50 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.50 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y4 @ Z ) )
% 5.17/5.50 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y4 ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_right
% 5.17/5.50 thf(fact_8927_max__add__distrib__right,axiom,
% 5.17/5.50 ! [X: int,Y4: int,Z: int] :
% 5.17/5.50 ( ( plus_plus_int @ X @ ( ord_max_int @ Y4 @ Z ) )
% 5.17/5.50 = ( ord_max_int @ ( plus_plus_int @ X @ Y4 ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_right
% 5.17/5.50 thf(fact_8928_max__add__distrib__right,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.50 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y4 @ Z ) )
% 5.17/5.50 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y4 ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_right
% 5.17/5.50 thf(fact_8929_max__add__distrib__right,axiom,
% 5.17/5.50 ! [X: code_integer,Y4: code_integer,Z: code_integer] :
% 5.17/5.50 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y4 @ Z ) )
% 5.17/5.50 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y4 ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_right
% 5.17/5.50 thf(fact_8930_max__add__distrib__left,axiom,
% 5.17/5.50 ! [X: real,Y4: real,Z: real] :
% 5.17/5.50 ( ( plus_plus_real @ ( ord_max_real @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_left
% 5.17/5.50 thf(fact_8931_max__add__distrib__left,axiom,
% 5.17/5.50 ! [X: rat,Y4: rat,Z: rat] :
% 5.17/5.50 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_left
% 5.17/5.50 thf(fact_8932_max__add__distrib__left,axiom,
% 5.17/5.50 ! [X: int,Y4: int,Z: int] :
% 5.17/5.50 ( ( plus_plus_int @ ( ord_max_int @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_left
% 5.17/5.50 thf(fact_8933_max__add__distrib__left,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat,Z: nat] :
% 5.17/5.50 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_left
% 5.17/5.50 thf(fact_8934_max__add__distrib__left,axiom,
% 5.17/5.50 ! [X: code_integer,Y4: code_integer,Z: code_integer] :
% 5.17/5.50 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y4 ) @ Z )
% 5.17/5.50 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y4 @ Z ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_add_distrib_left
% 5.17/5.50 thf(fact_8935_max__absorb2,axiom,
% 5.17/5.50 ! [X: extended_enat,Y4: extended_enat] :
% 5.17/5.50 ( ( ord_le2932123472753598470d_enat @ X @ Y4 )
% 5.17/5.50 => ( ( ord_ma741700101516333627d_enat @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8936_max__absorb2,axiom,
% 5.17/5.50 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.50 ( ( ord_le3102999989581377725nteger @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_Code_integer @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8937_max__absorb2,axiom,
% 5.17/5.50 ! [X: set_int,Y4: set_int] :
% 5.17/5.50 ( ( ord_less_eq_set_int @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_set_int @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8938_max__absorb2,axiom,
% 5.17/5.50 ! [X: rat,Y4: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_rat @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8939_max__absorb2,axiom,
% 5.17/5.50 ! [X: num,Y4: num] :
% 5.17/5.50 ( ( ord_less_eq_num @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_num @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8940_max__absorb2,axiom,
% 5.17/5.50 ! [X: nat,Y4: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_nat @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8941_max__absorb2,axiom,
% 5.17/5.50 ! [X: int,Y4: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_int @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8942_max__absorb2,axiom,
% 5.17/5.50 ! [X: real,Y4: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.50 => ( ( ord_max_real @ X @ Y4 )
% 5.17/5.50 = Y4 ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb2
% 5.17/5.50 thf(fact_8943_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: extended_enat,X: extended_enat] :
% 5.17/5.50 ( ( ord_le2932123472753598470d_enat @ Y4 @ X )
% 5.17/5.50 => ( ( ord_ma741700101516333627d_enat @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8944_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: code_integer,X: code_integer] :
% 5.17/5.50 ( ( ord_le3102999989581377725nteger @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_Code_integer @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8945_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: set_int,X: set_int] :
% 5.17/5.50 ( ( ord_less_eq_set_int @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_set_int @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8946_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: rat,X: rat] :
% 5.17/5.50 ( ( ord_less_eq_rat @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_rat @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8947_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: num,X: num] :
% 5.17/5.50 ( ( ord_less_eq_num @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_num @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8948_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: nat,X: nat] :
% 5.17/5.50 ( ( ord_less_eq_nat @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_nat @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8949_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: int,X: int] :
% 5.17/5.50 ( ( ord_less_eq_int @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_int @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8950_max__absorb1,axiom,
% 5.17/5.50 ! [Y4: real,X: real] :
% 5.17/5.50 ( ( ord_less_eq_real @ Y4 @ X )
% 5.17/5.50 => ( ( ord_max_real @ X @ Y4 )
% 5.17/5.50 = X ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_absorb1
% 5.17/5.50 thf(fact_8951_max__def,axiom,
% 5.17/5.50 ( ord_max_nat
% 5.17/5.50 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_def
% 5.17/5.50 thf(fact_8952_max__def,axiom,
% 5.17/5.50 ( ord_max_int
% 5.17/5.50 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_def
% 5.17/5.50 thf(fact_8953_max__def,axiom,
% 5.17/5.50 ( ord_max_real
% 5.17/5.50 = ( ^ [A3: real,B2: real] : ( if_real @ ( ord_less_eq_real @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_def
% 5.17/5.50 thf(fact_8954_or__not__num__neg_Osimps_I1_J,axiom,
% 5.17/5.50 ( ( bit_or_not_num_neg @ one @ one )
% 5.17/5.50 = one ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_num_neg.simps(1)
% 5.17/5.50 thf(fact_8955_or__not__num__neg_Osimps_I4_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.17/5.50 = ( bit0 @ one ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_num_neg.simps(4)
% 5.17/5.50 thf(fact_8956_drop__bit__nat__eq,axiom,
% 5.17/5.50 ! [N: nat,K: int] :
% 5.17/5.50 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.17/5.50 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_nat_eq
% 5.17/5.50 thf(fact_8957_or__not__num__neg_Osimps_I6_J,axiom,
% 5.17/5.50 ! [N: num,M: num] :
% 5.17/5.50 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.17/5.50 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_num_neg.simps(6)
% 5.17/5.50 thf(fact_8958_or__not__num__neg_Osimps_I7_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.17/5.50 = one ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_num_neg.simps(7)
% 5.17/5.50 thf(fact_8959_or__not__num__neg_Osimps_I3_J,axiom,
% 5.17/5.50 ! [M: num] :
% 5.17/5.50 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.17/5.50 = ( bit1 @ M ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_num_neg.simps(3)
% 5.17/5.50 thf(fact_8960_or__not__num__neg_Osimps_I2_J,axiom,
% 5.17/5.50 ! [M: num] :
% 5.17/5.50 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.17/5.50 = ( bit1 @ M ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_not_num_neg.simps(2)
% 5.17/5.50 thf(fact_8961_drop__bit__nat__def,axiom,
% 5.17/5.50 ( bit_se8570568707652914677it_nat
% 5.17/5.50 = ( ^ [N4: nat,M5: nat] : ( divide_divide_nat @ M5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % drop_bit_nat_def
% 5.17/5.50 thf(fact_8962_int__numeral__or__not__num__neg,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % int_numeral_or_not_num_neg
% 5.17/5.50 thf(fact_8963_int__numeral__not__or__num__neg,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % int_numeral_not_or_num_neg
% 5.17/5.50 thf(fact_8964_numeral__or__not__num__eq,axiom,
% 5.17/5.50 ! [M: num,N: num] :
% 5.17/5.50 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % numeral_or_not_num_eq
% 5.17/5.50 thf(fact_8965_or__minus__numerals_I1_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(1)
% 5.17/5.50 thf(fact_8966_or__minus__numerals_I5_J,axiom,
% 5.17/5.50 ! [N: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(5)
% 5.17/5.50 thf(fact_8967_or__nat__unfold,axiom,
% 5.17/5.50 ( bit_se1412395901928357646or_nat
% 5.17/5.50 = ( ^ [M5: nat,N4: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M5 @ ( 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 @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_nat_unfold
% 5.17/5.50 thf(fact_8968_or__minus__numerals_I7_J,axiom,
% 5.17/5.50 ! [N: num,M: num] :
% 5.17/5.50 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.17/5.50 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % or_minus_numerals(7)
% 5.17/5.50 thf(fact_8969_max__enat__simps_I2_J,axiom,
% 5.17/5.50 ! [Q2: extended_enat] :
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.17/5.50 = Q2 ) ).
% 5.17/5.50
% 5.17/5.50 % max_enat_simps(2)
% 5.17/5.50 thf(fact_8970_max__enat__simps_I3_J,axiom,
% 5.17/5.50 ! [Q2: extended_enat] :
% 5.17/5.50 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.17/5.50 = Q2 ) ).
% 5.17/5.50
% 5.17/5.50 % max_enat_simps(3)
% 5.17/5.50 thf(fact_8971_max__Suc__Suc,axiom,
% 5.17/5.50 ! [M: nat,N: nat] :
% 5.17/5.50 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.17/5.50 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_Suc_Suc
% 5.17/5.50 thf(fact_8972_max__0R,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.17/5.50 = N ) ).
% 5.17/5.50
% 5.17/5.50 % max_0R
% 5.17/5.50 thf(fact_8973_max__0L,axiom,
% 5.17/5.50 ! [N: nat] :
% 5.17/5.50 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.17/5.50 = N ) ).
% 5.17/5.50
% 5.17/5.50 % max_0L
% 5.17/5.50 thf(fact_8974_max__nat_Oright__neutral,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % max_nat.right_neutral
% 5.17/5.50 thf(fact_8975_max__nat_Oneutr__eq__iff,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( zero_zero_nat
% 5.17/5.50 = ( ord_max_nat @ A @ B ) )
% 5.17/5.50 = ( ( A = zero_zero_nat )
% 5.17/5.50 & ( B = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_nat.neutr_eq_iff
% 5.17/5.50 thf(fact_8976_max__nat_Oleft__neutral,axiom,
% 5.17/5.50 ! [A: nat] :
% 5.17/5.50 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.17/5.50 = A ) ).
% 5.17/5.50
% 5.17/5.50 % max_nat.left_neutral
% 5.17/5.50 thf(fact_8977_max__nat_Oeq__neutr__iff,axiom,
% 5.17/5.50 ! [A: nat,B: nat] :
% 5.17/5.50 ( ( ( ord_max_nat @ A @ B )
% 5.17/5.50 = zero_zero_nat )
% 5.17/5.50 = ( ( A = zero_zero_nat )
% 5.17/5.50 & ( B = zero_zero_nat ) ) ) ).
% 5.17/5.50
% 5.17/5.50 % max_nat.eq_neutr_iff
% 5.17/5.50 thf(fact_8978_pred__numeral__simps_I2_J,axiom,
% 5.17/5.50 ! [K: num] :
% 5.17/5.50 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.17/5.51 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % pred_numeral_simps(2)
% 5.17/5.51 thf(fact_8979_max__numeral__Suc,axiom,
% 5.17/5.51 ! [K: num,N: nat] :
% 5.17/5.51 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.17/5.51 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % max_numeral_Suc
% 5.17/5.51 thf(fact_8980_max__Suc__numeral,axiom,
% 5.17/5.51 ! [N: nat,K: num] :
% 5.17/5.51 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % max_Suc_numeral
% 5.17/5.51 thf(fact_8981_or__minus__numerals_I3_J,axiom,
% 5.17/5.51 ! [M: num,N: num] :
% 5.17/5.51 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % or_minus_numerals(3)
% 5.17/5.51 thf(fact_8982_nat__mult__max__right,axiom,
% 5.17/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.51 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.17/5.51 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_mult_max_right
% 5.17/5.51 thf(fact_8983_nat__mult__max__left,axiom,
% 5.17/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.51 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.17/5.51 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_mult_max_left
% 5.17/5.51 thf(fact_8984_nat__add__max__right,axiom,
% 5.17/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.51 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.17/5.51 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_add_max_right
% 5.17/5.51 thf(fact_8985_nat__add__max__left,axiom,
% 5.17/5.51 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.51 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.17/5.51 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_add_max_left
% 5.17/5.51 thf(fact_8986_semiring__norm_I26_J,axiom,
% 5.17/5.51 ( ( bitM @ one )
% 5.17/5.51 = one ) ).
% 5.17/5.51
% 5.17/5.51 % semiring_norm(26)
% 5.17/5.51 thf(fact_8987_nat__minus__add__max,axiom,
% 5.17/5.51 ! [N: nat,M: nat] :
% 5.17/5.51 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.17/5.51 = ( ord_max_nat @ N @ M ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_minus_add_max
% 5.17/5.51 thf(fact_8988_semiring__norm_I27_J,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( bitM @ ( bit0 @ N ) )
% 5.17/5.51 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % semiring_norm(27)
% 5.17/5.51 thf(fact_8989_semiring__norm_I28_J,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( bitM @ ( bit1 @ N ) )
% 5.17/5.51 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % semiring_norm(28)
% 5.17/5.51 thf(fact_8990_or__not__num__neg_Osimps_I5_J,axiom,
% 5.17/5.51 ! [N: num,M: num] :
% 5.17/5.51 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.17/5.51 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % or_not_num_neg.simps(5)
% 5.17/5.51 thf(fact_8991_inc__BitM__eq,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( inc @ ( bitM @ N ) )
% 5.17/5.51 = ( bit0 @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % inc_BitM_eq
% 5.17/5.51 thf(fact_8992_or__not__num__neg_Osimps_I9_J,axiom,
% 5.17/5.51 ! [N: num,M: num] :
% 5.17/5.51 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.17/5.51 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % or_not_num_neg.simps(9)
% 5.17/5.51 thf(fact_8993_BitM__inc__eq,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( bitM @ ( inc @ N ) )
% 5.17/5.51 = ( bit1 @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % BitM_inc_eq
% 5.17/5.51 thf(fact_8994_eval__nat__numeral_I2_J,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.17/5.51 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eval_nat_numeral(2)
% 5.17/5.51 thf(fact_8995_one__plus__BitM,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.17/5.51 = ( bit0 @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % one_plus_BitM
% 5.17/5.51 thf(fact_8996_BitM__plus__one,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.17/5.51 = ( bit0 @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % BitM_plus_one
% 5.17/5.51 thf(fact_8997_or__not__num__neg_Osimps_I8_J,axiom,
% 5.17/5.51 ! [N: num,M: num] :
% 5.17/5.51 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.17/5.51 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % or_not_num_neg.simps(8)
% 5.17/5.51 thf(fact_8998_or__not__num__neg_Oelims,axiom,
% 5.17/5.51 ! [X: num,Xa: num,Y4: num] :
% 5.17/5.51 ( ( ( bit_or_not_num_neg @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( X = one )
% 5.17/5.51 => ( ( Xa = one )
% 5.17/5.51 => ( Y4 != one ) ) )
% 5.17/5.51 => ( ( ( X = one )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit0 @ M4 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bit1 @ M4 ) ) ) )
% 5.17/5.51 => ( ( ( X = one )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bit1 @ M4 ) ) ) )
% 5.17/5.51 => ( ( ? [N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( bit0 @ N2 ) )
% 5.17/5.51 => ( ( Xa = one )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bit0 @ one ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit0 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit0 @ M4 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit0 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 5.17/5.51 => ( ( ? [N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( bit1 @ N2 ) )
% 5.17/5.51 => ( ( Xa = one )
% 5.17/5.51 => ( Y4 != one ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit1 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit0 @ M4 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) )
% 5.17/5.51 => ~ ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit1 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % or_not_num_neg.elims
% 5.17/5.51 thf(fact_8999_root__powr__inverse,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( root @ N @ X )
% 5.17/5.51 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % root_powr_inverse
% 5.17/5.51 thf(fact_9000_xor__minus__numerals_I2_J,axiom,
% 5.17/5.51 ! [K: int,N: num] :
% 5.17/5.51 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.51 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % xor_minus_numerals(2)
% 5.17/5.51 thf(fact_9001_xor__minus__numerals_I1_J,axiom,
% 5.17/5.51 ! [N: num,K: int] :
% 5.17/5.51 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.17/5.51 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % xor_minus_numerals(1)
% 5.17/5.51 thf(fact_9002_real__root__zero,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( root @ N @ zero_zero_real )
% 5.17/5.51 = zero_zero_real ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_zero
% 5.17/5.51 thf(fact_9003_real__root__Suc__0,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.17/5.51 = X ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_Suc_0
% 5.17/5.51 thf(fact_9004_root__0,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( root @ zero_zero_nat @ X )
% 5.17/5.51 = zero_zero_real ) ).
% 5.17/5.51
% 5.17/5.51 % root_0
% 5.17/5.51 thf(fact_9005_real__root__eq__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ( root @ N @ X )
% 5.17/5.51 = ( root @ N @ Y4 ) )
% 5.17/5.51 = ( X = Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_eq_iff
% 5.17/5.51 thf(fact_9006_real__root__eq__0__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ( root @ N @ X )
% 5.17/5.51 = zero_zero_real )
% 5.17/5.51 = ( X = zero_zero_real ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_eq_0_iff
% 5.17/5.51 thf(fact_9007_real__root__less__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) )
% 5.17/5.51 = ( ord_less_real @ X @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_less_iff
% 5.17/5.51 thf(fact_9008_real__root__le__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) )
% 5.17/5.51 = ( ord_less_eq_real @ X @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_le_iff
% 5.17/5.51 thf(fact_9009_real__root__one,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( root @ N @ one_one_real )
% 5.17/5.51 = one_one_real ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_one
% 5.17/5.51 thf(fact_9010_real__root__eq__1__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ( root @ N @ X )
% 5.17/5.51 = one_one_real )
% 5.17/5.51 = ( X = one_one_real ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_eq_1_iff
% 5.17/5.51 thf(fact_9011_real__root__gt__0__iff,axiom,
% 5.17/5.51 ! [N: nat,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y4 ) )
% 5.17/5.51 = ( ord_less_real @ zero_zero_real @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_gt_0_iff
% 5.17/5.51 thf(fact_9012_real__root__lt__0__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.17/5.51 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_lt_0_iff
% 5.17/5.51 thf(fact_9013_real__root__ge__0__iff,axiom,
% 5.17/5.51 ! [N: nat,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y4 ) )
% 5.17/5.51 = ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_ge_0_iff
% 5.17/5.51 thf(fact_9014_real__root__le__0__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.17/5.51 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_le_0_iff
% 5.17/5.51 thf(fact_9015_real__root__gt__1__iff,axiom,
% 5.17/5.51 ! [N: nat,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y4 ) )
% 5.17/5.51 = ( ord_less_real @ one_one_real @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_gt_1_iff
% 5.17/5.51 thf(fact_9016_real__root__lt__1__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 5.17/5.51 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_lt_1_iff
% 5.17/5.51 thf(fact_9017_real__root__ge__1__iff,axiom,
% 5.17/5.51 ! [N: nat,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y4 ) )
% 5.17/5.51 = ( ord_less_eq_real @ one_one_real @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_ge_1_iff
% 5.17/5.51 thf(fact_9018_real__root__le__1__iff,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 5.17/5.51 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_le_1_iff
% 5.17/5.51 thf(fact_9019_real__root__pow__pos2,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.17/5.51 = X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_pow_pos2
% 5.17/5.51 thf(fact_9020_real__root__inverse,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 5.17/5.51 = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_inverse
% 5.17/5.51 thf(fact_9021_real__root__mult__exp,axiom,
% 5.17/5.51 ! [M: nat,N: nat,X: real] :
% 5.17/5.51 ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 5.17/5.51 = ( root @ M @ ( root @ N @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_mult_exp
% 5.17/5.51 thf(fact_9022_real__root__mult,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( root @ N @ ( times_times_real @ X @ Y4 ) )
% 5.17/5.51 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_mult
% 5.17/5.51 thf(fact_9023_real__root__minus,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 5.17/5.51 = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_minus
% 5.17/5.51 thf(fact_9024_real__root__commute,axiom,
% 5.17/5.51 ! [M: nat,N: nat,X: real] :
% 5.17/5.51 ( ( root @ M @ ( root @ N @ X ) )
% 5.17/5.51 = ( root @ N @ ( root @ M @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_commute
% 5.17/5.51 thf(fact_9025_real__root__divide,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( root @ N @ ( divide_divide_real @ X @ Y4 ) )
% 5.17/5.51 = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_divide
% 5.17/5.51 thf(fact_9026_real__root__pos__pos__le,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_pos_pos_le
% 5.17/5.51 thf(fact_9027_real__root__less__mono,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ X @ Y4 )
% 5.17/5.51 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_less_mono
% 5.17/5.51 thf(fact_9028_real__root__le__mono,axiom,
% 5.17/5.51 ! [N: nat,X: real,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ X @ Y4 )
% 5.17/5.51 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_le_mono
% 5.17/5.51 thf(fact_9029_real__root__power,axiom,
% 5.17/5.51 ! [N: nat,X: real,K: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 5.17/5.51 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_power
% 5.17/5.51 thf(fact_9030_real__root__abs,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 5.17/5.51 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_abs
% 5.17/5.51 thf(fact_9031_sgn__root,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 5.17/5.51 = ( sgn_sgn_real @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sgn_root
% 5.17/5.51 thf(fact_9032_real__root__gt__zero,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_gt_zero
% 5.17/5.51 thf(fact_9033_real__root__strict__decreasing,axiom,
% 5.17/5.51 ! [N: nat,N5: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_nat @ N @ N5 )
% 5.17/5.51 => ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.51 => ( ord_less_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_strict_decreasing
% 5.17/5.51 thf(fact_9034_sqrt__def,axiom,
% 5.17/5.51 ( sqrt
% 5.17/5.51 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sqrt_def
% 5.17/5.51 thf(fact_9035_root__abs__power,axiom,
% 5.17/5.51 ! [N: nat,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y4 @ N ) ) )
% 5.17/5.51 = ( abs_abs_real @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % root_abs_power
% 5.17/5.51 thf(fact_9036_real__root__pos__pos,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_pos_pos
% 5.17/5.51 thf(fact_9037_real__root__strict__increasing,axiom,
% 5.17/5.51 ! [N: nat,N5: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_nat @ N @ N5 )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.51 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_strict_increasing
% 5.17/5.51 thf(fact_9038_real__root__decreasing,axiom,
% 5.17/5.51 ! [N: nat,N5: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.51 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.17/5.51 => ( ord_less_eq_real @ ( root @ N5 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_decreasing
% 5.17/5.51 thf(fact_9039_real__root__pow__pos,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.17/5.51 = X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_pow_pos
% 5.17/5.51 thf(fact_9040_real__root__pos__unique,axiom,
% 5.17/5.51 ! [N: nat,Y4: real,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.17/5.51 => ( ( ( power_power_real @ Y4 @ N )
% 5.17/5.51 = X )
% 5.17/5.51 => ( ( root @ N @ X )
% 5.17/5.51 = Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_pos_unique
% 5.17/5.51 thf(fact_9041_real__root__power__cancel,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.17/5.51 = X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_power_cancel
% 5.17/5.51 thf(fact_9042_odd__real__root__pow,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.51 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.17/5.51 = X ) ) ).
% 5.17/5.51
% 5.17/5.51 % odd_real_root_pow
% 5.17/5.51 thf(fact_9043_odd__real__root__unique,axiom,
% 5.17/5.51 ! [N: nat,Y4: real,X: real] :
% 5.17/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.51 => ( ( ( power_power_real @ Y4 @ N )
% 5.17/5.51 = X )
% 5.17/5.51 => ( ( root @ N @ X )
% 5.17/5.51 = Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % odd_real_root_unique
% 5.17/5.51 thf(fact_9044_odd__real__root__power__cancel,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.51 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.17/5.51 = X ) ) ).
% 5.17/5.51
% 5.17/5.51 % odd_real_root_power_cancel
% 5.17/5.51 thf(fact_9045_real__root__increasing,axiom,
% 5.17/5.51 ! [N: nat,N5: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.17/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.51 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N5 @ X ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % real_root_increasing
% 5.17/5.51 thf(fact_9046_sub__BitM__One__eq,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.17/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sub_BitM_One_eq
% 5.17/5.51 thf(fact_9047_root__sgn__power,axiom,
% 5.17/5.51 ! [N: nat,Y4: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) ) )
% 5.17/5.51 = Y4 ) ) ).
% 5.17/5.51
% 5.17/5.51 % root_sgn_power
% 5.17/5.51 thf(fact_9048_sgn__power__root,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 5.17/5.51 = X ) ) ).
% 5.17/5.51
% 5.17/5.51 % sgn_power_root
% 5.17/5.51 thf(fact_9049_ln__root,axiom,
% 5.17/5.51 ! [N: nat,B: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.51 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.17/5.51 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % ln_root
% 5.17/5.51 thf(fact_9050_log__root,axiom,
% 5.17/5.51 ! [N: nat,A: real,B: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.17/5.51 => ( ( log @ B @ ( root @ N @ A ) )
% 5.17/5.51 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % log_root
% 5.17/5.51 thf(fact_9051_log__base__root,axiom,
% 5.17/5.51 ! [N: nat,B: real,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.17/5.51 => ( ( log @ ( root @ N @ B ) @ X )
% 5.17/5.51 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % log_base_root
% 5.17/5.51 thf(fact_9052_split__root,axiom,
% 5.17/5.51 ! [P: real > $o,N: nat,X: real] :
% 5.17/5.51 ( ( P @ ( root @ N @ X ) )
% 5.17/5.51 = ( ( ( N = zero_zero_nat )
% 5.17/5.51 => ( P @ zero_zero_real ) )
% 5.17/5.51 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ! [Y6: real] :
% 5.17/5.51 ( ( ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 5.17/5.51 = X )
% 5.17/5.51 => ( P @ Y6 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % split_root
% 5.17/5.51 thf(fact_9053_VEBT__internal_Ocnt_Osimps_I2_J,axiom,
% 5.17/5.51 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.17/5.51 ( ( vEBT_VEBT_cnt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.17/5.51 = ( 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 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.cnt.simps(2)
% 5.17/5.51 thf(fact_9054_VEBT_Oinject_I1_J,axiom,
% 5.17/5.51 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.17/5.51 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.17/5.51 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.17/5.51 = ( ( X11 = Y11 )
% 5.17/5.51 & ( X12 = Y12 )
% 5.17/5.51 & ( X13 = Y13 )
% 5.17/5.51 & ( X14 = Y14 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.inject(1)
% 5.17/5.51 thf(fact_9055_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.17/5.51 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.17/5.51 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.simps(2)
% 5.17/5.51 thf(fact_9056_both__member__options__ding,axiom,
% 5.17/5.51 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.17/5.51 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.17/5.51 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.17/5.51 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % both_member_options_ding
% 5.17/5.51 thf(fact_9057_VEBT__internal_Ospace_Osimps_I2_J,axiom,
% 5.17/5.51 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.17/5.51 ( ( vEBT_VEBT_space @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.17/5.51 = ( 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 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space.simps(2)
% 5.17/5.51 thf(fact_9058_VEBT__internal_Ospace_H_Osimps_I2_J,axiom,
% 5.17/5.51 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.17/5.51 ( ( vEBT_VEBT_space2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 5.17/5.51 = ( 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 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space'.simps(2)
% 5.17/5.51 thf(fact_9059_both__member__options__def,axiom,
% 5.17/5.51 ( vEBT_V8194947554948674370ptions
% 5.17/5.51 = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 5.17/5.51 ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 5.17/5.51 | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % both_member_options_def
% 5.17/5.51 thf(fact_9060_VEBT_Oinject_I2_J,axiom,
% 5.17/5.51 ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 5.17/5.51 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.17/5.51 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 5.17/5.51 = ( ( X21 = Y21 )
% 5.17/5.51 & ( X222 = Y22 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.inject(2)
% 5.17/5.51 thf(fact_9061_VEBT__internal_Ospace_H_Ocases,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT] :
% 5.17/5.51 ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space'.cases
% 5.17/5.51 thf(fact_9062_VEBT_Oexhaust,axiom,
% 5.17/5.51 ! [Y4: vEBT_VEBT] :
% 5.17/5.51 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.17/5.51 ( Y4
% 5.17/5.51 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.17/5.51 => ~ ! [X212: $o,X223: $o] :
% 5.17/5.51 ( Y4
% 5.17/5.51 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.exhaust
% 5.17/5.51 thf(fact_9063_VEBT_Odistinct_I1_J,axiom,
% 5.17/5.51 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.17/5.51 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.17/5.51 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.distinct(1)
% 5.17/5.51 thf(fact_9064_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.17/5.51 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.17/5.51 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.simps(1)
% 5.17/5.51 thf(fact_9065_VEBT_Osize_I4_J,axiom,
% 5.17/5.51 ! [X21: $o,X222: $o] :
% 5.17/5.51 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.17/5.51 = zero_zero_nat ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.size(4)
% 5.17/5.51 thf(fact_9066_vebt__buildup_Osimps_I1_J,axiom,
% 5.17/5.51 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.17/5.51 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.17/5.51
% 5.17/5.51 % vebt_buildup.simps(1)
% 5.17/5.51 thf(fact_9067_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.17/5.51 ! [Uu: $o,Uv: $o,D: nat] :
% 5.17/5.51 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.17/5.51 = ( D = one_one_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.valid'.simps(1)
% 5.17/5.51 thf(fact_9068_VEBT__internal_Ocnt_Osimps_I1_J,axiom,
% 5.17/5.51 ! [A: $o,B: $o] :
% 5.17/5.51 ( ( vEBT_VEBT_cnt @ ( vEBT_Leaf @ A @ B ) )
% 5.17/5.51 = one_one_real ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.cnt.simps(1)
% 5.17/5.51 thf(fact_9069_invar__vebt_Ointros_I1_J,axiom,
% 5.17/5.51 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.intros(1)
% 5.17/5.51 thf(fact_9070_vebt__buildup_Osimps_I2_J,axiom,
% 5.17/5.51 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.17/5.51 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.17/5.51
% 5.17/5.51 % vebt_buildup.simps(2)
% 5.17/5.51 thf(fact_9071_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.17/5.51 ! [A: $o,B: $o,X: nat] :
% 5.17/5.51 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.17/5.51 = ( ( ( X = zero_zero_nat )
% 5.17/5.51 => A )
% 5.17/5.51 & ( ( X != zero_zero_nat )
% 5.17/5.51 => ( ( ( X = one_one_nat )
% 5.17/5.51 => B )
% 5.17/5.51 & ( X = one_one_nat ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.simps(1)
% 5.17/5.51 thf(fact_9072_VEBT__internal_Ospace_H_Osimps_I1_J,axiom,
% 5.17/5.51 ! [A: $o,B: $o] :
% 5.17/5.51 ( ( vEBT_VEBT_space2 @ ( vEBT_Leaf @ A @ B ) )
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space'.simps(1)
% 5.17/5.51 thf(fact_9073_VEBT__internal_Ospace_Osimps_I1_J,axiom,
% 5.17/5.51 ! [A: $o,B: $o] :
% 5.17/5.51 ( ( vEBT_VEBT_space @ ( vEBT_Leaf @ A @ B ) )
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space.simps(1)
% 5.17/5.51 thf(fact_9074_VEBT__internal_Ospace_H_Oelims,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_VEBT_space2 @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ? [A4: $o,B3: $o] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space'.elims
% 5.17/5.51 thf(fact_9075_VEBT__internal_Ospace_Oelims,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_VEBT_space @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ? [A4: $o,B3: $o] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space.elims
% 5.17/5.51 thf(fact_9076_VEBT__internal_Ocnt_Oelims,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Y4: real] :
% 5.17/5.51 ( ( ( vEBT_VEBT_cnt @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ? [A4: $o,B3: $o] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( Y4 != one_one_real ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.cnt.elims
% 5.17/5.51 thf(fact_9077_in__children__def,axiom,
% 5.17/5.51 ( vEBT_V5917875025757280293ildren
% 5.17/5.51 = ( ^ [N4: nat,TreeList3: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X3 @ N4 ) ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % in_children_def
% 5.17/5.51 thf(fact_9078_invar__vebt_Ointros_I3_J,axiom,
% 5.17/5.51 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.17/5.51 ( ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( M
% 5.17/5.51 = ( suc @ N ) )
% 5.17/5.51 => ( ( Deg
% 5.17/5.51 = ( plus_plus_nat @ N @ M ) )
% 5.17/5.51 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.17/5.51 => ( ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.intros(3)
% 5.17/5.51 thf(fact_9079_VEBT__internal_Ospace_Opelims,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_VEBT_space @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ X )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) )
% 5.17/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space.pelims
% 5.17/5.51 thf(fact_9080_invar__vebt_Ointros_I2_J,axiom,
% 5.17/5.51 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.17/5.51 ( ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( M = N )
% 5.17/5.51 => ( ( Deg
% 5.17/5.51 = ( plus_plus_nat @ N @ M ) )
% 5.17/5.51 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.17/5.51 => ( ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.intros(2)
% 5.17/5.51 thf(fact_9081_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.17/5.51 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.17/5.51 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.simps(2)
% 5.17/5.51 thf(fact_9082_VEBT__internal_Ospace_H_Opelims,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_VEBT_space2 @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ X )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 5.17/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.space'.pelims
% 5.17/5.51 thf(fact_9083_VEBT__internal_Ocnt_Opelims,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Y4: real] :
% 5.17/5.51 ( ( ( vEBT_VEBT_cnt @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ X )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( Y4 = one_one_real )
% 5.17/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Leaf @ A4 @ B3 ) ) ) )
% 5.17/5.51 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) )
% 5.17/5.51 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.cnt.pelims
% 5.17/5.51 thf(fact_9084_mi__ma__2__deg,axiom,
% 5.17/5.51 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.17/5.51 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.17/5.51 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.17/5.51 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % mi_ma_2_deg
% 5.17/5.51 thf(fact_9085_both__member__options__from__complete__tree__to__child,axiom,
% 5.17/5.51 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.17/5.51 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 5.17/5.51 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 | ( X = Mi )
% 5.17/5.51 | ( X = Ma ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % both_member_options_from_complete_tree_to_child
% 5.17/5.51 thf(fact_9086_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.17/5.51 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.17/5.51 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.17/5.51 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.17/5.51 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % both_member_options_from_chilf_to_complete_tree
% 5.17/5.51 thf(fact_9087_prod__decode__aux_Ocases,axiom,
% 5.17/5.51 ! [X: product_prod_nat_nat] :
% 5.17/5.51 ~ ! [K2: nat,M4: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_nat_nat @ K2 @ M4 ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_decode_aux.cases
% 5.17/5.51 thf(fact_9088_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.17/5.51 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.17/5.51 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 5.17/5.51 = ( ( X = Mi )
% 5.17/5.51 | ( X = Ma ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.simps(3)
% 5.17/5.51 thf(fact_9089_invar__vebt_Ointros_I4_J,axiom,
% 5.17/5.51 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.17/5.51 ( ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( M = N )
% 5.17/5.51 => ( ( Deg
% 5.17/5.51 = ( plus_plus_nat @ N @ M ) )
% 5.17/5.51 => ( ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X8 ) )
% 5.17/5.51 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.17/5.51 => ( ( ( Mi = Ma )
% 5.17/5.51 => ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 5.17/5.51 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.17/5.51 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.17/5.51 => ( ( ( Mi != Ma )
% 5.17/5.51 => ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.17/5.51 = I3 )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.17/5.51 & ! [X4: nat] :
% 5.17/5.51 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.17/5.51 = I3 )
% 5.17/5.51 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.17/5.51 => ( ( ord_less_nat @ Mi @ X4 )
% 5.17/5.51 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.intros(4)
% 5.17/5.51 thf(fact_9090_invar__vebt_Ointros_I5_J,axiom,
% 5.17/5.51 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.17/5.51 ( ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( M
% 5.17/5.51 = ( suc @ N ) )
% 5.17/5.51 => ( ( Deg
% 5.17/5.51 = ( plus_plus_nat @ N @ M ) )
% 5.17/5.51 => ( ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X8 ) )
% 5.17/5.51 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.17/5.51 => ( ( ( Mi = Ma )
% 5.17/5.51 => ! [X4: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.51 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_1 ) ) )
% 5.17/5.51 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.17/5.51 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.17/5.51 => ( ( ( Mi != Ma )
% 5.17/5.51 => ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.17/5.51 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.17/5.51 = I3 )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.17/5.51 & ! [X4: nat] :
% 5.17/5.51 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.17/5.51 = I3 )
% 5.17/5.51 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.17/5.51 => ( ( ord_less_nat @ Mi @ X4 )
% 5.17/5.51 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.intros(5)
% 5.17/5.51 thf(fact_9091_invar__vebt_Ocases,axiom,
% 5.17/5.51 ! [A1: vEBT_VEBT,A22: nat] :
% 5.17/5.51 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 5.17/5.51 => ( ( ? [A4: $o,B3: $o] :
% 5.17/5.51 ( A1
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( A22
% 5.17/5.51 != ( suc @ zero_zero_nat ) ) )
% 5.17/5.51 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.17/5.51 ( ( A1
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( A22 = Deg2 )
% 5.17/5.51 => ( ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( M4 = N2 )
% 5.17/5.51 => ( ( Deg2
% 5.17/5.51 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.17/5.51 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.17/5.51 => ~ ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.17/5.51 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.17/5.51 ( ( A1
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( A22 = Deg2 )
% 5.17/5.51 => ( ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( M4
% 5.17/5.51 = ( suc @ N2 ) )
% 5.17/5.51 => ( ( Deg2
% 5.17/5.51 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.17/5.51 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.17/5.51 => ~ ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.17/5.51 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.17/5.51 ( ( A1
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( A22 = Deg2 )
% 5.17/5.51 => ( ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( M4 = N2 )
% 5.17/5.51 => ( ( Deg2
% 5.17/5.51 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.17/5.51 => ( ! [I4: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 5.17/5.51 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.17/5.51 => ( ( ( Mi2 = Ma2 )
% 5.17/5.51 => ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.17/5.51 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.17/5.51 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.51 => ~ ( ( Mi2 != Ma2 )
% 5.17/5.51 => ! [I4: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 5.17/5.51 = I4 )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 5.17/5.51 & ! [X5: nat] :
% 5.17/5.51 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 5.17/5.51 = I4 )
% 5.17/5.51 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 5.17/5.51 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.17/5.51 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.17/5.51 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.17/5.51 ( ( A1
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.51 => ( ( A22 = Deg2 )
% 5.17/5.51 => ( ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.17/5.51 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.17/5.51 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( M4
% 5.17/5.51 = ( suc @ N2 ) )
% 5.17/5.51 => ( ( Deg2
% 5.17/5.51 = ( plus_plus_nat @ N2 @ M4 ) )
% 5.17/5.51 => ( ! [I4: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 5.17/5.51 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.17/5.51 => ( ( ( Mi2 = Ma2 )
% 5.17/5.51 => ! [X5: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.51 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.17/5.51 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.17/5.51 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.51 => ~ ( ( Mi2 != Ma2 )
% 5.17/5.51 => ! [I4: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.17/5.51 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 5.17/5.51 = I4 )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 5.17/5.51 & ! [X5: nat] :
% 5.17/5.51 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 5.17/5.51 = I4 )
% 5.17/5.51 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 5.17/5.51 => ( ( ord_less_nat @ Mi2 @ X5 )
% 5.17/5.51 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.cases
% 5.17/5.51 thf(fact_9092_invar__vebt_Osimps,axiom,
% 5.17/5.51 ( vEBT_invar_vebt
% 5.17/5.51 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.17/5.51 ( ( ? [A3: $o,B2: $o] :
% 5.17/5.51 ( A12
% 5.17/5.51 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.17/5.51 & ( A23
% 5.17/5.51 = ( suc @ zero_zero_nat ) ) )
% 5.17/5.51 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 5.17/5.51 ( ( A12
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.17/5.51 & ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.17/5.51 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 5.17/5.51 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.17/5.51 & ( A23
% 5.17/5.51 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.17/5.51 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 5.17/5.51 & ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.51 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT] :
% 5.17/5.51 ( ( A12
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.17/5.51 & ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.17/5.51 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 5.17/5.51 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.17/5.51 & ( A23
% 5.17/5.51 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.17/5.51 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 5.17/5.51 & ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.51 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.17/5.51 ( ( A12
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.17/5.51 & ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.17/5.51 & ( vEBT_invar_vebt @ Summary3 @ N4 )
% 5.17/5.51 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.17/5.51 & ( A23
% 5.17/5.51 = ( plus_plus_nat @ N4 @ N4 ) )
% 5.17/5.51 & ! [I2: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.17/5.51 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X8 ) )
% 5.17/5.51 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.17/5.51 & ( ( Mi3 = Ma3 )
% 5.17/5.51 => ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.51 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.51 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.17/5.51 & ( ( Mi3 != Ma3 )
% 5.17/5.51 => ! [I2: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 5.17/5.51 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.17/5.51 = I2 )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.17/5.51 & ! [X3: nat] :
% 5.17/5.51 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 5.17/5.51 = I2 )
% 5.17/5.51 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 5.17/5.51 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.51 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) )
% 5.17/5.51 | ? [TreeList3: list_VEBT_VEBT,N4: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.17/5.51 ( ( A12
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.17/5.51 & ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ( vEBT_invar_vebt @ X3 @ N4 ) )
% 5.17/5.51 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N4 ) )
% 5.17/5.51 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.17/5.51 & ( A23
% 5.17/5.51 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 5.17/5.51 & ! [I2: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.17/5.51 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X8 ) )
% 5.17/5.51 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I2 ) ) )
% 5.17/5.51 & ( ( Mi3 = Ma3 )
% 5.17/5.51 => ! [X3: vEBT_VEBT] :
% 5.17/5.51 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.17/5.51 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.51 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.51 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.17/5.51 & ( ( Mi3 != Ma3 )
% 5.17/5.51 => ! [I2: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 5.17/5.51 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 5.17/5.51 = I2 )
% 5.17/5.51 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 5.17/5.51 & ! [X3: nat] :
% 5.17/5.51 ( ( ( ( vEBT_VEBT_high @ X3 @ N4 )
% 5.17/5.51 = I2 )
% 5.17/5.51 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N4 ) ) )
% 5.17/5.51 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.51 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % invar_vebt.simps
% 5.17/5.51 thf(fact_9093_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.17/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.17/5.51 ( ! [Uu2: $o,Uv2: $o,D2: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D2 ) )
% 5.17/5.51 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.valid'.cases
% 5.17/5.51 thf(fact_9094_xor__num_Ocases,axiom,
% 5.17/5.51 ! [X: product_prod_num_num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 != ( product_Pair_num_num @ one @ one ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) )
% 5.17/5.51 => ( ! [M4: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.17/5.51 => ( ! [M4: num,N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) )
% 5.17/5.51 => ( ! [M4: num,N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) )
% 5.17/5.51 => ( ! [M4: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.17/5.51 => ( ! [M4: num,N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) )
% 5.17/5.51 => ~ ! [M4: num,N2: num] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % xor_num.cases
% 5.17/5.51 thf(fact_9095_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.17/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.17/5.51 ( ! [A4: $o,B3: $o,X4: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X4 ) )
% 5.17/5.51 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT,X4: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) @ X4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.cases
% 5.17/5.51 thf(fact_9096_VEBT__internal_Omembermima_Ocases,axiom,
% 5.17/5.51 ! [X: produc9072475918466114483BT_nat] :
% 5.17/5.51 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.17/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X4 ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X4: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ X4 ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X4: nat] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ X4 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.cases
% 5.17/5.51 thf(fact_9097_neg__eucl__rel__int__mult__2,axiom,
% 5.17/5.51 ! [B: int,A: int,Q2: int,R2: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.17/5.51 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( 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 ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % neg_eucl_rel_int_mult_2
% 5.17/5.51 thf(fact_9098_Divides_Oadjust__div__eq,axiom,
% 5.17/5.51 ! [Q2: int,R2: int] :
% 5.17/5.51 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Divides.adjust_div_eq
% 5.17/5.51 thf(fact_9099_numeral__div__minus__numeral,axiom,
% 5.17/5.51 ! [M: num,N: num] :
% 5.17/5.51 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % numeral_div_minus_numeral
% 5.17/5.51 thf(fact_9100_minus__numeral__div__numeral,axiom,
% 5.17/5.51 ! [M: num,N: num] :
% 5.17/5.51 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % minus_numeral_div_numeral
% 5.17/5.51 thf(fact_9101_one__div__minus__numeral,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % one_div_minus_numeral
% 5.17/5.51 thf(fact_9102_minus__one__div__numeral,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % minus_one_div_numeral
% 5.17/5.51 thf(fact_9103_divmod__BitM__2__eq,axiom,
% 5.17/5.51 ! [M: num] :
% 5.17/5.51 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.17/5.51 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_BitM_2_eq
% 5.17/5.51 thf(fact_9104_unique__quotient,axiom,
% 5.17/5.51 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.17/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.17/5.51 => ( Q2 = Q5 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % unique_quotient
% 5.17/5.51 thf(fact_9105_unique__remainder,axiom,
% 5.17/5.51 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 5.17/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 5.17/5.51 => ( R2 = R4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % unique_remainder
% 5.17/5.51 thf(fact_9106_eucl__rel__int__by0,axiom,
% 5.17/5.51 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int_by0
% 5.17/5.51 thf(fact_9107_div__int__unique,axiom,
% 5.17/5.51 ! [K: int,L: int,Q2: int,R2: int] :
% 5.17/5.51 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( ( divide_divide_int @ K @ L )
% 5.17/5.51 = Q2 ) ) ).
% 5.17/5.51
% 5.17/5.51 % div_int_unique
% 5.17/5.51 thf(fact_9108_mod__int__unique,axiom,
% 5.17/5.51 ! [K: int,L: int,Q2: int,R2: int] :
% 5.17/5.51 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( ( modulo_modulo_int @ K @ L )
% 5.17/5.51 = R2 ) ) ).
% 5.17/5.51
% 5.17/5.51 % mod_int_unique
% 5.17/5.51 thf(fact_9109_eucl__rel__int__dividesI,axiom,
% 5.17/5.51 ! [L: int,K: int,Q2: int] :
% 5.17/5.51 ( ( L != zero_zero_int )
% 5.17/5.51 => ( ( K
% 5.17/5.51 = ( times_times_int @ Q2 @ L ) )
% 5.17/5.51 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int_dividesI
% 5.17/5.51 thf(fact_9110_eucl__rel__int,axiom,
% 5.17/5.51 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int
% 5.17/5.51 thf(fact_9111_divmod__int__def,axiom,
% 5.17/5.51 ( unique5052692396658037445od_int
% 5.17/5.51 = ( ^ [M5: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_int_def
% 5.17/5.51 thf(fact_9112_divmod_H__nat__def,axiom,
% 5.17/5.51 ( unique5055182867167087721od_nat
% 5.17/5.51 = ( ^ [M5: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod'_nat_def
% 5.17/5.51 thf(fact_9113_zminus1__lemma,axiom,
% 5.17/5.51 ! [A: int,B: int,Q2: int,R2: int] :
% 5.17/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( ( B != zero_zero_int )
% 5.17/5.51 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % zminus1_lemma
% 5.17/5.51 thf(fact_9114_eucl__rel__int__iff,axiom,
% 5.17/5.51 ! [K: int,L: int,Q2: int,R2: int] :
% 5.17/5.51 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 = ( ( K
% 5.17/5.51 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R2 ) )
% 5.17/5.51 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.17/5.51 & ( ord_less_int @ R2 @ L ) ) )
% 5.17/5.51 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.17/5.51 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.17/5.51 => ( ( ord_less_int @ L @ R2 )
% 5.17/5.51 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.17/5.51 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.17/5.51 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int_iff
% 5.17/5.51 thf(fact_9115_eucl__rel__int__remainderI,axiom,
% 5.17/5.51 ! [R2: int,L: int,K: int,Q2: int] :
% 5.17/5.51 ( ( ( sgn_sgn_int @ R2 )
% 5.17/5.51 = ( sgn_sgn_int @ L ) )
% 5.17/5.51 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 5.17/5.51 => ( ( K
% 5.17/5.51 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R2 ) )
% 5.17/5.51 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int_remainderI
% 5.17/5.51 thf(fact_9116_eucl__rel__int_Osimps,axiom,
% 5.17/5.51 ( eucl_rel_int
% 5.17/5.51 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 5.17/5.51 ( ? [K3: int] :
% 5.17/5.51 ( ( A12 = K3 )
% 5.17/5.51 & ( A23 = zero_zero_int )
% 5.17/5.51 & ( A32
% 5.17/5.51 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.17/5.51 | ? [L3: int,K3: int,Q3: int] :
% 5.17/5.51 ( ( A12 = K3 )
% 5.17/5.51 & ( A23 = L3 )
% 5.17/5.51 & ( A32
% 5.17/5.51 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.17/5.51 & ( L3 != zero_zero_int )
% 5.17/5.51 & ( K3
% 5.17/5.51 = ( times_times_int @ Q3 @ L3 ) ) )
% 5.17/5.51 | ? [R5: int,L3: int,K3: int,Q3: int] :
% 5.17/5.51 ( ( A12 = K3 )
% 5.17/5.51 & ( A23 = L3 )
% 5.17/5.51 & ( A32
% 5.17/5.51 = ( product_Pair_int_int @ Q3 @ R5 ) )
% 5.17/5.51 & ( ( sgn_sgn_int @ R5 )
% 5.17/5.51 = ( sgn_sgn_int @ L3 ) )
% 5.17/5.51 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L3 ) )
% 5.17/5.51 & ( K3
% 5.17/5.51 = ( plus_plus_int @ ( times_times_int @ Q3 @ L3 ) @ R5 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int.simps
% 5.17/5.51 thf(fact_9117_eucl__rel__int_Ocases,axiom,
% 5.17/5.51 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 5.17/5.51 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 5.17/5.51 => ( ( ( A22 = zero_zero_int )
% 5.17/5.51 => ( A33
% 5.17/5.51 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.17/5.51 => ( ! [Q4: int] :
% 5.17/5.51 ( ( A33
% 5.17/5.51 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.17/5.51 => ( ( A22 != zero_zero_int )
% 5.17/5.51 => ( A1
% 5.17/5.51 != ( times_times_int @ Q4 @ A22 ) ) ) )
% 5.17/5.51 => ~ ! [R3: int,Q4: int] :
% 5.17/5.51 ( ( A33
% 5.17/5.51 = ( product_Pair_int_int @ Q4 @ R3 ) )
% 5.17/5.51 => ( ( ( sgn_sgn_int @ R3 )
% 5.17/5.51 = ( sgn_sgn_int @ A22 ) )
% 5.17/5.51 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 5.17/5.51 => ( A1
% 5.17/5.51 != ( plus_plus_int @ ( times_times_int @ Q4 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % eucl_rel_int.cases
% 5.17/5.51 thf(fact_9118_pos__eucl__rel__int__mult__2,axiom,
% 5.17/5.51 ! [B: int,A: int,Q2: int,R2: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.17/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.17/5.51 => ( 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 ) ) @ R2 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % pos_eucl_rel_int_mult_2
% 5.17/5.51 thf(fact_9119_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ~ ( vEBT_VEBT_membermima @ X @ Xa )
% 5.17/5.51 => ( ! [Uu2: $o,Uv2: $o] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat] :
% 5.17/5.51 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.17/5.51 => ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [Vc: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 5.17/5.51 => ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [Vd: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.17/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.elims(3)
% 5.17/5.51 thf(fact_9120_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat,Y4: $o] :
% 5.17/5.51 ( ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.51 => Y4 )
% 5.17/5.51 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.17/5.51 => Y4 )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat] :
% 5.17/5.51 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( ~ ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 ) ) ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [Vc: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( ~ ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [Vd: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.elims(1)
% 5.17/5.51 thf(fact_9121_prod__decode__aux_Osimps,axiom,
% 5.17/5.51 ( nat_prod_decode_aux
% 5.17/5.51 = ( ^ [K3: nat,M5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M5 @ K3 ) @ ( product_Pair_nat_nat @ M5 @ ( minus_minus_nat @ K3 @ M5 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M5 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_decode_aux.simps
% 5.17/5.51 thf(fact_9122_prod__decode__aux_Oelims,axiom,
% 5.17/5.51 ! [X: nat,Xa: nat,Y4: product_prod_nat_nat] :
% 5.17/5.51 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 5.17/5.51 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_decode_aux.elims
% 5.17/5.51 thf(fact_9123_foldr__same,axiom,
% 5.17/5.51 ! [Xs: list_real,Y4: real] :
% 5.17/5.51 ( ! [X4: real,Y: real] :
% 5.17/5.51 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.17/5.51 => ( ( member_real @ Y @ ( set_real2 @ Xs ) )
% 5.17/5.51 => ( X4 = Y ) ) )
% 5.17/5.51 => ( ! [X4: real] :
% 5.17/5.51 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.17/5.51 => ( X4 = Y4 ) )
% 5.17/5.51 => ( ( foldr_real_real @ plus_plus_real @ Xs @ zero_zero_real )
% 5.17/5.51 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs ) ) @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % foldr_same
% 5.17/5.51 thf(fact_9124_foldr__mono,axiom,
% 5.17/5.51 ! [Xs: list_nat,Ys: list_nat,C: nat,D: nat] :
% 5.17/5.51 ( ( ( size_size_list_nat @ Xs )
% 5.17/5.51 = ( size_size_list_nat @ Ys ) )
% 5.17/5.51 => ( ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.17/5.51 => ( ord_less_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Ys @ I3 ) ) )
% 5.17/5.51 => ( ( ord_less_eq_nat @ C @ D )
% 5.17/5.51 => ( 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 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % foldr_mono
% 5.17/5.51 thf(fact_9125_foldr__zero,axiom,
% 5.17/5.51 ! [Xs: list_nat,D: nat] :
% 5.17/5.51 ( ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.17/5.51 => ( ord_less_nat @ zero_zero_nat @ ( nth_nat @ Xs @ I3 ) ) )
% 5.17/5.51 => ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( minus_minus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ D ) @ D ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % foldr_zero
% 5.17/5.51 thf(fact_9126_nat__leq__as__int,axiom,
% 5.17/5.51 ( ord_less_eq_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_leq_as_int
% 5.17/5.51 thf(fact_9127_nat__less__as__int,axiom,
% 5.17/5.51 ( ord_less_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_less_as_int
% 5.17/5.51 thf(fact_9128_nat__plus__as__int,axiom,
% 5.17/5.51 ( plus_plus_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_plus_as_int
% 5.17/5.51 thf(fact_9129_nat__times__as__int,axiom,
% 5.17/5.51 ( times_times_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_times_as_int
% 5.17/5.51 thf(fact_9130_nat__minus__as__int,axiom,
% 5.17/5.51 ( minus_minus_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_minus_as_int
% 5.17/5.51 thf(fact_9131_nat__div__as__int,axiom,
% 5.17/5.51 ( divide_divide_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_div_as_int
% 5.17/5.51 thf(fact_9132_nat__mod__as__int,axiom,
% 5.17/5.51 ( modulo_modulo_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_mod_as_int
% 5.17/5.51 thf(fact_9133_diff__nat__eq__if,axiom,
% 5.17/5.51 ! [Z6: int,Z: int] :
% 5.17/5.51 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 5.17/5.51 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.17/5.51 = ( nat2 @ Z ) ) )
% 5.17/5.51 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 5.17/5.51 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.17/5.51 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % diff_nat_eq_if
% 5.17/5.51 thf(fact_9134_set__decode__def,axiom,
% 5.17/5.51 ( nat_set_decode
% 5.17/5.51 = ( ^ [X3: nat] :
% 5.17/5.51 ( collect_nat
% 5.17/5.51 @ ^ [N4: nat] :
% 5.17/5.51 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_decode_def
% 5.17/5.51 thf(fact_9135_vebt__buildup_Osimps_I3_J,axiom,
% 5.17/5.51 ! [Va2: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % vebt_buildup.simps(3)
% 5.17/5.51 thf(fact_9136_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I3_J,axiom,
% 5.17/5.51 ! [Va2: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(3)
% 5.17/5.51 thf(fact_9137_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I3_J,axiom,
% 5.17/5.51 ! [Va2: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(3)
% 5.17/5.51 thf(fact_9138_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.17/5.51 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 5.17/5.51 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S2 ) @ X )
% 5.17/5.51 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.simps(3)
% 5.17/5.51 thf(fact_9139_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Oelims,axiom,
% 5.17/5.51 ! [X: nat,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( X = zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 => ( ( ( X
% 5.17/5.51 = ( suc @ zero_zero_nat ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 => ~ ! [Va: nat] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.elims
% 5.17/5.51 thf(fact_9140_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Oelims,axiom,
% 5.17/5.51 ! [X: nat,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( X = zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.17/5.51 => ( ( ( X
% 5.17/5.51 = ( suc @ zero_zero_nat ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 5.17/5.51 => ~ ! [Va: nat] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.elims
% 5.17/5.51 thf(fact_9141_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.17/5.51 ! [V: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 5.17/5.51 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd2 ) @ X )
% 5.17/5.51 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.simps(5)
% 5.17/5.51 thf(fact_9142_vebt__buildup_Oelims,axiom,
% 5.17/5.51 ! [X: nat,Y4: vEBT_VEBT] :
% 5.17/5.51 ( ( ( vEBT_vebt_buildup @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( X = zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.17/5.51 => ( ( ( X
% 5.17/5.51 = ( suc @ zero_zero_nat ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.17/5.51 => ~ ! [Va: nat] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( 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 ) ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % vebt_buildup.elims
% 5.17/5.51 thf(fact_9143_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.17/5.51 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X: nat] :
% 5.17/5.51 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ X )
% 5.17/5.51 = ( ( X = Mi )
% 5.17/5.51 | ( X = Ma )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.simps(4)
% 5.17/5.51 thf(fact_9144_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat,Y4: $o] :
% 5.17/5.51 ( ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => A4 )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( ( ( Xa = one_one_nat )
% 5.17/5.51 => B3 )
% 5.17/5.51 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.17/5.51 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.17/5.51 => Y4 )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [S3: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.elims(1)
% 5.17/5.51 thf(fact_9145_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ~ ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => A4 )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( ( ( Xa = one_one_nat )
% 5.17/5.51 => B3 )
% 5.17/5.51 & ( Xa = one_one_nat ) ) ) ) )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [S3: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) )
% 5.17/5.51 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.elims(2)
% 5.17/5.51 thf(fact_9146_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => A4 )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( ( ( Xa = one_one_nat )
% 5.17/5.51 => B3 )
% 5.17/5.51 & ( Xa = one_one_nat ) ) ) ) )
% 5.17/5.51 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [S3: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) )
% 5.17/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.elims(3)
% 5.17/5.51 thf(fact_9147_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat] :
% 5.17/5.51 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.17/5.51 => ~ ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [Vc: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 5.17/5.51 => ~ ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT] :
% 5.17/5.51 ( ? [Vd: vEBT_VEBT] :
% 5.17/5.51 ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.17/5.51 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.elims(2)
% 5.17/5.51 thf(fact_9148_monoseq__arctan__series,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.51 => ( topolo6980174941875973593q_real
% 5.17/5.51 @ ^ [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 @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % monoseq_arctan_series
% 5.17/5.51 thf(fact_9149_ln__series,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.51 => ( ( ln_ln_real @ X )
% 5.17/5.51 = ( suminf_real
% 5.17/5.51 @ ^ [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 @ X @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % ln_series
% 5.17/5.51 thf(fact_9150_monoseq__realpow,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.51 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % monoseq_realpow
% 5.17/5.51 thf(fact_9151_pi__series,axiom,
% 5.17/5.51 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.51 = ( suminf_real
% 5.17/5.51 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % pi_series
% 5.17/5.51 thf(fact_9152_arctan__series,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.51 => ( ( arctan @ X )
% 5.17/5.51 = ( suminf_real
% 5.17/5.51 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % arctan_series
% 5.17/5.51 thf(fact_9153_bij__betw__nth__root__unity,axiom,
% 5.17/5.51 ! [C: complex,N: nat] :
% 5.17/5.51 ( ( C != zero_zero_complex )
% 5.17/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = one_one_complex ) )
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = C ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bij_betw_nth_root_unity
% 5.17/5.51 thf(fact_9154_summable__arctan__series,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.51 => ( summable_real
% 5.17/5.51 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % summable_arctan_series
% 5.17/5.51 thf(fact_9155_summable__rabs__comparison__test,axiom,
% 5.17/5.51 ! [F: nat > real,G: nat > real] :
% 5.17/5.51 ( ? [N7: nat] :
% 5.17/5.51 ! [N2: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ N7 @ N2 )
% 5.17/5.51 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 5.17/5.51 => ( ( summable_real @ G )
% 5.17/5.51 => ( summable_real
% 5.17/5.51 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % summable_rabs_comparison_test
% 5.17/5.51 thf(fact_9156_summable__rabs,axiom,
% 5.17/5.51 ! [F: nat > real] :
% 5.17/5.51 ( ( summable_real
% 5.17/5.51 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) )
% 5.17/5.51 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.17/5.51 @ ( suminf_real
% 5.17/5.51 @ ^ [N4: nat] : ( abs_abs_real @ ( F @ N4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % summable_rabs
% 5.17/5.51 thf(fact_9157_summable__power__series,axiom,
% 5.17/5.51 ! [F: nat > real,Z: real] :
% 5.17/5.51 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.17/5.51 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.17/5.51 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.17/5.51 => ( ( ord_less_real @ Z @ one_one_real )
% 5.17/5.51 => ( summable_real
% 5.17/5.51 @ ^ [I2: nat] : ( times_times_real @ ( F @ I2 ) @ ( power_power_real @ Z @ I2 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % summable_power_series
% 5.17/5.51 thf(fact_9158_sin__paired,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( sums_real
% 5.17/5.51 @ ^ [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 @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.17/5.51 @ ( sin_real @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % sin_paired
% 5.17/5.51 thf(fact_9159_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ~ ( vEBT_VEBT_membermima @ X @ Xa )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.51 => ( ! [Uu2: $o,Uv2: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) )
% 5.17/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.17/5.51 => ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 ) ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ Xa ) )
% 5.17/5.51 => ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ Xa ) )
% 5.17/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.pelims(3)
% 5.17/5.51 thf(fact_9160_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat,Y4: $o] :
% 5.17/5.51 ( ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.51 => ( ! [Uu2: $o,Uv2: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.51 => ( ~ Y4
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.17/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.17/5.51 => ( ~ Y4
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 ) ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ Xa ) ) ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.pelims(1)
% 5.17/5.51 thf(fact_9161_power__half__series,axiom,
% 5.17/5.51 ( sums_real
% 5.17/5.51 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 5.17/5.51 @ one_one_real ) ).
% 5.17/5.51
% 5.17/5.51 % power_half_series
% 5.17/5.51 thf(fact_9162_sums__if_H,axiom,
% 5.17/5.51 ! [G: nat > real,X: real] :
% 5.17/5.51 ( ( sums_real @ G @ X )
% 5.17/5.51 => ( sums_real
% 5.17/5.51 @ ^ [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 ) ) ) ) )
% 5.17/5.51 @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % sums_if'
% 5.17/5.51 thf(fact_9163_sums__if,axiom,
% 5.17/5.51 ! [G: nat > real,X: real,F: nat > real,Y4: real] :
% 5.17/5.51 ( ( sums_real @ G @ X )
% 5.17/5.51 => ( ( sums_real @ F @ Y4 )
% 5.17/5.51 => ( sums_real
% 5.17/5.51 @ ^ [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 ) ) ) ) )
% 5.17/5.51 @ ( plus_plus_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sums_if
% 5.17/5.51 thf(fact_9164_cos__paired,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( sums_real
% 5.17/5.51 @ ^ [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 @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.17/5.51 @ ( cos_real @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % cos_paired
% 5.17/5.51 thf(fact_9165_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ( vEBT_VEBT_membermima @ X @ Xa )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.17/5.51 => ~ ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 ) ) ) )
% 5.17/5.51 => ( ! [Mi2: nat,Ma2: nat,V3: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V3 ) @ TreeList2 @ Vc ) @ Xa ) )
% 5.17/5.51 => ~ ( ( Xa = Mi2 )
% 5.17/5.51 | ( Xa = Ma2 )
% 5.17/5.51 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.17/5.51 => ~ ! [V3: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V3 ) @ TreeList2 @ Vd ) @ Xa ) )
% 5.17/5.51 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.membermima.pelims(2)
% 5.17/5.51 thf(fact_9166_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) )
% 5.17/5.51 => ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => A4 )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( ( ( Xa = one_one_nat )
% 5.17/5.51 => B3 )
% 5.17/5.51 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.17/5.51 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) @ Xa ) )
% 5.17/5.51 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.pelims(3)
% 5.17/5.51 thf(fact_9167_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.51 ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) )
% 5.17/5.51 => ~ ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => A4 )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( ( ( Xa = one_one_nat )
% 5.17/5.51 => B3 )
% 5.17/5.51 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) @ Xa ) )
% 5.17/5.51 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.pelims(2)
% 5.17/5.51 thf(fact_9168_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.17/5.51 ! [X: vEBT_VEBT,Xa: nat,Y4: $o] :
% 5.17/5.51 ( ( ( vEBT_V5719532721284313246member @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.51 => ( ! [A4: $o,B3: $o] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => A4 )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( ( ( Xa = one_one_nat )
% 5.17/5.51 => B3 )
% 5.17/5.51 & ( Xa = one_one_nat ) ) ) ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa ) ) ) )
% 5.17/5.51 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.17/5.51 => ( ~ Y4
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.17/5.51 => ~ ! [Uy2: option4927543243414619207at_nat,V3: nat,TreeList2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.17/5.51 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.51 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.17/5.51 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V3 ) @ TreeList2 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.naive_member.pelims(1)
% 5.17/5.51 thf(fact_9169_Arg__def,axiom,
% 5.17/5.51 ( arg
% 5.17/5.51 = ( ^ [Z5: complex] :
% 5.17/5.51 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 5.17/5.51 @ ( fChoice_real
% 5.17/5.51 @ ^ [A3: real] :
% 5.17/5.51 ( ( ( sgn_sgn_complex @ Z5 )
% 5.17/5.51 = ( cis @ A3 ) )
% 5.17/5.51 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.17/5.51 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Arg_def
% 5.17/5.51 thf(fact_9170_set__vebt__def,axiom,
% 5.17/5.51 ( vEBT_set_vebt
% 5.17/5.51 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_vebt_def
% 5.17/5.51 thf(fact_9171_sum__choose__lower,axiom,
% 5.17/5.51 ! [R2: nat,N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.17/5.51 @ ( set_ord_atMost_nat @ N ) )
% 5.17/5.51 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_choose_lower
% 5.17/5.51 thf(fact_9172_sum__choose__upper,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.17/5.51 @ ( set_ord_atMost_nat @ N ) )
% 5.17/5.51 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_choose_upper
% 5.17/5.51 thf(fact_9173_sum__choose__diagonal,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ M ) )
% 5.17/5.51 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_choose_diagonal
% 5.17/5.51 thf(fact_9174_vandermonde,axiom,
% 5.17/5.51 ! [M: nat,N: nat,R2: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ R2 ) )
% 5.17/5.51 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.17/5.51
% 5.17/5.51 % vandermonde
% 5.17/5.51 thf(fact_9175_choose__row__sum,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % choose_row_sum
% 5.17/5.51 thf(fact_9176_binomial,axiom,
% 5.17/5.51 ! [A: nat,B: nat,N: nat] :
% 5.17/5.51 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.17/5.51 = ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % binomial
% 5.17/5.51 thf(fact_9177_polynomial__product__nat,axiom,
% 5.17/5.51 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 5.17/5.51 ( ! [I3: nat] :
% 5.17/5.51 ( ( ord_less_nat @ M @ I3 )
% 5.17/5.51 => ( ( A @ I3 )
% 5.17/5.51 = zero_zero_nat ) )
% 5.17/5.51 => ( ! [J2: nat] :
% 5.17/5.51 ( ( ord_less_nat @ N @ J2 )
% 5.17/5.51 => ( ( B @ J2 )
% 5.17/5.51 = zero_zero_nat ) )
% 5.17/5.51 => ( ( times_times_nat
% 5.17/5.51 @ ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( power_power_nat @ X @ I2 ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ M ) )
% 5.17/5.51 @ ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ N ) ) )
% 5.17/5.51 = ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [R5: nat] :
% 5.17/5.51 ( times_times_nat
% 5.17/5.51 @ ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ R5 ) )
% 5.17/5.51 @ ( power_power_nat @ X @ R5 ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % polynomial_product_nat
% 5.17/5.51 thf(fact_9178_choose__square__sum,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ N ) )
% 5.17/5.51 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % choose_square_sum
% 5.17/5.51 thf(fact_9179_binomial__r__part__sum,axiom,
% 5.17/5.51 ! [M: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.17/5.51 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % binomial_r_part_sum
% 5.17/5.51 thf(fact_9180_choose__linear__sum,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [I2: nat] : ( times_times_nat @ I2 @ ( binomial @ N @ I2 ) )
% 5.17/5.51 @ ( set_ord_atMost_nat @ N ) )
% 5.17/5.51 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % choose_linear_sum
% 5.17/5.51 thf(fact_9181_mask__eq__sum__exp__nat,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.17/5.51 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [Q3: nat] : ( ord_less_nat @ Q3 @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % mask_eq_sum_exp_nat
% 5.17/5.51 thf(fact_9182_bounded__Max__nat,axiom,
% 5.17/5.51 ! [P: nat > $o,X: nat,M10: nat] :
% 5.17/5.51 ( ( P @ X )
% 5.17/5.51 => ( ! [X4: nat] :
% 5.17/5.51 ( ( P @ X4 )
% 5.17/5.51 => ( ord_less_eq_nat @ X4 @ M10 ) )
% 5.17/5.51 => ~ ! [M4: nat] :
% 5.17/5.51 ( ( P @ M4 )
% 5.17/5.51 => ~ ! [X5: nat] :
% 5.17/5.51 ( ( P @ X5 )
% 5.17/5.51 => ( ord_less_eq_nat @ X5 @ M4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bounded_Max_nat
% 5.17/5.51 thf(fact_9183_sum__nth__roots,axiom,
% 5.17/5.51 ! [N: nat,C: complex] :
% 5.17/5.51 ( ( ord_less_nat @ one_one_nat @ N )
% 5.17/5.51 => ( ( groups7754918857620584856omplex
% 5.17/5.51 @ ^ [X3: complex] : X3
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = C ) ) )
% 5.17/5.51 = zero_zero_complex ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_nth_roots
% 5.17/5.51 thf(fact_9184_sum__roots__unity,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( ord_less_nat @ one_one_nat @ N )
% 5.17/5.51 => ( ( groups7754918857620584856omplex
% 5.17/5.51 @ ^ [X3: complex] : X3
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = one_one_complex ) ) )
% 5.17/5.51 = zero_zero_complex ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_roots_unity
% 5.17/5.51 thf(fact_9185_Maclaurin__minus__cos__expansion,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.51 => ? [T3: real] :
% 5.17/5.51 ( ( ord_less_real @ X @ T3 )
% 5.17/5.51 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.17/5.51 & ( ( cos_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_minus_cos_expansion
% 5.17/5.51 thf(fact_9186_Maclaurin__cos__expansion2,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ? [T3: real] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.17/5.51 & ( ord_less_real @ T3 @ X )
% 5.17/5.51 & ( ( cos_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_cos_expansion2
% 5.17/5.51 thf(fact_9187_Maclaurin__sin__expansion3,axiom,
% 5.17/5.51 ! [N: nat,X: real] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ? [T3: real] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.17/5.51 & ( ord_less_real @ T3 @ X )
% 5.17/5.51 & ( ( sin_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_sin_expansion3
% 5.17/5.51 thf(fact_9188_Maclaurin__sin__expansion4,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.51 => ? [T3: real] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.17/5.51 & ( ord_less_eq_real @ T3 @ X )
% 5.17/5.51 & ( ( sin_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_sin_expansion4
% 5.17/5.51 thf(fact_9189_sumr__cos__zero__one,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ zero_zero_real @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.17/5.51 = one_one_real ) ).
% 5.17/5.51
% 5.17/5.51 % sumr_cos_zero_one
% 5.17/5.51 thf(fact_9190_lessThan__Suc__atMost,axiom,
% 5.17/5.51 ! [K: nat] :
% 5.17/5.51 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.17/5.51 = ( set_ord_atMost_nat @ K ) ) ).
% 5.17/5.51
% 5.17/5.51 % lessThan_Suc_atMost
% 5.17/5.51 thf(fact_9191_Maclaurin__lemma,axiom,
% 5.17/5.51 ! [H: real,F: real > real,J: nat > real,N: nat] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ H )
% 5.17/5.51 => ? [B8: real] :
% 5.17/5.51 ( ( F @ H )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_lemma
% 5.17/5.51 thf(fact_9192_sum__split__even__odd,axiom,
% 5.17/5.51 ! [F: nat > real,G: nat > real,N: nat] :
% 5.17/5.51 ( ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [I2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ ( F @ I2 ) @ ( G @ I2 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [I2: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [I2: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I2 ) @ one_one_nat ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_split_even_odd
% 5.17/5.51 thf(fact_9193_Maclaurin__exp__le,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ? [T3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.51 & ( ( exp_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_exp_le
% 5.17/5.51 thf(fact_9194_Maclaurin__sin__bound,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ( ord_less_eq_real
% 5.17/5.51 @ ( abs_abs_real
% 5.17/5.51 @ ( minus_minus_real @ ( sin_real @ X )
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.17/5.51 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_sin_bound
% 5.17/5.51 thf(fact_9195_sum__pos__lt__pair,axiom,
% 5.17/5.51 ! [F: nat > real,K: nat] :
% 5.17/5.51 ( ( summable_real @ F )
% 5.17/5.51 => ( ! [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 ) ) ) ) )
% 5.17/5.51 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_pos_lt_pair
% 5.17/5.51 thf(fact_9196_Maclaurin__exp__lt,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ( ( X != zero_zero_real )
% 5.17/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ? [T3: real] :
% 5.17/5.51 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.17/5.51 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.51 & ( ( exp_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_exp_lt
% 5.17/5.51 thf(fact_9197_Maclaurin__sin__expansion,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ? [T3: real] :
% 5.17/5.51 ( ( sin_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_sin_expansion
% 5.17/5.51 thf(fact_9198_Maclaurin__sin__expansion2,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ? [T3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.51 & ( ( sin_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_sin_expansion2
% 5.17/5.51 thf(fact_9199_Maclaurin__cos__expansion,axiom,
% 5.17/5.51 ! [X: real,N: nat] :
% 5.17/5.51 ? [T3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.51 & ( ( cos_real @ X )
% 5.17/5.51 = ( plus_plus_real
% 5.17/5.51 @ ( groups6591440286371151544t_real
% 5.17/5.51 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.51 @ ( 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 @ X @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Maclaurin_cos_expansion
% 5.17/5.51 thf(fact_9200_bij__betw__roots__unity,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( bij_betw_nat_complex
% 5.17/5.51 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.17/5.51 @ ( set_ord_lessThan_nat @ N )
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = one_one_complex ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bij_betw_roots_unity
% 5.17/5.51 thf(fact_9201_all__nat__less,axiom,
% 5.17/5.51 ! [N: nat,P: nat > $o] :
% 5.17/5.51 ( ( ! [M5: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M5 @ N )
% 5.17/5.51 => ( P @ M5 ) ) )
% 5.17/5.51 = ( ! [X3: nat] :
% 5.17/5.51 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 => ( P @ X3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % all_nat_less
% 5.17/5.51 thf(fact_9202_ex__nat__less,axiom,
% 5.17/5.51 ! [N: nat,P: nat > $o] :
% 5.17/5.51 ( ( ? [M5: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M5 @ N )
% 5.17/5.51 & ( P @ M5 ) ) )
% 5.17/5.51 = ( ? [X3: nat] :
% 5.17/5.51 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 & ( P @ X3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % ex_nat_less
% 5.17/5.51 thf(fact_9203_atMost__atLeast0,axiom,
% 5.17/5.51 ( set_ord_atMost_nat
% 5.17/5.51 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % atMost_atLeast0
% 5.17/5.51 thf(fact_9204_gauss__sum__nat,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gauss_sum_nat
% 5.17/5.51 thf(fact_9205_arith__series__nat,axiom,
% 5.17/5.51 ! [A: nat,D: nat,N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [I2: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I2 @ D ) )
% 5.17/5.51 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 = ( 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 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % arith_series_nat
% 5.17/5.51 thf(fact_9206_Sum__Icc__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.17/5.51 = ( 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 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Sum_Icc_nat
% 5.17/5.51 thf(fact_9207_bset_I1_J,axiom,
% 5.17/5.51 ! [D3: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.17/5.51 ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ B4 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ B4 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( Q @ X4 )
% 5.17/5.51 => ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ( P @ X5 )
% 5.17/5.51 & ( Q @ X5 ) )
% 5.17/5.51 => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 5.17/5.51 & ( Q @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(1)
% 5.17/5.51 thf(fact_9208_bset_I2_J,axiom,
% 5.17/5.51 ! [D3: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.17/5.51 ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ B4 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ B4 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( Q @ X4 )
% 5.17/5.51 => ( Q @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ( P @ X5 )
% 5.17/5.51 | ( Q @ X5 ) )
% 5.17/5.51 => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 5.17/5.51 | ( Q @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(2)
% 5.17/5.51 thf(fact_9209_aset_I1_J,axiom,
% 5.17/5.51 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.17/5.51 ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ A2 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ A2 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( Q @ X4 )
% 5.17/5.51 => ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ( P @ X5 )
% 5.17/5.51 & ( Q @ X5 ) )
% 5.17/5.51 => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 5.17/5.51 & ( Q @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(1)
% 5.17/5.51 thf(fact_9210_aset_I2_J,axiom,
% 5.17/5.51 ! [D3: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.17/5.51 ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ A2 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ A2 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( Q @ X4 )
% 5.17/5.51 => ( Q @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ( P @ X5 )
% 5.17/5.51 | ( Q @ X5 ) )
% 5.17/5.51 => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 5.17/5.51 | ( Q @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(2)
% 5.17/5.51 thf(fact_9211_bset_I9_J,axiom,
% 5.17/5.51 ! [D: int,D3: int,B4: set_int,T: int] :
% 5.17/5.51 ( ( dvd_dvd_int @ D @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.17/5.51 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(9)
% 5.17/5.51 thf(fact_9212_bset_I10_J,axiom,
% 5.17/5.51 ! [D: int,D3: int,B4: set_int,T: int] :
% 5.17/5.51 ( ( dvd_dvd_int @ D @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.17/5.51 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(10)
% 5.17/5.51 thf(fact_9213_aset_I9_J,axiom,
% 5.17/5.51 ! [D: int,D3: int,A2: set_int,T: int] :
% 5.17/5.51 ( ( dvd_dvd_int @ D @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.17/5.51 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(9)
% 5.17/5.51 thf(fact_9214_aset_I10_J,axiom,
% 5.17/5.51 ! [D: int,D3: int,A2: set_int,T: int] :
% 5.17/5.51 ( ( dvd_dvd_int @ D @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 5.17/5.51 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(10)
% 5.17/5.51 thf(fact_9215_periodic__finite__ex,axiom,
% 5.17/5.51 ! [D: int,P: int > $o] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.17/5.51 => ( ! [X4: int,K2: int] :
% 5.17/5.51 ( ( P @ X4 )
% 5.17/5.51 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.17/5.51 => ( ( ? [X8: int] : ( P @ X8 ) )
% 5.17/5.51 = ( ? [X3: int] :
% 5.17/5.51 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.17/5.51 & ( P @ X3 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % periodic_finite_ex
% 5.17/5.51 thf(fact_9216_bset_I3_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,B4: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( X5 = T )
% 5.17/5.51 => ( ( minus_minus_int @ X5 @ D3 )
% 5.17/5.51 = T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(3)
% 5.17/5.51 thf(fact_9217_bset_I4_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,B4: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ T @ B4 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( X5 != T )
% 5.17/5.51 => ( ( minus_minus_int @ X5 @ D3 )
% 5.17/5.51 != T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(4)
% 5.17/5.51 thf(fact_9218_bset_I5_J,axiom,
% 5.17/5.51 ! [D3: int,B4: set_int,T: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_int @ X5 @ T )
% 5.17/5.51 => ( ord_less_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(5)
% 5.17/5.51 thf(fact_9219_bset_I7_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,B4: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ T @ B4 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_int @ T @ X5 )
% 5.17/5.51 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(7)
% 5.17/5.51 thf(fact_9220_aset_I3_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,A2: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( X5 = T )
% 5.17/5.51 => ( ( plus_plus_int @ X5 @ D3 )
% 5.17/5.51 = T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(3)
% 5.17/5.51 thf(fact_9221_aset_I4_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,A2: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ T @ A2 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( X5 != T )
% 5.17/5.51 => ( ( plus_plus_int @ X5 @ D3 )
% 5.17/5.51 != T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(4)
% 5.17/5.51 thf(fact_9222_aset_I5_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,A2: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ T @ A2 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_int @ X5 @ T )
% 5.17/5.51 => ( ord_less_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(5)
% 5.17/5.51 thf(fact_9223_aset_I7_J,axiom,
% 5.17/5.51 ! [D3: int,A2: set_int,T: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_int @ T @ X5 )
% 5.17/5.51 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(7)
% 5.17/5.51 thf(fact_9224_fact__eq__fact__times,axiom,
% 5.17/5.51 ! [N: nat,M: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.51 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.17/5.51 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.17/5.51 @ ( groups708209901874060359at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % fact_eq_fact_times
% 5.17/5.51 thf(fact_9225_bset_I6_J,axiom,
% 5.17/5.51 ! [D3: int,B4: set_int,T: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_eq_int @ X5 @ T )
% 5.17/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D3 ) @ T ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(6)
% 5.17/5.51 thf(fact_9226_bset_I8_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,B4: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ B4 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_eq_int @ T @ X5 )
% 5.17/5.51 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bset(8)
% 5.17/5.51 thf(fact_9227_aset_I6_J,axiom,
% 5.17/5.51 ! [D3: int,T: int,A2: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_eq_int @ X5 @ T )
% 5.17/5.51 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D3 ) @ T ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(6)
% 5.17/5.51 thf(fact_9228_aset_I8_J,axiom,
% 5.17/5.51 ! [D3: int,A2: set_int,T: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ! [X5: int] :
% 5.17/5.51 ( ! [Xa3: int] :
% 5.17/5.51 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb2: int] :
% 5.17/5.51 ( ( member_int @ Xb2 @ A2 )
% 5.17/5.51 => ( X5
% 5.17/5.51 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.17/5.51 => ( ( ord_less_eq_int @ T @ X5 )
% 5.17/5.51 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % aset(8)
% 5.17/5.51 thf(fact_9229_cppi,axiom,
% 5.17/5.51 ! [D3: int,P: int > $o,P4: int > $o,A2: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ? [Z3: int] :
% 5.17/5.51 ! [X4: int] :
% 5.17/5.51 ( ( ord_less_int @ Z3 @ X4 )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 = ( P4 @ X4 ) ) )
% 5.17/5.51 => ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ A2 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( minus_minus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 => ( P @ ( plus_plus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ( ! [X4: int,K2: int] :
% 5.17/5.51 ( ( P4 @ X4 )
% 5.17/5.51 = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.17/5.51 => ( ( ? [X8: int] : ( P @ X8 ) )
% 5.17/5.51 = ( ? [X3: int] :
% 5.17/5.51 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 & ( P4 @ X3 ) )
% 5.17/5.51 | ? [X3: int] :
% 5.17/5.51 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 & ? [Y6: int] :
% 5.17/5.51 ( ( member_int @ Y6 @ A2 )
% 5.17/5.51 & ( P @ ( minus_minus_int @ Y6 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % cppi
% 5.17/5.51 thf(fact_9230_cpmi,axiom,
% 5.17/5.51 ! [D3: int,P: int > $o,P4: int > $o,B4: set_int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.17/5.51 => ( ? [Z3: int] :
% 5.17/5.51 ! [X4: int] :
% 5.17/5.51 ( ( ord_less_int @ X4 @ Z3 )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 = ( P4 @ X4 ) ) )
% 5.17/5.51 => ( ! [X4: int] :
% 5.17/5.51 ( ! [Xa2: int] :
% 5.17/5.51 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 => ! [Xb: int] :
% 5.17/5.51 ( ( member_int @ Xb @ B4 )
% 5.17/5.51 => ( X4
% 5.17/5.51 != ( plus_plus_int @ Xb @ Xa2 ) ) ) )
% 5.17/5.51 => ( ( P @ X4 )
% 5.17/5.51 => ( P @ ( minus_minus_int @ X4 @ D3 ) ) ) )
% 5.17/5.51 => ( ! [X4: int,K2: int] :
% 5.17/5.51 ( ( P4 @ X4 )
% 5.17/5.51 = ( P4 @ ( minus_minus_int @ X4 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.17/5.51 => ( ( ? [X8: int] : ( P @ X8 ) )
% 5.17/5.51 = ( ? [X3: int] :
% 5.17/5.51 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 & ( P4 @ X3 ) )
% 5.17/5.51 | ? [X3: int] :
% 5.17/5.51 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.17/5.51 & ? [Y6: int] :
% 5.17/5.51 ( ( member_int @ Y6 @ B4 )
% 5.17/5.51 & ( P @ ( plus_plus_int @ Y6 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % cpmi
% 5.17/5.51 thf(fact_9231_fact__div__fact,axiom,
% 5.17/5.51 ! [N: nat,M: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.51 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.17/5.51 = ( groups708209901874060359at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % fact_div_fact
% 5.17/5.51 thf(fact_9232_divmod__step__nat__def,axiom,
% 5.17/5.51 ( unique5026877609467782581ep_nat
% 5.17/5.51 = ( ^ [L3: num] :
% 5.17/5.51 ( produc2626176000494625587at_nat
% 5.17/5.51 @ ^ [Q3: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L3 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L3 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_step_nat_def
% 5.17/5.51 thf(fact_9233_divmod__step__int__def,axiom,
% 5.17/5.51 ( unique5024387138958732305ep_int
% 5.17/5.51 = ( ^ [L3: num] :
% 5.17/5.51 ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [Q3: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L3 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L3 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_step_int_def
% 5.17/5.51 thf(fact_9234_Sum__Icc__int,axiom,
% 5.17/5.51 ! [M: int,N: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ M @ N )
% 5.17/5.51 => ( ( groups4538972089207619220nt_int
% 5.17/5.51 @ ^ [X3: int] : X3
% 5.17/5.51 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.17/5.51 = ( 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 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Sum_Icc_int
% 5.17/5.51 thf(fact_9235_divmod__nat__if,axiom,
% 5.17/5.51 ( divmod_nat
% 5.17/5.51 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.51 ( if_Pro6206227464963214023at_nat
% 5.17/5.51 @ ( ( N4 = zero_zero_nat )
% 5.17/5.51 | ( ord_less_nat @ M5 @ N4 ) )
% 5.17/5.51 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 5.17/5.51 @ ( produc2626176000494625587at_nat
% 5.17/5.51 @ ^ [Q3: nat] : ( product_Pair_nat_nat @ ( suc @ Q3 ) )
% 5.17/5.51 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N4 ) @ N4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_nat_if
% 5.17/5.51 thf(fact_9236_vebt__buildup_Opelims,axiom,
% 5.17/5.51 ! [X: nat,Y4: vEBT_VEBT] :
% 5.17/5.51 ( ( ( vEBT_vebt_buildup @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.17/5.51 => ( ( ( X = zero_zero_nat )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( vEBT_Leaf @ $false @ $false ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.17/5.51 => ( ( ( X
% 5.17/5.51 = ( suc @ zero_zero_nat ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( vEBT_Leaf @ $false @ $false ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.17/5.51 => ~ ! [Va: nat] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( 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 ) ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( 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 ) ) ) ) ) ) ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % vebt_buildup.pelims
% 5.17/5.51 thf(fact_9237_arctan__def,axiom,
% 5.17/5.51 ( arctan
% 5.17/5.51 = ( ^ [Y6: real] :
% 5.17/5.51 ( the_real
% 5.17/5.51 @ ^ [X3: real] :
% 5.17/5.51 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.17/5.51 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.51 & ( ( tan_real @ X3 )
% 5.17/5.51 = Y6 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % arctan_def
% 5.17/5.51 thf(fact_9238_prod__int__eq,axiom,
% 5.17/5.51 ! [I: nat,J: nat] :
% 5.17/5.51 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.17/5.51 = ( groups1705073143266064639nt_int
% 5.17/5.51 @ ^ [X3: int] : X3
% 5.17/5.51 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_int_eq
% 5.17/5.51 thf(fact_9239_prod__int__plus__eq,axiom,
% 5.17/5.51 ! [I: nat,J: nat] :
% 5.17/5.51 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.17/5.51 = ( groups1705073143266064639nt_int
% 5.17/5.51 @ ^ [X3: int] : X3
% 5.17/5.51 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_int_plus_eq
% 5.17/5.51 thf(fact_9240_ln__neg__is__const,axiom,
% 5.17/5.51 ! [X: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.17/5.51 => ( ( ln_ln_real @ X )
% 5.17/5.51 = ( the_real
% 5.17/5.51 @ ^ [X3: real] : $false ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % ln_neg_is_const
% 5.17/5.51 thf(fact_9241_arccos__def,axiom,
% 5.17/5.51 ( arccos
% 5.17/5.51 = ( ^ [Y6: real] :
% 5.17/5.51 ( the_real
% 5.17/5.51 @ ^ [X3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.17/5.51 & ( ord_less_eq_real @ X3 @ pi )
% 5.17/5.51 & ( ( cos_real @ X3 )
% 5.17/5.51 = Y6 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % arccos_def
% 5.17/5.51 thf(fact_9242_divmod__nat__def,axiom,
% 5.17/5.51 ( divmod_nat
% 5.17/5.51 = ( ^ [M5: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M5 @ N4 ) @ ( modulo_modulo_nat @ M5 @ N4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_nat_def
% 5.17/5.51 thf(fact_9243_pi__half,axiom,
% 5.17/5.51 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.51 = ( the_real
% 5.17/5.51 @ ^ [X3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.17/5.51 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.51 & ( ( cos_real @ X3 )
% 5.17/5.51 = zero_zero_real ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % pi_half
% 5.17/5.51 thf(fact_9244_pi__def,axiom,
% 5.17/5.51 ( pi
% 5.17/5.51 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.17/5.51 @ ( the_real
% 5.17/5.51 @ ^ [X3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.17/5.51 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.17/5.51 & ( ( cos_real @ X3 )
% 5.17/5.51 = zero_zero_real ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % pi_def
% 5.17/5.51 thf(fact_9245_arcsin__def,axiom,
% 5.17/5.51 ( arcsin
% 5.17/5.51 = ( ^ [Y6: real] :
% 5.17/5.51 ( the_real
% 5.17/5.51 @ ^ [X3: real] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.17/5.51 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.51 & ( ( sin_real @ X3 )
% 5.17/5.51 = Y6 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % arcsin_def
% 5.17/5.51 thf(fact_9246_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Opelims,axiom,
% 5.17/5.51 ! [X: nat,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_nat @ vEBT_V1247956027447740395_p_rel @ X )
% 5.17/5.51 => ( ( ( X = zero_zero_nat )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ zero_zero_nat ) ) )
% 5.17/5.51 => ( ( ( X
% 5.17/5.51 = ( suc @ zero_zero_nat ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.17/5.51 => ~ ! [Va: nat] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.pelims
% 5.17/5.51 thf(fact_9247_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Opelims,axiom,
% 5.17/5.51 ! [X: nat,Y4: nat] :
% 5.17/5.51 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_nat @ vEBT_V5144397997797733112_d_rel @ X )
% 5.17/5.51 => ( ( ( X = zero_zero_nat )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ zero_zero_nat ) ) )
% 5.17/5.51 => ( ( ( X
% 5.17/5.51 = ( suc @ zero_zero_nat ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.17/5.51 => ~ ! [Va: nat] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.17/5.51 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.pelims
% 5.17/5.51 thf(fact_9248_set__encode__def,axiom,
% 5.17/5.51 ( nat_set_encode
% 5.17/5.51 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_encode_def
% 5.17/5.51 thf(fact_9249_set__decode__inverse,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 5.17/5.51 = N ) ).
% 5.17/5.51
% 5.17/5.51 % set_decode_inverse
% 5.17/5.51 thf(fact_9250_VEBT_Osize_I3_J,axiom,
% 5.17/5.51 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.17/5.51 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.size(3)
% 5.17/5.51 thf(fact_9251_Sum__Ico__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.17/5.51 = ( 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 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Sum_Ico_nat
% 5.17/5.51 thf(fact_9252_sum__power2,axiom,
% 5.17/5.51 ! [K: nat] :
% 5.17/5.51 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.17/5.51 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_power2
% 5.17/5.51 thf(fact_9253_ex__nat__less__eq,axiom,
% 5.17/5.51 ! [N: nat,P: nat > $o] :
% 5.17/5.51 ( ( ? [M5: nat] :
% 5.17/5.51 ( ( ord_less_nat @ M5 @ N )
% 5.17/5.51 & ( P @ M5 ) ) )
% 5.17/5.51 = ( ? [X3: nat] :
% 5.17/5.51 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 & ( P @ X3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % ex_nat_less_eq
% 5.17/5.51 thf(fact_9254_all__nat__less__eq,axiom,
% 5.17/5.51 ! [N: nat,P: nat > $o] :
% 5.17/5.51 ( ( ! [M5: nat] :
% 5.17/5.51 ( ( ord_less_nat @ M5 @ N )
% 5.17/5.51 => ( P @ M5 ) ) )
% 5.17/5.51 = ( ! [X3: nat] :
% 5.17/5.51 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 => ( P @ X3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % all_nat_less_eq
% 5.17/5.51 thf(fact_9255_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.17/5.51 ! [L: nat,U: nat] :
% 5.17/5.51 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.17/5.51 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastLessThanSuc_atLeastAtMost
% 5.17/5.51 thf(fact_9256_lessThan__atLeast0,axiom,
% 5.17/5.51 ( set_ord_lessThan_nat
% 5.17/5.51 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % lessThan_atLeast0
% 5.17/5.51 thf(fact_9257_prod__Suc__Suc__fact,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.17/5.51 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_Suc_Suc_fact
% 5.17/5.51 thf(fact_9258_prod__Suc__fact,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_Suc_fact
% 5.17/5.51 thf(fact_9259_Chebyshev__sum__upper__nat,axiom,
% 5.17/5.51 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.17/5.51 ( ! [I3: nat,J2: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.17/5.51 => ( ( ord_less_nat @ J2 @ N )
% 5.17/5.51 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 5.17/5.51 => ( ! [I3: nat,J2: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.17/5.51 => ( ( ord_less_nat @ J2 @ N )
% 5.17/5.51 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 5.17/5.51 => ( ord_less_eq_nat
% 5.17/5.51 @ ( times_times_nat @ N
% 5.17/5.51 @ ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [I2: nat] : ( times_times_nat @ ( A @ I2 ) @ ( B @ I2 ) )
% 5.17/5.51 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.17/5.51 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Chebyshev_sum_upper_nat
% 5.17/5.51 thf(fact_9260_VEBT_Osize__gen_I1_J,axiom,
% 5.17/5.51 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.17/5.51 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.17/5.51 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.size_gen(1)
% 5.17/5.51 thf(fact_9261_VEBT_Osize__gen_I2_J,axiom,
% 5.17/5.51 ! [X21: $o,X222: $o] :
% 5.17/5.51 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.17/5.51 = zero_zero_nat ) ).
% 5.17/5.51
% 5.17/5.51 % VEBT.size_gen(2)
% 5.17/5.51 thf(fact_9262_int__of__nat__def,axiom,
% 5.17/5.51 code_T6385005292777649522of_nat = semiri1314217659103216013at_int ).
% 5.17/5.51
% 5.17/5.51 % int_of_nat_def
% 5.17/5.51 thf(fact_9263_prod__decode__aux_Opelims,axiom,
% 5.17/5.51 ! [X: nat,Xa: nat,Y4: product_prod_nat_nat] :
% 5.17/5.51 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.17/5.51 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 5.17/5.51 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 5.17/5.51 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % prod_decode_aux.pelims
% 5.17/5.51 thf(fact_9264_or__not__num__neg_Opelims,axiom,
% 5.17/5.51 ! [X: num,Xa: num,Y4: num] :
% 5.17/5.51 ( ( ( bit_or_not_num_neg @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.17/5.51 => ( ( ( X = one )
% 5.17/5.51 => ( ( Xa = one )
% 5.17/5.51 => ( ( Y4 = one )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.17/5.51 => ( ( ( X = one )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit0 @ M4 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.17/5.51 => ( ( ( X = one )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit0 @ N2 ) )
% 5.17/5.51 => ( ( Xa = one )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bit0 @ one ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ one ) ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit0 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit0 @ M4 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit0 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit1 @ N2 ) )
% 5.17/5.51 => ( ( Xa = one )
% 5.17/5.51 => ( ( Y4 = one )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ one ) ) ) ) )
% 5.17/5.51 => ( ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit1 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit0 @ M4 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.17/5.51 => ~ ! [N2: num] :
% 5.17/5.51 ( ( X
% 5.17/5.51 = ( bit1 @ N2 ) )
% 5.17/5.51 => ! [M4: num] :
% 5.17/5.51 ( ( Xa
% 5.17/5.51 = ( bit1 @ M4 ) )
% 5.17/5.51 => ( ( Y4
% 5.17/5.51 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M4 ) ) )
% 5.17/5.51 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N2 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % or_not_num_neg.pelims
% 5.17/5.51 thf(fact_9265_int__ge__less__than__def,axiom,
% 5.17/5.51 ( int_ge_less_than
% 5.17/5.51 = ( ^ [D4: int] :
% 5.17/5.51 ( collec213857154873943460nt_int
% 5.17/5.51 @ ( produc4947309494688390418_int_o
% 5.17/5.51 @ ^ [Z7: int,Z5: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ D4 @ Z7 )
% 5.17/5.51 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % int_ge_less_than_def
% 5.17/5.51 thf(fact_9266_int__ge__less__than2__def,axiom,
% 5.17/5.51 ( int_ge_less_than2
% 5.17/5.51 = ( ^ [D4: int] :
% 5.17/5.51 ( collec213857154873943460nt_int
% 5.17/5.51 @ ( produc4947309494688390418_int_o
% 5.17/5.51 @ ^ [Z7: int,Z5: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ D4 @ Z5 )
% 5.17/5.51 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % int_ge_less_than2_def
% 5.17/5.51 thf(fact_9267_upto_Opinduct,axiom,
% 5.17/5.51 ! [A0: int,A1: int,P: int > int > $o] :
% 5.17/5.51 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.17/5.51 => ( ! [I3: int,J2: int] :
% 5.17/5.51 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.17/5.51 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.17/5.51 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.17/5.51 => ( P @ I3 @ J2 ) ) )
% 5.17/5.51 => ( P @ A0 @ A1 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % upto.pinduct
% 5.17/5.51 thf(fact_9268_Code__Target__Int_Opositive__def,axiom,
% 5.17/5.51 code_Target_positive = numeral_numeral_int ).
% 5.17/5.51
% 5.17/5.51 % Code_Target_Int.positive_def
% 5.17/5.51 thf(fact_9269_divmod__step__integer__def,axiom,
% 5.17/5.51 ( unique4921790084139445826nteger
% 5.17/5.51 = ( ^ [L3: num] :
% 5.17/5.51 ( produc6916734918728496179nteger
% 5.17/5.51 @ ^ [Q3: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L3 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L3 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R5 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_step_integer_def
% 5.17/5.51 thf(fact_9270_less__eq__integer__code_I1_J,axiom,
% 5.17/5.51 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.17/5.51
% 5.17/5.51 % less_eq_integer_code(1)
% 5.17/5.51 thf(fact_9271_plus__integer__code_I1_J,axiom,
% 5.17/5.51 ! [K: code_integer] :
% 5.17/5.51 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.17/5.51 = K ) ).
% 5.17/5.51
% 5.17/5.51 % plus_integer_code(1)
% 5.17/5.51 thf(fact_9272_plus__integer__code_I2_J,axiom,
% 5.17/5.51 ! [L: code_integer] :
% 5.17/5.51 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 5.17/5.51 = L ) ).
% 5.17/5.51
% 5.17/5.51 % plus_integer_code(2)
% 5.17/5.51 thf(fact_9273_times__integer__code_I2_J,axiom,
% 5.17/5.51 ! [L: code_integer] :
% 5.17/5.51 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 5.17/5.51 = zero_z3403309356797280102nteger ) ).
% 5.17/5.51
% 5.17/5.51 % times_integer_code(2)
% 5.17/5.51 thf(fact_9274_times__integer__code_I1_J,axiom,
% 5.17/5.51 ! [K: code_integer] :
% 5.17/5.51 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.17/5.51 = zero_z3403309356797280102nteger ) ).
% 5.17/5.51
% 5.17/5.51 % times_integer_code(1)
% 5.17/5.51 thf(fact_9275_minus__integer__code_I2_J,axiom,
% 5.17/5.51 ! [L: code_integer] :
% 5.17/5.51 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 5.17/5.51 = ( uminus1351360451143612070nteger @ L ) ) ).
% 5.17/5.51
% 5.17/5.51 % minus_integer_code(2)
% 5.17/5.51 thf(fact_9276_minus__integer__code_I1_J,axiom,
% 5.17/5.51 ! [K: code_integer] :
% 5.17/5.51 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.17/5.51 = K ) ).
% 5.17/5.51
% 5.17/5.51 % minus_integer_code(1)
% 5.17/5.51 thf(fact_9277_sgn__integer__code,axiom,
% 5.17/5.51 ( sgn_sgn_Code_integer
% 5.17/5.51 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sgn_integer_code
% 5.17/5.51 thf(fact_9278_nat_Odisc__eq__case_I2_J,axiom,
% 5.17/5.51 ! [Nat: nat] :
% 5.17/5.51 ( ( Nat != zero_zero_nat )
% 5.17/5.51 = ( case_nat_o @ $false
% 5.17/5.51 @ ^ [Uu3: nat] : $true
% 5.17/5.51 @ Nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat.disc_eq_case(2)
% 5.17/5.51 thf(fact_9279_nat_Odisc__eq__case_I1_J,axiom,
% 5.17/5.51 ! [Nat: nat] :
% 5.17/5.51 ( ( Nat = zero_zero_nat )
% 5.17/5.51 = ( case_nat_o @ $true
% 5.17/5.51 @ ^ [Uu3: nat] : $false
% 5.17/5.51 @ Nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat.disc_eq_case(1)
% 5.17/5.51 thf(fact_9280_zero__natural_Orsp,axiom,
% 5.17/5.51 zero_zero_nat = zero_zero_nat ).
% 5.17/5.51
% 5.17/5.51 % zero_natural.rsp
% 5.17/5.51 thf(fact_9281_zero__integer_Orsp,axiom,
% 5.17/5.51 zero_zero_int = zero_zero_int ).
% 5.17/5.51
% 5.17/5.51 % zero_integer.rsp
% 5.17/5.51 thf(fact_9282_less__eq__nat_Osimps_I2_J,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.17/5.51 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % less_eq_nat.simps(2)
% 5.17/5.51 thf(fact_9283_max__Suc2,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.17/5.51 = ( case_nat_nat @ ( suc @ N )
% 5.17/5.51 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 5.17/5.51 @ M ) ) ).
% 5.17/5.51
% 5.17/5.51 % max_Suc2
% 5.17/5.51 thf(fact_9284_max__Suc1,axiom,
% 5.17/5.51 ! [N: nat,M: nat] :
% 5.17/5.51 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.17/5.51 = ( case_nat_nat @ ( suc @ N )
% 5.17/5.51 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 5.17/5.51 @ M ) ) ).
% 5.17/5.51
% 5.17/5.51 % max_Suc1
% 5.17/5.51 thf(fact_9285_diff__Suc,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.17/5.51 = ( case_nat_nat @ zero_zero_nat
% 5.17/5.51 @ ^ [K3: nat] : K3
% 5.17/5.51 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % diff_Suc
% 5.17/5.51 thf(fact_9286_integer__of__int__code,axiom,
% 5.17/5.51 ( code_integer_of_int
% 5.17/5.51 = ( ^ [K3: int] :
% 5.17/5.51 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.17/5.51 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.17/5.51 @ ( if_Code_integer
% 5.17/5.51 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.17/5.51 = zero_zero_int )
% 5.17/5.51 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % integer_of_int_code
% 5.17/5.51 thf(fact_9287_flip__bit__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: nat,X: int] :
% 5.17/5.51 ( ( bit_se1345352211410354436nteger @ Xa @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % flip_bit_integer.abs_eq
% 5.17/5.51 thf(fact_9288_zero__integer__def,axiom,
% 5.17/5.51 ( zero_z3403309356797280102nteger
% 5.17/5.51 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % zero_integer_def
% 5.17/5.51 thf(fact_9289_unset__bit__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: nat,X: int] :
% 5.17/5.51 ( ( bit_se8260200283734997820nteger @ Xa @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % unset_bit_integer.abs_eq
% 5.17/5.51 thf(fact_9290_divide__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: int,X: int] :
% 5.17/5.51 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( code_integer_of_int @ ( divide_divide_int @ Xa @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divide_integer.abs_eq
% 5.17/5.51 thf(fact_9291_set__bit__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: nat,X: int] :
% 5.17/5.51 ( ( bit_se2793503036327961859nteger @ Xa @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_bit_integer.abs_eq
% 5.17/5.51 thf(fact_9292_uminus__integer__code_I1_J,axiom,
% 5.17/5.51 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.17/5.51 = zero_z3403309356797280102nteger ) ).
% 5.17/5.51
% 5.17/5.51 % uminus_integer_code(1)
% 5.17/5.51 thf(fact_9293_less__integer__code_I1_J,axiom,
% 5.17/5.51 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.17/5.51
% 5.17/5.51 % less_integer_code(1)
% 5.17/5.51 thf(fact_9294_abs__integer__code,axiom,
% 5.17/5.51 ( abs_abs_Code_integer
% 5.17/5.51 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % abs_integer_code
% 5.17/5.51 thf(fact_9295_times__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: int,X: int] :
% 5.17/5.51 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( code_integer_of_int @ ( times_times_int @ Xa @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % times_integer.abs_eq
% 5.17/5.51 thf(fact_9296_less__eq__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: int,X: int] :
% 5.17/5.51 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( ord_less_eq_int @ Xa @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % less_eq_integer.abs_eq
% 5.17/5.51 thf(fact_9297_minus__integer_Oabs__eq,axiom,
% 5.17/5.51 ! [Xa: int,X: int] :
% 5.17/5.51 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.17/5.51 = ( code_integer_of_int @ ( minus_minus_int @ Xa @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % minus_integer.abs_eq
% 5.17/5.51 thf(fact_9298_floor__real__def,axiom,
% 5.17/5.51 ( archim6058952711729229775r_real
% 5.17/5.51 = ( ^ [X3: real] :
% 5.17/5.51 ( the_int
% 5.17/5.51 @ ^ [Z5: int] :
% 5.17/5.51 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X3 )
% 5.17/5.51 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % floor_real_def
% 5.17/5.51 thf(fact_9299_floor__rat__def,axiom,
% 5.17/5.51 ( archim3151403230148437115or_rat
% 5.17/5.51 = ( ^ [X3: rat] :
% 5.17/5.51 ( the_int
% 5.17/5.51 @ ^ [Z5: int] :
% 5.17/5.51 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X3 )
% 5.17/5.51 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % floor_rat_def
% 5.17/5.51 thf(fact_9300_integer__of__num_I3_J,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.17/5.51 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.17/5.51
% 5.17/5.51 % integer_of_num(3)
% 5.17/5.51 thf(fact_9301_less__eq__rat__def,axiom,
% 5.17/5.51 ( ord_less_eq_rat
% 5.17/5.51 = ( ^ [X3: rat,Y6: rat] :
% 5.17/5.51 ( ( ord_less_rat @ X3 @ Y6 )
% 5.17/5.51 | ( X3 = Y6 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % less_eq_rat_def
% 5.17/5.51 thf(fact_9302_obtain__pos__sum,axiom,
% 5.17/5.51 ! [R2: rat] :
% 5.17/5.51 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.17/5.51 => ~ ! [S3: rat] :
% 5.17/5.51 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.17/5.51 => ! [T3: rat] :
% 5.17/5.51 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.17/5.51 => ( R2
% 5.17/5.51 != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % obtain_pos_sum
% 5.17/5.51 thf(fact_9303_sgn__rat__def,axiom,
% 5.17/5.51 ( sgn_sgn_rat
% 5.17/5.51 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sgn_rat_def
% 5.17/5.51 thf(fact_9304_abs__rat__def,axiom,
% 5.17/5.51 ( abs_abs_rat
% 5.17/5.51 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % abs_rat_def
% 5.17/5.51 thf(fact_9305_integer__of__num__triv_I1_J,axiom,
% 5.17/5.51 ( ( code_integer_of_num @ one )
% 5.17/5.51 = one_one_Code_integer ) ).
% 5.17/5.51
% 5.17/5.51 % integer_of_num_triv(1)
% 5.17/5.51 thf(fact_9306_integer__of__num_I2_J,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.17/5.51 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % integer_of_num(2)
% 5.17/5.51 thf(fact_9307_integer__of__num__triv_I2_J,axiom,
% 5.17/5.51 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.17/5.51 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % integer_of_num_triv(2)
% 5.17/5.51 thf(fact_9308_pred__def,axiom,
% 5.17/5.51 ( pred
% 5.17/5.51 = ( case_nat_nat @ zero_zero_nat
% 5.17/5.51 @ ^ [X23: nat] : X23 ) ) ).
% 5.17/5.51
% 5.17/5.51 % pred_def
% 5.17/5.51 thf(fact_9309_rat__inverse__code,axiom,
% 5.17/5.51 ! [P5: rat] :
% 5.17/5.51 ( ( quotient_of @ ( inverse_inverse_rat @ P5 ) )
% 5.17/5.51 = ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 5.17/5.51 @ ( quotient_of @ P5 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_inverse_code
% 5.17/5.51 thf(fact_9310_normalize__negative,axiom,
% 5.17/5.51 ! [Q2: int,P5: int] :
% 5.17/5.51 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.17/5.51 => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.17/5.51 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P5 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % normalize_negative
% 5.17/5.51 thf(fact_9311_bit__cut__integer__def,axiom,
% 5.17/5.51 ( code_bit_cut_integer
% 5.17/5.51 = ( ^ [K3: code_integer] :
% 5.17/5.51 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.17/5.51 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bit_cut_integer_def
% 5.17/5.51 thf(fact_9312_quotient__of__number_I3_J,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.17/5.51 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % quotient_of_number(3)
% 5.17/5.51 thf(fact_9313_normalize__denom__zero,axiom,
% 5.17/5.51 ! [P5: int] :
% 5.17/5.51 ( ( normalize @ ( product_Pair_int_int @ P5 @ zero_zero_int ) )
% 5.17/5.51 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % normalize_denom_zero
% 5.17/5.51 thf(fact_9314_rat__zero__code,axiom,
% 5.17/5.51 ( ( quotient_of @ zero_zero_rat )
% 5.17/5.51 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_zero_code
% 5.17/5.51 thf(fact_9315_quotient__of__number_I5_J,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.17/5.51 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % quotient_of_number(5)
% 5.17/5.51 thf(fact_9316_diff__rat__def,axiom,
% 5.17/5.51 ( minus_minus_rat
% 5.17/5.51 = ( ^ [Q3: rat,R5: rat] : ( plus_plus_rat @ Q3 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % diff_rat_def
% 5.17/5.51 thf(fact_9317_rat__times__code,axiom,
% 5.17/5.51 ! [P5: rat,Q2: rat] :
% 5.17/5.51 ( ( quotient_of @ ( times_times_rat @ P5 @ Q2 ) )
% 5.17/5.51 = ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [A3: int,C5: int] :
% 5.17/5.51 ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B2 ) @ ( times_times_int @ C5 @ D4 ) ) )
% 5.17/5.51 @ ( quotient_of @ Q2 ) )
% 5.17/5.51 @ ( quotient_of @ P5 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_times_code
% 5.17/5.51 thf(fact_9318_rat__divide__code,axiom,
% 5.17/5.51 ! [P5: rat,Q2: rat] :
% 5.17/5.51 ( ( quotient_of @ ( divide_divide_rat @ P5 @ Q2 ) )
% 5.17/5.51 = ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [A3: int,C5: int] :
% 5.17/5.51 ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C5 @ B2 ) ) )
% 5.17/5.51 @ ( quotient_of @ Q2 ) )
% 5.17/5.51 @ ( quotient_of @ P5 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_divide_code
% 5.17/5.51 thf(fact_9319_rat__plus__code,axiom,
% 5.17/5.51 ! [P5: rat,Q2: rat] :
% 5.17/5.51 ( ( quotient_of @ ( plus_plus_rat @ P5 @ Q2 ) )
% 5.17/5.51 = ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [A3: int,C5: int] :
% 5.17/5.51 ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B2 @ C5 ) ) @ ( times_times_int @ C5 @ D4 ) ) )
% 5.17/5.51 @ ( quotient_of @ Q2 ) )
% 5.17/5.51 @ ( quotient_of @ P5 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_plus_code
% 5.17/5.51 thf(fact_9320_rat__minus__code,axiom,
% 5.17/5.51 ! [P5: rat,Q2: rat] :
% 5.17/5.51 ( ( quotient_of @ ( minus_minus_rat @ P5 @ Q2 ) )
% 5.17/5.51 = ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [A3: int,C5: int] :
% 5.17/5.51 ( produc4245557441103728435nt_int
% 5.17/5.51 @ ^ [B2: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B2 @ C5 ) ) @ ( times_times_int @ C5 @ D4 ) ) )
% 5.17/5.51 @ ( quotient_of @ Q2 ) )
% 5.17/5.51 @ ( quotient_of @ P5 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_minus_code
% 5.17/5.51 thf(fact_9321_quotient__of__denom__pos,axiom,
% 5.17/5.51 ! [R2: rat,P5: int,Q2: int] :
% 5.17/5.51 ( ( ( quotient_of @ R2 )
% 5.17/5.51 = ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.17/5.51 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.17/5.51
% 5.17/5.51 % quotient_of_denom_pos
% 5.17/5.51 thf(fact_9322_normalize__denom__pos,axiom,
% 5.17/5.51 ! [R2: product_prod_int_int,P5: int,Q2: int] :
% 5.17/5.51 ( ( ( normalize @ R2 )
% 5.17/5.51 = ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.17/5.51 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.17/5.51
% 5.17/5.51 % normalize_denom_pos
% 5.17/5.51 thf(fact_9323_normalize__crossproduct,axiom,
% 5.17/5.51 ! [Q2: int,S2: int,P5: int,R2: int] :
% 5.17/5.51 ( ( Q2 != zero_zero_int )
% 5.17/5.51 => ( ( S2 != zero_zero_int )
% 5.17/5.51 => ( ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.17/5.51 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 5.17/5.51 => ( ( times_times_int @ P5 @ S2 )
% 5.17/5.51 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % normalize_crossproduct
% 5.17/5.51 thf(fact_9324_rat__less__code,axiom,
% 5.17/5.51 ( ord_less_rat
% 5.17/5.51 = ( ^ [P6: rat,Q3: rat] :
% 5.17/5.51 ( produc4947309494688390418_int_o
% 5.17/5.51 @ ^ [A3: int,C5: int] :
% 5.17/5.51 ( produc4947309494688390418_int_o
% 5.17/5.51 @ ^ [B2: int,D4: int] : ( ord_less_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C5 @ B2 ) )
% 5.17/5.51 @ ( quotient_of @ Q3 ) )
% 5.17/5.51 @ ( quotient_of @ P6 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_less_code
% 5.17/5.51 thf(fact_9325_rat__less__eq__code,axiom,
% 5.17/5.51 ( ord_less_eq_rat
% 5.17/5.51 = ( ^ [P6: rat,Q3: rat] :
% 5.17/5.51 ( produc4947309494688390418_int_o
% 5.17/5.51 @ ^ [A3: int,C5: int] :
% 5.17/5.51 ( produc4947309494688390418_int_o
% 5.17/5.51 @ ^ [B2: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C5 @ B2 ) )
% 5.17/5.51 @ ( quotient_of @ Q3 ) )
% 5.17/5.51 @ ( quotient_of @ P6 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % rat_less_eq_code
% 5.17/5.51 thf(fact_9326_bit__cut__integer__code,axiom,
% 5.17/5.51 ( code_bit_cut_integer
% 5.17/5.51 = ( ^ [K3: code_integer] :
% 5.17/5.51 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.17/5.51 @ ( produc9125791028180074456eger_o
% 5.17/5.51 @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 5.17/5.51 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bit_cut_integer_code
% 5.17/5.51 thf(fact_9327_bezw__0,axiom,
% 5.17/5.51 ! [X: nat] :
% 5.17/5.51 ( ( bezw @ X @ zero_zero_nat )
% 5.17/5.51 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezw_0
% 5.17/5.51 thf(fact_9328_set__encode__inverse,axiom,
% 5.17/5.51 ! [A2: set_nat] :
% 5.17/5.51 ( ( finite_finite_nat @ A2 )
% 5.17/5.51 => ( ( nat_set_decode @ ( nat_set_encode @ A2 ) )
% 5.17/5.51 = A2 ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_encode_inverse
% 5.17/5.51 thf(fact_9329_finite__set__decode,axiom,
% 5.17/5.51 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_set_decode
% 5.17/5.51 thf(fact_9330_set__encode__eq,axiom,
% 5.17/5.51 ! [A2: set_nat,B4: set_nat] :
% 5.17/5.51 ( ( finite_finite_nat @ A2 )
% 5.17/5.51 => ( ( finite_finite_nat @ B4 )
% 5.17/5.51 => ( ( ( nat_set_encode @ A2 )
% 5.17/5.51 = ( nat_set_encode @ B4 ) )
% 5.17/5.51 = ( A2 = B4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_encode_eq
% 5.17/5.51 thf(fact_9331_finite__nat__set__iff__bounded__le,axiom,
% 5.17/5.51 ( finite_finite_nat
% 5.17/5.51 = ( ^ [N8: set_nat] :
% 5.17/5.51 ? [M5: nat] :
% 5.17/5.51 ! [X3: nat] :
% 5.17/5.51 ( ( member_nat @ X3 @ N8 )
% 5.17/5.51 => ( ord_less_eq_nat @ X3 @ M5 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_nat_set_iff_bounded_le
% 5.17/5.51 thf(fact_9332_finite__less__ub,axiom,
% 5.17/5.51 ! [F: nat > nat,U: nat] :
% 5.17/5.51 ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 5.17/5.51 => ( finite_finite_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F @ N4 ) @ U ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_less_ub
% 5.17/5.51 thf(fact_9333_set__encode__inf,axiom,
% 5.17/5.51 ! [A2: set_nat] :
% 5.17/5.51 ( ~ ( finite_finite_nat @ A2 )
% 5.17/5.51 => ( ( nat_set_encode @ A2 )
% 5.17/5.51 = zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_encode_inf
% 5.17/5.51 thf(fact_9334_finite__divisors__nat,axiom,
% 5.17/5.51 ! [M: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.51 => ( finite_finite_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_divisors_nat
% 5.17/5.51 thf(fact_9335_subset__eq__atLeast0__atMost__finite,axiom,
% 5.17/5.51 ! [N5: set_nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_set_nat @ N5 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 => ( finite_finite_nat @ N5 ) ) ).
% 5.17/5.51
% 5.17/5.51 % subset_eq_atLeast0_atMost_finite
% 5.17/5.51 thf(fact_9336_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.17/5.51 ! [N5: set_nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 => ( finite_finite_nat @ N5 ) ) ).
% 5.17/5.51
% 5.17/5.51 % subset_eq_atLeast0_lessThan_finite
% 5.17/5.51 thf(fact_9337_divmod__abs__code_I6_J,axiom,
% 5.17/5.51 ! [J: code_integer] :
% 5.17/5.51 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.17/5.51 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_abs_code(6)
% 5.17/5.51 thf(fact_9338_divmod__abs__code_I5_J,axiom,
% 5.17/5.51 ! [J: code_integer] :
% 5.17/5.51 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.17/5.51 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_abs_code(5)
% 5.17/5.51 thf(fact_9339_even__set__encode__iff,axiom,
% 5.17/5.51 ! [A2: set_nat] :
% 5.17/5.51 ( ( finite_finite_nat @ A2 )
% 5.17/5.51 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.17/5.51 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % even_set_encode_iff
% 5.17/5.51 thf(fact_9340_finite__Collect__le__nat,axiom,
% 5.17/5.51 ! [K: nat] :
% 5.17/5.51 ( finite_finite_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_Collect_le_nat
% 5.17/5.51 thf(fact_9341_finite__interval__int1,axiom,
% 5.17/5.51 ! [A: int,B: int] :
% 5.17/5.51 ( finite_finite_int
% 5.17/5.51 @ ( collect_int
% 5.17/5.51 @ ^ [I2: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ A @ I2 )
% 5.17/5.51 & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_interval_int1
% 5.17/5.51 thf(fact_9342_finite__interval__int4,axiom,
% 5.17/5.51 ! [A: int,B: int] :
% 5.17/5.51 ( finite_finite_int
% 5.17/5.51 @ ( collect_int
% 5.17/5.51 @ ^ [I2: int] :
% 5.17/5.51 ( ( ord_less_int @ A @ I2 )
% 5.17/5.51 & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_interval_int4
% 5.17/5.51 thf(fact_9343_finite__interval__int2,axiom,
% 5.17/5.51 ! [A: int,B: int] :
% 5.17/5.51 ( finite_finite_int
% 5.17/5.51 @ ( collect_int
% 5.17/5.51 @ ^ [I2: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ A @ I2 )
% 5.17/5.51 & ( ord_less_int @ I2 @ B ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_interval_int2
% 5.17/5.51 thf(fact_9344_finite__interval__int3,axiom,
% 5.17/5.51 ! [A: int,B: int] :
% 5.17/5.51 ( finite_finite_int
% 5.17/5.51 @ ( collect_int
% 5.17/5.51 @ ^ [I2: int] :
% 5.17/5.51 ( ( ord_less_int @ A @ I2 )
% 5.17/5.51 & ( ord_less_eq_int @ I2 @ B ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_interval_int3
% 5.17/5.51 thf(fact_9345_finite__nth__roots,axiom,
% 5.17/5.51 ! [N: nat,C: complex] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( finite3207457112153483333omplex
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = C ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_nth_roots
% 5.17/5.51 thf(fact_9346_finite__atLeastZeroLessThan__int,axiom,
% 5.17/5.51 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_atLeastZeroLessThan_int
% 5.17/5.51 thf(fact_9347_finite__divisors__int,axiom,
% 5.17/5.51 ! [I: int] :
% 5.17/5.51 ( ( I != zero_zero_int )
% 5.17/5.51 => ( finite_finite_int
% 5.17/5.51 @ ( collect_int
% 5.17/5.51 @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_divisors_int
% 5.17/5.51 thf(fact_9348_finite__nat__iff__bounded__le,axiom,
% 5.17/5.51 ( finite_finite_nat
% 5.17/5.51 = ( ^ [S5: set_nat] :
% 5.17/5.51 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_nat_iff_bounded_le
% 5.17/5.51 thf(fact_9349_finite__nat__bounded,axiom,
% 5.17/5.51 ! [S: set_nat] :
% 5.17/5.51 ( ( finite_finite_nat @ S )
% 5.17/5.51 => ? [K2: nat] : ( ord_less_eq_set_nat @ S @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_nat_bounded
% 5.17/5.51 thf(fact_9350_finite__nat__iff__bounded,axiom,
% 5.17/5.51 ( finite_finite_nat
% 5.17/5.51 = ( ^ [S5: set_nat] :
% 5.17/5.51 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % finite_nat_iff_bounded
% 5.17/5.51 thf(fact_9351_infinite__int__iff__unbounded__le,axiom,
% 5.17/5.51 ! [S: set_int] :
% 5.17/5.51 ( ( ~ ( finite_finite_int @ S ) )
% 5.17/5.51 = ( ! [M5: int] :
% 5.17/5.51 ? [N4: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ M5 @ ( abs_abs_int @ N4 ) )
% 5.17/5.51 & ( member_int @ N4 @ S ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % infinite_int_iff_unbounded_le
% 5.17/5.51 thf(fact_9352_infinite__nat__iff__unbounded__le,axiom,
% 5.17/5.51 ! [S: set_nat] :
% 5.17/5.51 ( ( ~ ( finite_finite_nat @ S ) )
% 5.17/5.51 = ( ! [M5: nat] :
% 5.17/5.51 ? [N4: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M5 @ N4 )
% 5.17/5.51 & ( member_nat @ N4 @ S ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % infinite_nat_iff_unbounded_le
% 5.17/5.51 thf(fact_9353_Frct__code__post_I5_J,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.17/5.51 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Frct_code_post(5)
% 5.17/5.51 thf(fact_9354_set__encode__insert,axiom,
% 5.17/5.51 ! [A2: set_nat,N: nat] :
% 5.17/5.51 ( ( finite_finite_nat @ A2 )
% 5.17/5.51 => ( ~ ( member_nat @ N @ A2 )
% 5.17/5.51 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.17/5.51 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_encode_insert
% 5.17/5.51 thf(fact_9355_lessThan__Suc,axiom,
% 5.17/5.51 ! [K: nat] :
% 5.17/5.51 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.17/5.51 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % lessThan_Suc
% 5.17/5.51 thf(fact_9356_atMost__Suc,axiom,
% 5.17/5.51 ! [K: nat] :
% 5.17/5.51 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.17/5.51 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atMost_Suc
% 5.17/5.51 thf(fact_9357_atLeast0__atMost__Suc,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.17/5.51 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeast0_atMost_Suc
% 5.17/5.51 thf(fact_9358_atLeast0__lessThan__Suc,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.17/5.51 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeast0_lessThan_Suc
% 5.17/5.51 thf(fact_9359_atLeastAtMost__insertL,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.17/5.51 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastAtMost_insertL
% 5.17/5.51 thf(fact_9360_atLeastAtMostSuc__conv,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.17/5.51 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.17/5.51 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastAtMostSuc_conv
% 5.17/5.51 thf(fact_9361_Icc__eq__insert__lb__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.17/5.51 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Icc_eq_insert_lb_nat
% 5.17/5.51 thf(fact_9362_lessThan__nat__numeral,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % lessThan_nat_numeral
% 5.17/5.51 thf(fact_9363_atMost__nat__numeral,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atMost_nat_numeral
% 5.17/5.51 thf(fact_9364_Frct__code__post_I2_J,axiom,
% 5.17/5.51 ! [A: int] :
% 5.17/5.51 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.17/5.51 = zero_zero_rat ) ).
% 5.17/5.51
% 5.17/5.51 % Frct_code_post(2)
% 5.17/5.51 thf(fact_9365_Frct__code__post_I1_J,axiom,
% 5.17/5.51 ! [A: int] :
% 5.17/5.51 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.17/5.51 = zero_zero_rat ) ).
% 5.17/5.51
% 5.17/5.51 % Frct_code_post(1)
% 5.17/5.51 thf(fact_9366_set__decode__plus__power__2,axiom,
% 5.17/5.51 ! [N: nat,Z: nat] :
% 5.17/5.51 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.17/5.51 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.17/5.51 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % set_decode_plus_power_2
% 5.17/5.51 thf(fact_9367_Frct__code__post_I4_J,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.17/5.51 = ( numeral_numeral_rat @ K ) ) ).
% 5.17/5.51
% 5.17/5.51 % Frct_code_post(4)
% 5.17/5.51 thf(fact_9368_Frct__code__post_I6_J,axiom,
% 5.17/5.51 ! [K: num,L: num] :
% 5.17/5.51 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.17/5.51 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Frct_code_post(6)
% 5.17/5.51 thf(fact_9369_divmod__integer__code,axiom,
% 5.17/5.51 ( code_divmod_integer
% 5.17/5.51 = ( ^ [K3: code_integer,L3: code_integer] :
% 5.17/5.51 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.17/5.51 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L3 )
% 5.17/5.51 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L3 )
% 5.17/5.51 @ ( produc6916734918728496179nteger
% 5.17/5.51 @ ^ [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 @ L3 @ S4 ) ) )
% 5.17/5.51 @ ( code_divmod_abs @ K3 @ L3 ) ) )
% 5.17/5.51 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.17/5.51 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.17/5.51 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L3 )
% 5.17/5.51 @ ( produc6916734918728496179nteger
% 5.17/5.51 @ ^ [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 @ L3 ) @ S4 ) ) )
% 5.17/5.51 @ ( code_divmod_abs @ K3 @ L3 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % divmod_integer_code
% 5.17/5.51 thf(fact_9370_card__atMost,axiom,
% 5.17/5.51 ! [U: nat] :
% 5.17/5.51 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.17/5.51 = ( suc @ U ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_atMost
% 5.17/5.51 thf(fact_9371_card__atLeastLessThan,axiom,
% 5.17/5.51 ! [L: nat,U: nat] :
% 5.17/5.51 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.17/5.51 = ( minus_minus_nat @ U @ L ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_atLeastLessThan
% 5.17/5.51 thf(fact_9372_card__Collect__le__nat,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( finite_card_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [I2: nat] : ( ord_less_eq_nat @ I2 @ N ) ) )
% 5.17/5.51 = ( suc @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_Collect_le_nat
% 5.17/5.51 thf(fact_9373_card__atLeastAtMost,axiom,
% 5.17/5.51 ! [L: nat,U: nat] :
% 5.17/5.51 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.17/5.51 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_atLeastAtMost
% 5.17/5.51 thf(fact_9374_card__atLeastLessThan__int,axiom,
% 5.17/5.51 ! [L: int,U: int] :
% 5.17/5.51 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.17/5.51 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_atLeastLessThan_int
% 5.17/5.51 thf(fact_9375_card__atLeastAtMost__int,axiom,
% 5.17/5.51 ! [L: int,U: int] :
% 5.17/5.51 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.17/5.51 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_atLeastAtMost_int
% 5.17/5.51 thf(fact_9376_card__length__sum__list__rec,axiom,
% 5.17/5.51 ! [M: nat,N5: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.17/5.51 => ( ( finite_card_list_nat
% 5.17/5.51 @ ( collect_list_nat
% 5.17/5.51 @ ^ [L3: list_nat] :
% 5.17/5.51 ( ( ( size_size_list_nat @ L3 )
% 5.17/5.51 = M )
% 5.17/5.51 & ( ( groups4561878855575611511st_nat @ L3 )
% 5.17/5.51 = N5 ) ) ) )
% 5.17/5.51 = ( plus_plus_nat
% 5.17/5.51 @ ( finite_card_list_nat
% 5.17/5.51 @ ( collect_list_nat
% 5.17/5.51 @ ^ [L3: list_nat] :
% 5.17/5.51 ( ( ( size_size_list_nat @ L3 )
% 5.17/5.51 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.17/5.51 & ( ( groups4561878855575611511st_nat @ L3 )
% 5.17/5.51 = N5 ) ) ) )
% 5.17/5.51 @ ( finite_card_list_nat
% 5.17/5.51 @ ( collect_list_nat
% 5.17/5.51 @ ^ [L3: list_nat] :
% 5.17/5.51 ( ( ( size_size_list_nat @ L3 )
% 5.17/5.51 = M )
% 5.17/5.51 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L3 ) @ one_one_nat )
% 5.17/5.51 = N5 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_length_sum_list_rec
% 5.17/5.51 thf(fact_9377_card__length__sum__list,axiom,
% 5.17/5.51 ! [M: nat,N5: nat] :
% 5.17/5.51 ( ( finite_card_list_nat
% 5.17/5.51 @ ( collect_list_nat
% 5.17/5.51 @ ^ [L3: list_nat] :
% 5.17/5.51 ( ( ( size_size_list_nat @ L3 )
% 5.17/5.51 = M )
% 5.17/5.51 & ( ( groups4561878855575611511st_nat @ L3 )
% 5.17/5.51 = N5 ) ) ) )
% 5.17/5.51 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M ) @ one_one_nat ) @ N5 ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_length_sum_list
% 5.17/5.51 thf(fact_9378_card__less__Suc2,axiom,
% 5.17/5.51 ! [M10: set_nat,I: nat] :
% 5.17/5.51 ( ~ ( member_nat @ zero_zero_nat @ M10 )
% 5.17/5.51 => ( ( finite_card_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [K3: nat] :
% 5.17/5.51 ( ( member_nat @ ( suc @ K3 ) @ M10 )
% 5.17/5.51 & ( ord_less_nat @ K3 @ I ) ) ) )
% 5.17/5.51 = ( finite_card_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [K3: nat] :
% 5.17/5.51 ( ( member_nat @ K3 @ M10 )
% 5.17/5.51 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_less_Suc2
% 5.17/5.51 thf(fact_9379_card__less__Suc,axiom,
% 5.17/5.51 ! [M10: set_nat,I: nat] :
% 5.17/5.51 ( ( member_nat @ zero_zero_nat @ M10 )
% 5.17/5.51 => ( ( suc
% 5.17/5.51 @ ( finite_card_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [K3: nat] :
% 5.17/5.51 ( ( member_nat @ ( suc @ K3 ) @ M10 )
% 5.17/5.51 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 5.17/5.51 = ( finite_card_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [K3: nat] :
% 5.17/5.51 ( ( member_nat @ K3 @ M10 )
% 5.17/5.51 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_less_Suc
% 5.17/5.51 thf(fact_9380_card__less,axiom,
% 5.17/5.51 ! [M10: set_nat,I: nat] :
% 5.17/5.51 ( ( member_nat @ zero_zero_nat @ M10 )
% 5.17/5.51 => ( ( finite_card_nat
% 5.17/5.51 @ ( collect_nat
% 5.17/5.51 @ ^ [K3: nat] :
% 5.17/5.51 ( ( member_nat @ K3 @ M10 )
% 5.17/5.51 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 5.17/5.51 != zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_less
% 5.17/5.51 thf(fact_9381_card__atLeastZeroLessThan__int,axiom,
% 5.17/5.51 ! [U: int] :
% 5.17/5.51 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.17/5.51 = ( nat2 @ U ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_atLeastZeroLessThan_int
% 5.17/5.51 thf(fact_9382_subset__card__intvl__is__intvl,axiom,
% 5.17/5.51 ! [A2: set_nat,K: nat] :
% 5.17/5.51 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.17/5.51 => ( A2
% 5.17/5.51 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % subset_card_intvl_is_intvl
% 5.17/5.51 thf(fact_9383_atLeastAtMostPlus1__int__conv,axiom,
% 5.17/5.51 ! [M: int,N: int] :
% 5.17/5.51 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.17/5.51 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.17/5.51 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastAtMostPlus1_int_conv
% 5.17/5.51 thf(fact_9384_subset__eq__atLeast0__lessThan__card,axiom,
% 5.17/5.51 ! [N5: set_nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.17/5.51 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % subset_eq_atLeast0_lessThan_card
% 5.17/5.51 thf(fact_9385_card__sum__le__nat__sum,axiom,
% 5.17/5.51 ! [S: set_nat] :
% 5.17/5.51 ( ord_less_eq_nat
% 5.17/5.51 @ ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 5.17/5.51 @ ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ S ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_sum_le_nat_sum
% 5.17/5.51 thf(fact_9386_card__nth__roots,axiom,
% 5.17/5.51 ! [C: complex,N: nat] :
% 5.17/5.51 ( ( C != zero_zero_complex )
% 5.17/5.51 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( finite_card_complex
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = C ) ) )
% 5.17/5.51 = N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_nth_roots
% 5.17/5.51 thf(fact_9387_card__roots__unity__eq,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.51 => ( ( finite_card_complex
% 5.17/5.51 @ ( collect_complex
% 5.17/5.51 @ ^ [Z5: complex] :
% 5.17/5.51 ( ( power_power_complex @ Z5 @ N )
% 5.17/5.51 = one_one_complex ) ) )
% 5.17/5.51 = N ) ) ).
% 5.17/5.51
% 5.17/5.51 % card_roots_unity_eq
% 5.17/5.51 thf(fact_9388_and__int_Osimps,axiom,
% 5.17/5.51 ( bit_se725231765392027082nd_int
% 5.17/5.51 = ( ^ [K3: int,L3: int] :
% 5.17/5.51 ( if_int
% 5.17/5.51 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 @ ( uminus_uminus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) ) )
% 5.17/5.51 @ ( plus_plus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L3 ) ) )
% 5.17/5.51 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % and_int.simps
% 5.17/5.51 thf(fact_9389_and__int_Oelims,axiom,
% 5.17/5.51 ! [X: int,Xa: int,Y4: int] :
% 5.17/5.51 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( uminus_uminus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.17/5.51 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % and_int.elims
% 5.17/5.51 thf(fact_9390_and__int_Opsimps,axiom,
% 5.17/5.51 ! [K: int,L: int] :
% 5.17/5.51 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.17/5.51 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.17/5.51 = ( uminus_uminus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.17/5.51 = ( plus_plus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.17/5.51 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % and_int.psimps
% 5.17/5.51 thf(fact_9391_and__int_Opelims,axiom,
% 5.17/5.51 ! [X: int,Xa: int,Y4: int] :
% 5.17/5.51 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 5.17/5.51 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( uminus_uminus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.17/5.51 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( plus_plus_int
% 5.17/5.51 @ ( zero_n2684676970156552555ol_int
% 5.17/5.51 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.17/5.51 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.17/5.51 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.17/5.51 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % and_int.pelims
% 5.17/5.51 thf(fact_9392_and__int_Opinduct,axiom,
% 5.17/5.51 ! [A0: int,A1: int,P: int > int > $o] :
% 5.17/5.51 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.17/5.51 => ( ! [K2: int,L2: int] :
% 5.17/5.51 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L2 ) )
% 5.17/5.51 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.17/5.51 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.17/5.51 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.17/5.51 => ( P @ K2 @ L2 ) ) )
% 5.17/5.51 => ( P @ A0 @ A1 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % and_int.pinduct
% 5.17/5.51 thf(fact_9393_lessThan__0,axiom,
% 5.17/5.51 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.17/5.51 = bot_bot_set_nat ) ).
% 5.17/5.51
% 5.17/5.51 % lessThan_0
% 5.17/5.51 thf(fact_9394_set__decode__zero,axiom,
% 5.17/5.51 ( ( nat_set_decode @ zero_zero_nat )
% 5.17/5.51 = bot_bot_set_nat ) ).
% 5.17/5.51
% 5.17/5.51 % set_decode_zero
% 5.17/5.51 thf(fact_9395_set__encode__empty,axiom,
% 5.17/5.51 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.17/5.51 = zero_zero_nat ) ).
% 5.17/5.51
% 5.17/5.51 % set_encode_empty
% 5.17/5.51 thf(fact_9396_atLeastLessThan__singleton,axiom,
% 5.17/5.51 ! [M: nat] :
% 5.17/5.51 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.17/5.51 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastLessThan_singleton
% 5.17/5.51 thf(fact_9397_atMost__0,axiom,
% 5.17/5.51 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.17/5.51 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % atMost_0
% 5.17/5.51 thf(fact_9398_bot__enat__def,axiom,
% 5.17/5.51 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.17/5.51
% 5.17/5.51 % bot_enat_def
% 5.17/5.51 thf(fact_9399_bot__nat__def,axiom,
% 5.17/5.51 bot_bot_nat = zero_zero_nat ).
% 5.17/5.51
% 5.17/5.51 % bot_nat_def
% 5.17/5.51 thf(fact_9400_atLeastLessThan0,axiom,
% 5.17/5.51 ! [M: nat] :
% 5.17/5.51 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.17/5.51 = bot_bot_set_nat ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastLessThan0
% 5.17/5.51 thf(fact_9401_lessThan__empty__iff,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( ( set_ord_lessThan_nat @ N )
% 5.17/5.51 = bot_bot_set_nat )
% 5.17/5.51 = ( N = zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % lessThan_empty_iff
% 5.17/5.51 thf(fact_9402_atLeastLessThanSuc,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.17/5.51 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.17/5.51 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.17/5.51 = bot_bot_set_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastLessThanSuc
% 5.17/5.51 thf(fact_9403_atLeast1__lessThan__eq__remove0,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.51 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeast1_lessThan_eq_remove0
% 5.17/5.51 thf(fact_9404_atLeast1__atMost__eq__remove0,axiom,
% 5.17/5.51 ! [N: nat] :
% 5.17/5.51 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.17/5.51 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeast1_atMost_eq_remove0
% 5.17/5.51 thf(fact_9405_atLeastLessThan__nat__numeral,axiom,
% 5.17/5.51 ! [M: nat,K: num] :
% 5.17/5.51 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.17/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.17/5.51 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.17/5.51 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = bot_bot_set_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastLessThan_nat_numeral
% 5.17/5.51 thf(fact_9406_length__upt,axiom,
% 5.17/5.51 ! [I: nat,J: nat] :
% 5.17/5.51 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 5.17/5.51 = ( minus_minus_nat @ J @ I ) ) ).
% 5.17/5.51
% 5.17/5.51 % length_upt
% 5.17/5.51 thf(fact_9407_sum__list__upt,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.17/5.51 = ( groups3542108847815614940at_nat
% 5.17/5.51 @ ^ [X3: nat] : X3
% 5.17/5.51 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sum_list_upt
% 5.17/5.51 thf(fact_9408_map__Suc__upt,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.17/5.51 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % map_Suc_upt
% 5.17/5.51 thf(fact_9409_map__add__upt,axiom,
% 5.17/5.51 ! [N: nat,M: nat] :
% 5.17/5.51 ( ( map_nat_nat
% 5.17/5.51 @ ^ [I2: nat] : ( plus_plus_nat @ I2 @ N )
% 5.17/5.51 @ ( upt @ zero_zero_nat @ M ) )
% 5.17/5.51 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % map_add_upt
% 5.17/5.51 thf(fact_9410_map__decr__upt,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( map_nat_nat
% 5.17/5.51 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 5.17/5.51 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.17/5.51 = ( upt @ M @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % map_decr_upt
% 5.17/5.51 thf(fact_9411_atLeastAtMost__upt,axiom,
% 5.17/5.51 ( set_or1269000886237332187st_nat
% 5.17/5.51 = ( ^ [N4: nat,M5: nat] : ( set_nat2 @ ( upt @ N4 @ ( suc @ M5 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeastAtMost_upt
% 5.17/5.51 thf(fact_9412_atLeast__upt,axiom,
% 5.17/5.51 ( set_ord_lessThan_nat
% 5.17/5.51 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atLeast_upt
% 5.17/5.51 thf(fact_9413_atMost__upto,axiom,
% 5.17/5.51 ( set_ord_atMost_nat
% 5.17/5.51 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % atMost_upto
% 5.17/5.51 thf(fact_9414_sorted__upt,axiom,
% 5.17/5.51 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % sorted_upt
% 5.17/5.51 thf(fact_9415_sorted__wrt__less__idx,axiom,
% 5.17/5.51 ! [Ns: list_nat,I: nat] :
% 5.17/5.51 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.17/5.51 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.17/5.51 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % sorted_wrt_less_idx
% 5.17/5.51 thf(fact_9416_binomial__def,axiom,
% 5.17/5.51 ( binomial
% 5.17/5.51 = ( ^ [N4: nat,K3: nat] :
% 5.17/5.51 ( finite_card_set_nat
% 5.17/5.51 @ ( collect_set_nat
% 5.17/5.51 @ ^ [K7: set_nat] :
% 5.17/5.51 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 5.17/5.51 & ( ( finite_card_nat @ K7 )
% 5.17/5.51 = K3 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % binomial_def
% 5.17/5.51 thf(fact_9417_Suc__0__div__numeral,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Suc_0_div_numeral
% 5.17/5.51 thf(fact_9418_Suc__0__mod__numeral,axiom,
% 5.17/5.51 ! [K: num] :
% 5.17/5.51 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.51 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Suc_0_mod_numeral
% 5.17/5.51 thf(fact_9419_fst__divmod__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.17/5.51 = ( divide_divide_nat @ M @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % fst_divmod_nat
% 5.17/5.51 thf(fact_9420_snd__divmod__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.17/5.51 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.17/5.51
% 5.17/5.51 % snd_divmod_nat
% 5.17/5.51 thf(fact_9421_quotient__of__denom__pos_H,axiom,
% 5.17/5.51 ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % quotient_of_denom_pos'
% 5.17/5.51 thf(fact_9422_bezw__non__0,axiom,
% 5.17/5.51 ! [Y4: nat,X: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ Y4 )
% 5.17/5.51 => ( ( bezw @ X @ Y4 )
% 5.17/5.51 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y4 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezw_non_0
% 5.17/5.51 thf(fact_9423_bezw_Osimps,axiom,
% 5.17/5.51 ( bezw
% 5.17/5.51 = ( ^ [X3: nat,Y6: nat] : ( if_Pro3027730157355071871nt_int @ ( Y6 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X3 @ Y6 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X3 @ Y6 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X3 @ Y6 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y6 ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezw.simps
% 5.17/5.51 thf(fact_9424_bezw_Oelims,axiom,
% 5.17/5.51 ! [X: nat,Xa: nat,Y4: product_prod_int_int] :
% 5.17/5.51 ( ( ( bezw @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezw.elims
% 5.17/5.51 thf(fact_9425_bezw_Opelims,axiom,
% 5.17/5.51 ! [X: nat,Xa: nat,Y4: product_prod_int_int] :
% 5.17/5.51 ( ( ( bezw @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.17/5.51 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 5.17/5.51 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezw.pelims
% 5.17/5.51 thf(fact_9426_one__mod__minus__numeral,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % one_mod_minus_numeral
% 5.17/5.51 thf(fact_9427_minus__one__mod__numeral,axiom,
% 5.17/5.51 ! [N: num] :
% 5.17/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.51 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % minus_one_mod_numeral
% 5.17/5.51 thf(fact_9428_minus__numeral__mod__numeral,axiom,
% 5.17/5.51 ! [M: num,N: num] :
% 5.17/5.51 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.51 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % minus_numeral_mod_numeral
% 5.17/5.51 thf(fact_9429_numeral__mod__minus__numeral,axiom,
% 5.17/5.51 ! [M: num,N: num] :
% 5.17/5.51 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.51 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % numeral_mod_minus_numeral
% 5.17/5.51 thf(fact_9430_Divides_Oadjust__mod__def,axiom,
% 5.17/5.51 ( adjust_mod
% 5.17/5.51 = ( ^ [L3: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L3 @ R5 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % Divides.adjust_mod_def
% 5.17/5.51 thf(fact_9431_normalize__def,axiom,
% 5.17/5.51 ( normalize
% 5.17/5.51 = ( ^ [P6: product_prod_int_int] :
% 5.17/5.51 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P6 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) )
% 5.17/5.51 @ ( if_Pro3027730157355071871nt_int
% 5.17/5.51 @ ( ( product_snd_int_int @ P6 )
% 5.17/5.51 = zero_zero_int )
% 5.17/5.51 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.17/5.51 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P6 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P6 ) @ ( product_snd_int_int @ P6 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % normalize_def
% 5.17/5.51 thf(fact_9432_gcd__pos__int,axiom,
% 5.17/5.51 ! [M: int,N: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.17/5.51 = ( ( M != zero_zero_int )
% 5.17/5.51 | ( N != zero_zero_int ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_pos_int
% 5.17/5.51 thf(fact_9433_gcd__neg__numeral__1__int,axiom,
% 5.17/5.51 ! [N: num,X: int] :
% 5.17/5.51 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 5.17/5.51 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_neg_numeral_1_int
% 5.17/5.51 thf(fact_9434_gcd__neg__numeral__2__int,axiom,
% 5.17/5.51 ! [X: int,N: num] :
% 5.17/5.51 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.51 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_neg_numeral_2_int
% 5.17/5.51 thf(fact_9435_gcd__0__int,axiom,
% 5.17/5.51 ! [X: int] :
% 5.17/5.51 ( ( gcd_gcd_int @ X @ zero_zero_int )
% 5.17/5.51 = ( abs_abs_int @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_0_int
% 5.17/5.51 thf(fact_9436_gcd__0__left__int,axiom,
% 5.17/5.51 ! [X: int] :
% 5.17/5.51 ( ( gcd_gcd_int @ zero_zero_int @ X )
% 5.17/5.51 = ( abs_abs_int @ X ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_0_left_int
% 5.17/5.51 thf(fact_9437_gcd__proj2__if__dvd__int,axiom,
% 5.17/5.51 ! [Y4: int,X: int] :
% 5.17/5.51 ( ( dvd_dvd_int @ Y4 @ X )
% 5.17/5.51 => ( ( gcd_gcd_int @ X @ Y4 )
% 5.17/5.51 = ( abs_abs_int @ Y4 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_proj2_if_dvd_int
% 5.17/5.51 thf(fact_9438_gcd__proj1__if__dvd__int,axiom,
% 5.17/5.51 ! [X: int,Y4: int] :
% 5.17/5.51 ( ( dvd_dvd_int @ X @ Y4 )
% 5.17/5.51 => ( ( gcd_gcd_int @ X @ Y4 )
% 5.17/5.51 = ( abs_abs_int @ X ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_proj1_if_dvd_int
% 5.17/5.51 thf(fact_9439_gcd__ge__0__int,axiom,
% 5.17/5.51 ! [X: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y4 ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_ge_0_int
% 5.17/5.51 thf(fact_9440_bezout__int,axiom,
% 5.17/5.51 ! [X: int,Y4: int] :
% 5.17/5.51 ? [U2: int,V3: int] :
% 5.17/5.51 ( ( plus_plus_int @ ( times_times_int @ U2 @ X ) @ ( times_times_int @ V3 @ Y4 ) )
% 5.17/5.51 = ( gcd_gcd_int @ X @ Y4 ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezout_int
% 5.17/5.51 thf(fact_9441_gcd__mult__distrib__int,axiom,
% 5.17/5.51 ! [K: int,M: int,N: int] :
% 5.17/5.51 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.17/5.51 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_mult_distrib_int
% 5.17/5.51 thf(fact_9442_gcd__le1__int,axiom,
% 5.17/5.51 ! [A: int,B: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ A )
% 5.17/5.51 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_le1_int
% 5.17/5.51 thf(fact_9443_gcd__le2__int,axiom,
% 5.17/5.51 ! [B: int,A: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.51 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_le2_int
% 5.17/5.51 thf(fact_9444_gcd__cases__int,axiom,
% 5.17/5.51 ! [X: int,Y4: int,P: int > $o] :
% 5.17/5.51 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.51 => ( P @ ( gcd_gcd_int @ X @ Y4 ) ) ) )
% 5.17/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.17/5.51 => ( ( ord_less_eq_int @ Y4 @ zero_zero_int )
% 5.17/5.51 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y4 ) ) ) ) )
% 5.17/5.51 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.17/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.17/5.51 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y4 ) ) ) )
% 5.17/5.51 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.17/5.51 => ( ( ord_less_eq_int @ Y4 @ zero_zero_int )
% 5.17/5.51 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y4 ) ) ) ) )
% 5.17/5.51 => ( P @ ( gcd_gcd_int @ X @ Y4 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_cases_int
% 5.17/5.51 thf(fact_9445_gcd__unique__int,axiom,
% 5.17/5.51 ! [D: int,A: int,B: int] :
% 5.17/5.51 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.17/5.51 & ( dvd_dvd_int @ D @ A )
% 5.17/5.51 & ( dvd_dvd_int @ D @ B )
% 5.17/5.51 & ! [E3: int] :
% 5.17/5.51 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.17/5.51 & ( dvd_dvd_int @ E3 @ B ) )
% 5.17/5.51 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.17/5.51 = ( D
% 5.17/5.51 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_unique_int
% 5.17/5.51 thf(fact_9446_gcd__non__0__int,axiom,
% 5.17/5.51 ! [Y4: int,X: int] :
% 5.17/5.51 ( ( ord_less_int @ zero_zero_int @ Y4 )
% 5.17/5.51 => ( ( gcd_gcd_int @ X @ Y4 )
% 5.17/5.51 = ( gcd_gcd_int @ Y4 @ ( modulo_modulo_int @ X @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_non_0_int
% 5.17/5.51 thf(fact_9447_gcd__code__int,axiom,
% 5.17/5.51 ( gcd_gcd_int
% 5.17/5.51 = ( ^ [K3: int,L3: int] : ( abs_abs_int @ ( if_int @ ( L3 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L3 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L3 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_code_int
% 5.17/5.51 thf(fact_9448_gcd__0__left__nat,axiom,
% 5.17/5.51 ! [X: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 5.17/5.51 = X ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_0_left_nat
% 5.17/5.51 thf(fact_9449_gcd__0__nat,axiom,
% 5.17/5.51 ! [X: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 5.17/5.51 = X ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_0_nat
% 5.17/5.51 thf(fact_9450_gcd__nat_Oright__neutral,axiom,
% 5.17/5.51 ! [A: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 5.17/5.51 = A ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.right_neutral
% 5.17/5.51 thf(fact_9451_gcd__nat_Oneutr__eq__iff,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( zero_zero_nat
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) )
% 5.17/5.51 = ( ( A = zero_zero_nat )
% 5.17/5.51 & ( B = zero_zero_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.neutr_eq_iff
% 5.17/5.51 thf(fact_9452_gcd__nat_Oleft__neutral,axiom,
% 5.17/5.51 ! [A: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 5.17/5.51 = A ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.left_neutral
% 5.17/5.51 thf(fact_9453_gcd__nat_Oeq__neutr__iff,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 = zero_zero_nat )
% 5.17/5.51 = ( ( A = zero_zero_nat )
% 5.17/5.51 & ( B = zero_zero_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.eq_neutr_iff
% 5.17/5.51 thf(fact_9454_gcd__nat_Oabsorb1,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 => ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 = A ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.absorb1
% 5.17/5.51 thf(fact_9455_gcd__nat_Oabsorb2,axiom,
% 5.17/5.51 ! [B: nat,A: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.51 => ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 = B ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.absorb2
% 5.17/5.51 thf(fact_9456_gcd__nat_Obounded__iff,axiom,
% 5.17/5.51 ! [A: nat,B: nat,C: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 5.17/5.51 = ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 & ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.bounded_iff
% 5.17/5.51 thf(fact_9457_gcd__proj1__if__dvd__nat,axiom,
% 5.17/5.51 ! [X: nat,Y4: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ X @ Y4 )
% 5.17/5.51 => ( ( gcd_gcd_nat @ X @ Y4 )
% 5.17/5.51 = X ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_proj1_if_dvd_nat
% 5.17/5.51 thf(fact_9458_gcd__proj2__if__dvd__nat,axiom,
% 5.17/5.51 ! [Y4: nat,X: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ Y4 @ X )
% 5.17/5.51 => ( ( gcd_gcd_nat @ X @ Y4 )
% 5.17/5.51 = Y4 ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_proj2_if_dvd_nat
% 5.17/5.51 thf(fact_9459_gcd__Suc__0,axiom,
% 5.17/5.51 ! [M: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.17/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_Suc_0
% 5.17/5.51 thf(fact_9460_gcd__pos__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.17/5.51 = ( ( M != zero_zero_nat )
% 5.17/5.51 | ( N != zero_zero_nat ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_pos_nat
% 5.17/5.51 thf(fact_9461_gcd__int__int__eq,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.51 = ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_int_int_eq
% 5.17/5.51 thf(fact_9462_gcd__nat__abs__right__eq,axiom,
% 5.17/5.51 ! [N: nat,K: int] :
% 5.17/5.51 ( ( gcd_gcd_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.17/5.51 = ( nat2 @ ( gcd_gcd_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat_abs_right_eq
% 5.17/5.51 thf(fact_9463_gcd__nat__abs__left__eq,axiom,
% 5.17/5.51 ! [K: int,N: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.17/5.51 = ( nat2 @ ( gcd_gcd_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat_abs_left_eq
% 5.17/5.51 thf(fact_9464_gcd__mult__distrib__nat,axiom,
% 5.17/5.51 ! [K: nat,M: nat,N: nat] :
% 5.17/5.51 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.17/5.51 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_mult_distrib_nat
% 5.17/5.51 thf(fact_9465_gcd__nat_Omono,axiom,
% 5.17/5.51 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.51 => ( ( dvd_dvd_nat @ B @ D )
% 5.17/5.51 => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ ( gcd_gcd_nat @ C @ D ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.mono
% 5.17/5.51 thf(fact_9466_gcd__nat_OorderE,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 => ( A
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.orderE
% 5.17/5.51 thf(fact_9467_gcd__nat_OorderI,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( A
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) )
% 5.17/5.51 => ( dvd_dvd_nat @ A @ B ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.orderI
% 5.17/5.51 thf(fact_9468_gcd__nat_Oabsorb3,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 & ( A != B ) )
% 5.17/5.51 => ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 = A ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.absorb3
% 5.17/5.51 thf(fact_9469_gcd__nat_Oabsorb4,axiom,
% 5.17/5.51 ! [B: nat,A: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ B @ A )
% 5.17/5.51 & ( B != A ) )
% 5.17/5.51 => ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 = B ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.absorb4
% 5.17/5.51 thf(fact_9470_gcd__nat_OboundedE,axiom,
% 5.17/5.51 ! [A: nat,B: nat,C: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 5.17/5.51 => ~ ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 => ~ ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.boundedE
% 5.17/5.51 thf(fact_9471_gcd__nat_OboundedI,axiom,
% 5.17/5.51 ! [A: nat,B: nat,C: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 => ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.51 => ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.boundedI
% 5.17/5.51 thf(fact_9472_gcd__nat_Oorder__iff,axiom,
% 5.17/5.51 ( dvd_dvd_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.51 ( A3
% 5.17/5.51 = ( gcd_gcd_nat @ A3 @ B2 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.order_iff
% 5.17/5.51 thf(fact_9473_gcd__nat_Ocobounded1,axiom,
% 5.17/5.51 ! [A: nat,B: nat] : ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.cobounded1
% 5.17/5.51 thf(fact_9474_gcd__nat_Ocobounded2,axiom,
% 5.17/5.51 ! [A: nat,B: nat] : ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.cobounded2
% 5.17/5.51 thf(fact_9475_gcd__nat_Oabsorb__iff1,axiom,
% 5.17/5.51 ( dvd_dvd_nat
% 5.17/5.51 = ( ^ [A3: nat,B2: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ A3 @ B2 )
% 5.17/5.51 = A3 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.absorb_iff1
% 5.17/5.51 thf(fact_9476_gcd__nat_Oabsorb__iff2,axiom,
% 5.17/5.51 ( dvd_dvd_nat
% 5.17/5.51 = ( ^ [B2: nat,A3: nat] :
% 5.17/5.51 ( ( gcd_gcd_nat @ A3 @ B2 )
% 5.17/5.51 = B2 ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.absorb_iff2
% 5.17/5.51 thf(fact_9477_gcd__nat_OcoboundedI1,axiom,
% 5.17/5.51 ! [A: nat,C: nat,B: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.51 => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.coboundedI1
% 5.17/5.51 thf(fact_9478_gcd__nat_OcoboundedI2,axiom,
% 5.17/5.51 ! [B: nat,C: nat,A: nat] :
% 5.17/5.51 ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.51 => ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.coboundedI2
% 5.17/5.51 thf(fact_9479_gcd__nat_Ostrict__boundedE,axiom,
% 5.17/5.51 ! [A: nat,B: nat,C: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ A @ ( gcd_gcd_nat @ B @ C ) )
% 5.17/5.51 & ( A
% 5.17/5.51 != ( gcd_gcd_nat @ B @ C ) ) )
% 5.17/5.51 => ~ ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 & ( A != B ) )
% 5.17/5.51 => ~ ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.51 & ( A != C ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.strict_boundedE
% 5.17/5.51 thf(fact_9480_gcd__nat_Ostrict__order__iff,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ A @ B )
% 5.17/5.51 & ( A != B ) )
% 5.17/5.51 = ( ( A
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) )
% 5.17/5.51 & ( A != B ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.strict_order_iff
% 5.17/5.51 thf(fact_9481_gcd__nat_Ostrict__coboundedI1,axiom,
% 5.17/5.51 ! [A: nat,C: nat,B: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ A @ C )
% 5.17/5.51 & ( A != C ) )
% 5.17/5.51 => ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C )
% 5.17/5.51 & ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 != C ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.strict_coboundedI1
% 5.17/5.51 thf(fact_9482_gcd__nat_Ostrict__coboundedI2,axiom,
% 5.17/5.51 ! [B: nat,C: nat,A: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ B @ C )
% 5.17/5.51 & ( B != C ) )
% 5.17/5.51 => ( ( dvd_dvd_nat @ ( gcd_gcd_nat @ A @ B ) @ C )
% 5.17/5.51 & ( ( gcd_gcd_nat @ A @ B )
% 5.17/5.51 != C ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.strict_coboundedI2
% 5.17/5.51 thf(fact_9483_gcd__unique__nat,axiom,
% 5.17/5.51 ! [D: nat,A: nat,B: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ D @ A )
% 5.17/5.51 & ( dvd_dvd_nat @ D @ B )
% 5.17/5.51 & ! [E3: nat] :
% 5.17/5.51 ( ( ( dvd_dvd_nat @ E3 @ A )
% 5.17/5.51 & ( dvd_dvd_nat @ E3 @ B ) )
% 5.17/5.51 => ( dvd_dvd_nat @ E3 @ D ) ) )
% 5.17/5.51 = ( D
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_unique_nat
% 5.17/5.51 thf(fact_9484_gcd__le2__nat,axiom,
% 5.17/5.51 ! [B: nat,A: nat] :
% 5.17/5.51 ( ( B != zero_zero_nat )
% 5.17/5.51 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_le2_nat
% 5.17/5.51 thf(fact_9485_gcd__le1__nat,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( A != zero_zero_nat )
% 5.17/5.51 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_le1_nat
% 5.17/5.51 thf(fact_9486_gcd__diff1__nat,axiom,
% 5.17/5.51 ! [N: nat,M: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ N @ M )
% 5.17/5.51 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.17/5.51 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_diff1_nat
% 5.17/5.51 thf(fact_9487_gcd__diff2__nat,axiom,
% 5.17/5.51 ! [M: nat,N: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ M @ N )
% 5.17/5.51 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.17/5.51 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_diff2_nat
% 5.17/5.51 thf(fact_9488_gcd__nat_Oelims,axiom,
% 5.17/5.51 ! [X: nat,Xa: nat,Y4: nat] :
% 5.17/5.51 ( ( ( gcd_gcd_nat @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => ( Y4 = X ) )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.elims
% 5.17/5.51 thf(fact_9489_gcd__nat_Osimps,axiom,
% 5.17/5.51 ( gcd_gcd_nat
% 5.17/5.51 = ( ^ [X3: nat,Y6: nat] : ( if_nat @ ( Y6 = zero_zero_nat ) @ X3 @ ( gcd_gcd_nat @ Y6 @ ( modulo_modulo_nat @ X3 @ Y6 ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.simps
% 5.17/5.51 thf(fact_9490_gcd__non__0__nat,axiom,
% 5.17/5.51 ! [Y4: nat,X: nat] :
% 5.17/5.51 ( ( Y4 != zero_zero_nat )
% 5.17/5.51 => ( ( gcd_gcd_nat @ X @ Y4 )
% 5.17/5.51 = ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_non_0_nat
% 5.17/5.51 thf(fact_9491_gcd__code__integer,axiom,
% 5.17/5.51 ( gcd_gcd_Code_integer
% 5.17/5.51 = ( ^ [K3: code_integer,L3: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L3 = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L3 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L3 ) ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_code_integer
% 5.17/5.51 thf(fact_9492_bezout__nat,axiom,
% 5.17/5.51 ! [A: nat,B: nat] :
% 5.17/5.51 ( ( A != zero_zero_nat )
% 5.17/5.51 => ? [X4: nat,Y: nat] :
% 5.17/5.51 ( ( times_times_nat @ A @ X4 )
% 5.17/5.51 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezout_nat
% 5.17/5.51 thf(fact_9493_bezout__gcd__nat_H,axiom,
% 5.17/5.51 ! [B: nat,A: nat] :
% 5.17/5.51 ? [X4: nat,Y: nat] :
% 5.17/5.51 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y ) @ ( times_times_nat @ A @ X4 ) )
% 5.17/5.51 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y ) )
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.17/5.51 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y ) @ ( times_times_nat @ B @ X4 ) )
% 5.17/5.51 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y ) )
% 5.17/5.51 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezout_gcd_nat'
% 5.17/5.51 thf(fact_9494_gcd__int__def,axiom,
% 5.17/5.51 ( gcd_gcd_int
% 5.17/5.51 = ( ^ [X3: int,Y6: int] : ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ ( nat2 @ ( abs_abs_int @ X3 ) ) @ ( nat2 @ ( abs_abs_int @ Y6 ) ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_int_def
% 5.17/5.51 thf(fact_9495_bezw__aux,axiom,
% 5.17/5.51 ! [X: nat,Y4: nat] :
% 5.17/5.51 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y4 ) )
% 5.17/5.51 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y4 ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y4 ) ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % bezw_aux
% 5.17/5.51 thf(fact_9496_nat__descend__induct,axiom,
% 5.17/5.51 ! [N: nat,P: nat > $o,M: nat] :
% 5.17/5.51 ( ! [K2: nat] :
% 5.17/5.51 ( ( ord_less_nat @ N @ K2 )
% 5.17/5.51 => ( P @ K2 ) )
% 5.17/5.51 => ( ! [K2: nat] :
% 5.17/5.51 ( ( ord_less_eq_nat @ K2 @ N )
% 5.17/5.51 => ( ! [I4: nat] :
% 5.17/5.51 ( ( ord_less_nat @ K2 @ I4 )
% 5.17/5.51 => ( P @ I4 ) )
% 5.17/5.51 => ( P @ K2 ) ) )
% 5.17/5.51 => ( P @ M ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % nat_descend_induct
% 5.17/5.51 thf(fact_9497_gcd__nat_Opelims,axiom,
% 5.17/5.51 ! [X: nat,Xa: nat,Y4: nat] :
% 5.17/5.51 ( ( ( gcd_gcd_nat @ X @ Xa )
% 5.17/5.51 = Y4 )
% 5.17/5.51 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.17/5.51 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.17/5.51 => ( Y4 = X ) )
% 5.17/5.51 & ( ( Xa != zero_zero_nat )
% 5.17/5.51 => ( Y4
% 5.17/5.51 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 5.17/5.51 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.17/5.51
% 5.17/5.51 % gcd_nat.pelims
% 5.17/5.51 thf(fact_9498_Sup__nat__empty,axiom,
% 5.17/5.51 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.17/5.51 = zero_zero_nat ) ).
% 5.17/5.51
% 5.17/5.51 % Sup_nat_empty
% 5.17/5.51 thf(fact_9499_divmod__integer__eq__cases,axiom,
% 5.17/5.51 ( code_divmod_integer
% 5.17/5.51 = ( ^ [K3: code_integer,L3: code_integer] :
% 5.17/5.51 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.17/5.51 @ ( if_Pro6119634080678213985nteger @ ( L3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.17/5.51 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L3
% 5.17/5.51 @ ( if_Pro6119634080678213985nteger
% 5.17/5.51 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.17/5.51 = ( sgn_sgn_Code_integer @ L3 ) )
% 5.17/5.51 @ ( code_divmod_abs @ K3 @ L3 )
% 5.17/5.51 @ ( produc6916734918728496179nteger
% 5.17/5.51 @ ^ [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 @ L3 ) @ S4 ) ) )
% 5.17/5.52 @ ( code_divmod_abs @ K3 @ L3 ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % divmod_integer_eq_cases
% 5.17/5.52 thf(fact_9500_card__greaterThanLessThan__int,axiom,
% 5.17/5.52 ! [L: int,U: int] :
% 5.17/5.52 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.17/5.52 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_greaterThanLessThan_int
% 5.17/5.52 thf(fact_9501_Suc__funpow,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( compow_nat_nat @ N @ suc )
% 5.17/5.52 = ( plus_plus_nat @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % Suc_funpow
% 5.17/5.52 thf(fact_9502_card__greaterThanLessThan,axiom,
% 5.17/5.52 ! [L: nat,U: nat] :
% 5.17/5.52 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.17/5.52 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_greaterThanLessThan
% 5.17/5.52 thf(fact_9503_card_Ocomp__fun__commute__on,axiom,
% 5.17/5.52 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.17/5.52 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.17/5.52
% 5.17/5.52 % card.comp_fun_commute_on
% 5.17/5.52 thf(fact_9504_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.17/5.52 ! [L: nat,U: nat] :
% 5.17/5.52 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.17/5.52 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeastSucLessThan_greaterThanLessThan
% 5.17/5.52 thf(fact_9505_greaterThanLessThan__upt,axiom,
% 5.17/5.52 ( set_or5834768355832116004an_nat
% 5.17/5.52 = ( ^ [N4: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ M5 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % greaterThanLessThan_upt
% 5.17/5.52 thf(fact_9506_Code__Target__Int_Onegative__def,axiom,
% 5.17/5.52 ( code_Target_negative
% 5.17/5.52 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.17/5.52
% 5.17/5.52 % Code_Target_Int.negative_def
% 5.17/5.52 thf(fact_9507_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.17/5.52 ! [N: nat,J: nat,I: nat] :
% 5.17/5.52 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.17/5.52 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.17/5.52 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nth_sorted_list_of_set_greaterThanLessThan
% 5.17/5.52 thf(fact_9508_nat__of__integer__non__positive,axiom,
% 5.17/5.52 ! [K: code_integer] :
% 5.17/5.52 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.17/5.52 => ( ( code_nat_of_integer @ K )
% 5.17/5.52 = zero_zero_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_of_integer_non_positive
% 5.17/5.52 thf(fact_9509_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.17/5.52 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] : ( ord_less_eq_nat @ Y6 @ X3 )
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] : ( ord_less_nat @ Y6 @ X3 ) ) ).
% 5.17/5.52
% 5.17/5.52 % max_nat.semilattice_neutr_order_axioms
% 5.17/5.52 thf(fact_9510_of__nat__of__integer,axiom,
% 5.17/5.52 ! [K: code_integer] :
% 5.17/5.52 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 5.17/5.52 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 5.17/5.52
% 5.17/5.52 % of_nat_of_integer
% 5.17/5.52 thf(fact_9511_nat__of__integer__code__post_I1_J,axiom,
% 5.17/5.52 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.17/5.52 = zero_zero_nat ) ).
% 5.17/5.52
% 5.17/5.52 % nat_of_integer_code_post(1)
% 5.17/5.52 thf(fact_9512_nat__of__integer__code__post_I3_J,axiom,
% 5.17/5.52 ! [K: num] :
% 5.17/5.52 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.17/5.52 = ( numeral_numeral_nat @ K ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_of_integer_code_post(3)
% 5.17/5.52 thf(fact_9513_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.17/5.52 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.17/5.52 @ ^ [M5: nat,N4: nat] :
% 5.17/5.52 ( ( dvd_dvd_nat @ M5 @ N4 )
% 5.17/5.52 & ( M5 != N4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % gcd_nat.semilattice_neutr_order_axioms
% 5.17/5.52 thf(fact_9514_nat__of__integer__code,axiom,
% 5.17/5.52 ( code_nat_of_integer
% 5.17/5.52 = ( ^ [K3: code_integer] :
% 5.17/5.52 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.17/5.52 @ ( produc1555791787009142072er_nat
% 5.17/5.52 @ ^ [L3: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L3 ) @ ( code_nat_of_integer @ L3 ) ) @ one_one_nat ) )
% 5.17/5.52 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_of_integer_code
% 5.17/5.52 thf(fact_9515_int__of__integer__code,axiom,
% 5.17/5.52 ( code_int_of_integer
% 5.17/5.52 = ( ^ [K3: code_integer] :
% 5.17/5.52 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.17/5.52 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.17/5.52 @ ( produc1553301316500091796er_int
% 5.17/5.52 @ ^ [L3: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L3 ) ) @ one_one_int ) )
% 5.17/5.52 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_of_integer_code
% 5.17/5.52 thf(fact_9516_times__int_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.17/5.52 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( abs_Integ
% 5.17/5.52 @ ( produc27273713700761075at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y6 @ U3 ) ) ) )
% 5.17/5.52 @ Xa
% 5.17/5.52 @ X ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % times_int.abs_eq
% 5.17/5.52 thf(fact_9517_zero__integer_Orep__eq,axiom,
% 5.17/5.52 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 5.17/5.52 = zero_zero_int ) ).
% 5.17/5.52
% 5.17/5.52 % zero_integer.rep_eq
% 5.17/5.52 thf(fact_9518_int__of__integer__numeral,axiom,
% 5.17/5.52 ! [K: num] :
% 5.17/5.52 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.17/5.52 = ( numeral_numeral_int @ K ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_of_integer_numeral
% 5.17/5.52 thf(fact_9519_times__integer_Orep__eq,axiom,
% 5.17/5.52 ! [X: code_integer,Xa: code_integer] :
% 5.17/5.52 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa ) )
% 5.17/5.52 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % times_integer.rep_eq
% 5.17/5.52 thf(fact_9520_minus__integer_Orep__eq,axiom,
% 5.17/5.52 ! [X: code_integer,Xa: code_integer] :
% 5.17/5.52 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa ) )
% 5.17/5.52 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % minus_integer.rep_eq
% 5.17/5.52 thf(fact_9521_divide__integer_Orep__eq,axiom,
% 5.17/5.52 ! [X: code_integer,Xa: code_integer] :
% 5.17/5.52 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa ) )
% 5.17/5.52 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % divide_integer.rep_eq
% 5.17/5.52 thf(fact_9522_int__of__integer__of__nat,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.17/5.52 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_of_integer_of_nat
% 5.17/5.52 thf(fact_9523_eq__Abs__Integ,axiom,
% 5.17/5.52 ! [Z: int] :
% 5.17/5.52 ~ ! [X4: nat,Y: nat] :
% 5.17/5.52 ( Z
% 5.17/5.52 != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % eq_Abs_Integ
% 5.17/5.52 thf(fact_9524_int_Oabs__induct,axiom,
% 5.17/5.52 ! [P: int > $o,X: int] :
% 5.17/5.52 ( ! [Y: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y ) )
% 5.17/5.52 => ( P @ X ) ) ).
% 5.17/5.52
% 5.17/5.52 % int.abs_induct
% 5.17/5.52 thf(fact_9525_less__eq__integer_Orep__eq,axiom,
% 5.17/5.52 ( ord_le3102999989581377725nteger
% 5.17/5.52 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_eq_integer.rep_eq
% 5.17/5.52 thf(fact_9526_integer__less__eq__iff,axiom,
% 5.17/5.52 ( ord_le3102999989581377725nteger
% 5.17/5.52 = ( ^ [K3: code_integer,L3: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % integer_less_eq_iff
% 5.17/5.52 thf(fact_9527_nat_Oabs__eq,axiom,
% 5.17/5.52 ! [X: product_prod_nat_nat] :
% 5.17/5.52 ( ( nat2 @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat.abs_eq
% 5.17/5.52 thf(fact_9528_unset__bit__integer_Orep__eq,axiom,
% 5.17/5.52 ! [X: nat,Xa: code_integer] :
% 5.17/5.52 ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X @ Xa ) )
% 5.17/5.52 = ( bit_se4203085406695923979it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % unset_bit_integer.rep_eq
% 5.17/5.52 thf(fact_9529_set__bit__integer_Orep__eq,axiom,
% 5.17/5.52 ! [X: nat,Xa: code_integer] :
% 5.17/5.52 ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X @ Xa ) )
% 5.17/5.52 = ( bit_se7879613467334960850it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % set_bit_integer.rep_eq
% 5.17/5.52 thf(fact_9530_flip__bit__integer_Orep__eq,axiom,
% 5.17/5.52 ! [X: nat,Xa: code_integer] :
% 5.17/5.52 ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X @ Xa ) )
% 5.17/5.52 = ( bit_se2159334234014336723it_int @ X @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % flip_bit_integer.rep_eq
% 5.17/5.52 thf(fact_9531_zero__int__def,axiom,
% 5.17/5.52 ( zero_zero_int
% 5.17/5.52 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % zero_int_def
% 5.17/5.52 thf(fact_9532_int__def,axiom,
% 5.17/5.52 ( semiri1314217659103216013at_int
% 5.17/5.52 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_def
% 5.17/5.52 thf(fact_9533_uminus__int_Oabs__eq,axiom,
% 5.17/5.52 ! [X: product_prod_nat_nat] :
% 5.17/5.52 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( abs_Integ
% 5.17/5.52 @ ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X3 )
% 5.17/5.52 @ X ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % uminus_int.abs_eq
% 5.17/5.52 thf(fact_9534_one__int__def,axiom,
% 5.17/5.52 ( one_one_int
% 5.17/5.52 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % one_int_def
% 5.17/5.52 thf(fact_9535_less__int_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.17/5.52 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( produc8739625826339149834_nat_o
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) )
% 5.17/5.52 @ Xa
% 5.17/5.52 @ X ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_int.abs_eq
% 5.17/5.52 thf(fact_9536_less__eq__int_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.17/5.52 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( produc8739625826339149834_nat_o
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) )
% 5.17/5.52 @ Xa
% 5.17/5.52 @ X ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_eq_int.abs_eq
% 5.17/5.52 thf(fact_9537_plus__int_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.17/5.52 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( abs_Integ
% 5.17/5.52 @ ( produc27273713700761075at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) )
% 5.17/5.52 @ Xa
% 5.17/5.52 @ X ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % plus_int.abs_eq
% 5.17/5.52 thf(fact_9538_minus__int_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.17/5.52 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.17/5.52 = ( abs_Integ
% 5.17/5.52 @ ( produc27273713700761075at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y6 @ U3 ) ) )
% 5.17/5.52 @ Xa
% 5.17/5.52 @ X ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % minus_int.abs_eq
% 5.17/5.52 thf(fact_9539_Gcd__remove0__nat,axiom,
% 5.17/5.52 ! [M10: set_nat] :
% 5.17/5.52 ( ( finite_finite_nat @ M10 )
% 5.17/5.52 => ( ( gcd_Gcd_nat @ M10 )
% 5.17/5.52 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M10 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_remove0_nat
% 5.17/5.52 thf(fact_9540_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.17/5.52 ! [N: nat,J: nat,I: nat] :
% 5.17/5.52 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.17/5.52 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.17/5.52 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nth_sorted_list_of_set_greaterThanAtMost
% 5.17/5.52 thf(fact_9541_card__greaterThanAtMost,axiom,
% 5.17/5.52 ! [L: nat,U: nat] :
% 5.17/5.52 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.17/5.52 = ( minus_minus_nat @ U @ L ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_greaterThanAtMost
% 5.17/5.52 thf(fact_9542_Gcd__dvd__nat,axiom,
% 5.17/5.52 ! [A: nat,A2: set_nat] :
% 5.17/5.52 ( ( member_nat @ A @ A2 )
% 5.17/5.52 => ( dvd_dvd_nat @ ( gcd_Gcd_nat @ A2 ) @ A ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_dvd_nat
% 5.17/5.52 thf(fact_9543_Gcd__greatest__nat,axiom,
% 5.17/5.52 ! [A2: set_nat,A: nat] :
% 5.17/5.52 ( ! [B3: nat] :
% 5.17/5.52 ( ( member_nat @ B3 @ A2 )
% 5.17/5.52 => ( dvd_dvd_nat @ A @ B3 ) )
% 5.17/5.52 => ( dvd_dvd_nat @ A @ ( gcd_Gcd_nat @ A2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_greatest_nat
% 5.17/5.52 thf(fact_9544_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.17/5.52 ! [L: nat,U: nat] :
% 5.17/5.52 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.17/5.52 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeastSucAtMost_greaterThanAtMost
% 5.17/5.52 thf(fact_9545_greaterThanAtMost__upt,axiom,
% 5.17/5.52 ( set_or6659071591806873216st_nat
% 5.17/5.52 = ( ^ [N4: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ ( suc @ M5 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % greaterThanAtMost_upt
% 5.17/5.52 thf(fact_9546_less__eq__int_Orep__eq,axiom,
% 5.17/5.52 ( ord_less_eq_int
% 5.17/5.52 = ( ^ [X3: int,Xa4: int] :
% 5.17/5.52 ( produc8739625826339149834_nat_o
% 5.17/5.52 @ ^ [Y6: nat,Z5: nat] :
% 5.17/5.52 ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U3 @ Z5 ) ) )
% 5.17/5.52 @ ( rep_Integ @ X3 )
% 5.17/5.52 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_eq_int.rep_eq
% 5.17/5.52 thf(fact_9547_less__int_Orep__eq,axiom,
% 5.17/5.52 ( ord_less_int
% 5.17/5.52 = ( ^ [X3: int,Xa4: int] :
% 5.17/5.52 ( produc8739625826339149834_nat_o
% 5.17/5.52 @ ^ [Y6: nat,Z5: nat] :
% 5.17/5.52 ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U3 @ Z5 ) ) )
% 5.17/5.52 @ ( rep_Integ @ X3 )
% 5.17/5.52 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_int.rep_eq
% 5.17/5.52 thf(fact_9548_card__greaterThanAtMost__int,axiom,
% 5.17/5.52 ! [L: int,U: int] :
% 5.17/5.52 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.17/5.52 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_greaterThanAtMost_int
% 5.17/5.52 thf(fact_9549_Gcd__dvd__int,axiom,
% 5.17/5.52 ! [A: int,A2: set_int] :
% 5.17/5.52 ( ( member_int @ A @ A2 )
% 5.17/5.52 => ( dvd_dvd_int @ ( gcd_Gcd_int @ A2 ) @ A ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_dvd_int
% 5.17/5.52 thf(fact_9550_Gcd__greatest__int,axiom,
% 5.17/5.52 ! [A2: set_int,A: int] :
% 5.17/5.52 ( ! [B3: int] :
% 5.17/5.52 ( ( member_int @ B3 @ A2 )
% 5.17/5.52 => ( dvd_dvd_int @ A @ B3 ) )
% 5.17/5.52 => ( dvd_dvd_int @ A @ ( gcd_Gcd_int @ A2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_greatest_int
% 5.17/5.52 thf(fact_9551_Gcd__int__greater__eq__0,axiom,
% 5.17/5.52 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_int_greater_eq_0
% 5.17/5.52 thf(fact_9552_nat_Orep__eq,axiom,
% 5.17/5.52 ( nat2
% 5.17/5.52 = ( ^ [X3: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat.rep_eq
% 5.17/5.52 thf(fact_9553_uminus__int__def,axiom,
% 5.17/5.52 ( uminus_uminus_int
% 5.17/5.52 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.17/5.52 @ ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % uminus_int_def
% 5.17/5.52 thf(fact_9554_prod__encode__def,axiom,
% 5.17/5.52 ( nat_prod_encode
% 5.17/5.52 = ( produc6842872674320459806at_nat
% 5.17/5.52 @ ^ [M5: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M5 @ N4 ) ) @ M5 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % prod_encode_def
% 5.17/5.52 thf(fact_9555_num__of__nat_Osimps_I2_J,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( num_of_nat @ ( suc @ N ) )
% 5.17/5.52 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( num_of_nat @ ( suc @ N ) )
% 5.17/5.52 = one ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_nat.simps(2)
% 5.17/5.52 thf(fact_9556_prod__encode__eq,axiom,
% 5.17/5.52 ! [X: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.17/5.52 ( ( ( nat_prod_encode @ X )
% 5.17/5.52 = ( nat_prod_encode @ Y4 ) )
% 5.17/5.52 = ( X = Y4 ) ) ).
% 5.17/5.52
% 5.17/5.52 % prod_encode_eq
% 5.17/5.52 thf(fact_9557_num__of__nat__numeral__eq,axiom,
% 5.17/5.52 ! [Q2: num] :
% 5.17/5.52 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.17/5.52 = Q2 ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_nat_numeral_eq
% 5.17/5.52 thf(fact_9558_num__of__nat_Osimps_I1_J,axiom,
% 5.17/5.52 ( ( num_of_nat @ zero_zero_nat )
% 5.17/5.52 = one ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_nat.simps(1)
% 5.17/5.52 thf(fact_9559_le__prod__encode__1,axiom,
% 5.17/5.52 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % le_prod_encode_1
% 5.17/5.52 thf(fact_9560_le__prod__encode__2,axiom,
% 5.17/5.52 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % le_prod_encode_2
% 5.17/5.52 thf(fact_9561_numeral__num__of__nat,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.17/5.52 = N ) ) ).
% 5.17/5.52
% 5.17/5.52 % numeral_num_of_nat
% 5.17/5.52 thf(fact_9562_num__of__nat__One,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.17/5.52 => ( ( num_of_nat @ N )
% 5.17/5.52 = one ) ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_nat_One
% 5.17/5.52 thf(fact_9563_num__of__nat__double,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.17/5.52 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_nat_double
% 5.17/5.52 thf(fact_9564_num__of__nat__plus__distrib,axiom,
% 5.17/5.52 ! [M: nat,N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.17/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.17/5.52 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_nat_plus_distrib
% 5.17/5.52 thf(fact_9565_prod__encode__prod__decode__aux,axiom,
% 5.17/5.52 ! [K: nat,M: nat] :
% 5.17/5.52 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.17/5.52 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.17/5.52
% 5.17/5.52 % prod_encode_prod_decode_aux
% 5.17/5.52 thf(fact_9566_times__int__def,axiom,
% 5.17/5.52 ( times_times_int
% 5.17/5.52 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.17/5.52 @ ( produc27273713700761075at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y6 @ U3 ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % times_int_def
% 5.17/5.52 thf(fact_9567_minus__int__def,axiom,
% 5.17/5.52 ( minus_minus_int
% 5.17/5.52 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.17/5.52 @ ( produc27273713700761075at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y6 @ U3 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % minus_int_def
% 5.17/5.52 thf(fact_9568_plus__int__def,axiom,
% 5.17/5.52 ( plus_plus_int
% 5.17/5.52 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.17/5.52 @ ( produc27273713700761075at_nat
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc2626176000494625587at_nat
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % plus_int_def
% 5.17/5.52 thf(fact_9569_pred__nat__def,axiom,
% 5.17/5.52 ( pred_nat
% 5.17/5.52 = ( collec3392354462482085612at_nat
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [M5: nat,N4: nat] :
% 5.17/5.52 ( N4
% 5.17/5.52 = ( suc @ M5 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % pred_nat_def
% 5.17/5.52 thf(fact_9570_pow_Osimps_I3_J,axiom,
% 5.17/5.52 ! [X: num,Y4: num] :
% 5.17/5.52 ( ( pow @ X @ ( bit1 @ Y4 ) )
% 5.17/5.52 = ( times_times_num @ ( sqr @ ( pow @ X @ Y4 ) ) @ X ) ) ).
% 5.17/5.52
% 5.17/5.52 % pow.simps(3)
% 5.17/5.52 thf(fact_9571_image__minus__const__atLeastLessThan__nat,axiom,
% 5.17/5.52 ! [C: nat,Y4: nat,X: nat] :
% 5.17/5.52 ( ( ( ord_less_nat @ C @ Y4 )
% 5.17/5.52 => ( ( image_nat_nat
% 5.17/5.52 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.17/5.52 @ ( set_or4665077453230672383an_nat @ X @ Y4 ) )
% 5.17/5.52 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y4 @ C ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_nat @ C @ Y4 )
% 5.17/5.52 => ( ( ( ord_less_nat @ X @ Y4 )
% 5.17/5.52 => ( ( image_nat_nat
% 5.17/5.52 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.17/5.52 @ ( set_or4665077453230672383an_nat @ X @ Y4 ) )
% 5.17/5.52 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.17/5.52 & ( ~ ( ord_less_nat @ X @ Y4 )
% 5.17/5.52 => ( ( image_nat_nat
% 5.17/5.52 @ ^ [I2: nat] : ( minus_minus_nat @ I2 @ C )
% 5.17/5.52 @ ( set_or4665077453230672383an_nat @ X @ Y4 ) )
% 5.17/5.52 = bot_bot_set_nat ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_minus_const_atLeastLessThan_nat
% 5.17/5.52 thf(fact_9572_bij__betw__Suc,axiom,
% 5.17/5.52 ! [M10: set_nat,N5: set_nat] :
% 5.17/5.52 ( ( bij_betw_nat_nat @ suc @ M10 @ N5 )
% 5.17/5.52 = ( ( image_nat_nat @ suc @ M10 )
% 5.17/5.52 = N5 ) ) ).
% 5.17/5.52
% 5.17/5.52 % bij_betw_Suc
% 5.17/5.52 thf(fact_9573_image__Suc__atLeastAtMost,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.17/5.52 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_Suc_atLeastAtMost
% 5.17/5.52 thf(fact_9574_image__Suc__atLeastLessThan,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.17/5.52 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_Suc_atLeastLessThan
% 5.17/5.52 thf(fact_9575_sqr_Osimps_I2_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( sqr @ ( bit0 @ N ) )
% 5.17/5.52 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sqr.simps(2)
% 5.17/5.52 thf(fact_9576_sqr_Osimps_I1_J,axiom,
% 5.17/5.52 ( ( sqr @ one )
% 5.17/5.52 = one ) ).
% 5.17/5.52
% 5.17/5.52 % sqr.simps(1)
% 5.17/5.52 thf(fact_9577_zero__notin__Suc__image,axiom,
% 5.17/5.52 ! [A2: set_nat] :
% 5.17/5.52 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.17/5.52
% 5.17/5.52 % zero_notin_Suc_image
% 5.17/5.52 thf(fact_9578_sqr__conv__mult,axiom,
% 5.17/5.52 ( sqr
% 5.17/5.52 = ( ^ [X3: num] : ( times_times_num @ X3 @ X3 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sqr_conv_mult
% 5.17/5.52 thf(fact_9579_image__Suc__lessThan,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_Suc_lessThan
% 5.17/5.52 thf(fact_9580_image__Suc__atMost,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.17/5.52 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_Suc_atMost
% 5.17/5.52 thf(fact_9581_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.17/5.52 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeast0_atMost_Suc_eq_insert_0
% 5.17/5.52 thf(fact_9582_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.17/5.52 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeast0_lessThan_Suc_eq_insert_0
% 5.17/5.52 thf(fact_9583_lessThan__Suc__eq__insert__0,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.17/5.52 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lessThan_Suc_eq_insert_0
% 5.17/5.52 thf(fact_9584_atMost__Suc__eq__insert__0,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.17/5.52 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % atMost_Suc_eq_insert_0
% 5.17/5.52 thf(fact_9585_pow_Osimps_I2_J,axiom,
% 5.17/5.52 ! [X: num,Y4: num] :
% 5.17/5.52 ( ( pow @ X @ ( bit0 @ Y4 ) )
% 5.17/5.52 = ( sqr @ ( pow @ X @ Y4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % pow.simps(2)
% 5.17/5.52 thf(fact_9586_sqr_Osimps_I3_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( sqr @ ( bit1 @ N ) )
% 5.17/5.52 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sqr.simps(3)
% 5.17/5.52 thf(fact_9587_Gcd__int__eq,axiom,
% 5.17/5.52 ! [N5: set_nat] :
% 5.17/5.52 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N5 ) )
% 5.17/5.52 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N5 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_int_eq
% 5.17/5.52 thf(fact_9588_Inf__real__def,axiom,
% 5.17/5.52 ( comple4887499456419720421f_real
% 5.17/5.52 = ( ^ [X8: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X8 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Inf_real_def
% 5.17/5.52 thf(fact_9589_finite__int__iff__bounded,axiom,
% 5.17/5.52 ( finite_finite_int
% 5.17/5.52 = ( ^ [S5: set_int] :
% 5.17/5.52 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % finite_int_iff_bounded
% 5.17/5.52 thf(fact_9590_finite__int__iff__bounded__le,axiom,
% 5.17/5.52 ( finite_finite_int
% 5.17/5.52 = ( ^ [S5: set_int] :
% 5.17/5.52 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % finite_int_iff_bounded_le
% 5.17/5.52 thf(fact_9591_image__int__atLeastAtMost,axiom,
% 5.17/5.52 ! [A: nat,B: nat] :
% 5.17/5.52 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.17/5.52 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_int_atLeastAtMost
% 5.17/5.52 thf(fact_9592_image__int__atLeastLessThan,axiom,
% 5.17/5.52 ! [A: nat,B: nat] :
% 5.17/5.52 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.17/5.52 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_int_atLeastLessThan
% 5.17/5.52 thf(fact_9593_image__add__int__atLeastLessThan,axiom,
% 5.17/5.52 ! [L: int,U: int] :
% 5.17/5.52 ( ( image_int_int
% 5.17/5.52 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 5.17/5.52 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.17/5.52 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_add_int_atLeastLessThan
% 5.17/5.52 thf(fact_9594_Gcd__int__def,axiom,
% 5.17/5.52 ( gcd_Gcd_int
% 5.17/5.52 = ( ^ [K7: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K7 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_int_def
% 5.17/5.52 thf(fact_9595_image__atLeastZeroLessThan__int,axiom,
% 5.17/5.52 ! [U: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.17/5.52 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.17/5.52 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % image_atLeastZeroLessThan_int
% 5.17/5.52 thf(fact_9596_range__mod,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( image_nat_nat
% 5.17/5.52 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N )
% 5.17/5.52 @ top_top_set_nat )
% 5.17/5.52 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % range_mod
% 5.17/5.52 thf(fact_9597_suminf__eq__SUP__real,axiom,
% 5.17/5.52 ! [X9: nat > real] :
% 5.17/5.52 ( ( summable_real @ X9 )
% 5.17/5.52 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X9 @ I3 ) )
% 5.17/5.52 => ( ( suminf_real @ X9 )
% 5.17/5.52 = ( comple1385675409528146559p_real
% 5.17/5.52 @ ( image_nat_real
% 5.17/5.52 @ ^ [I2: nat] : ( groups6591440286371151544t_real @ X9 @ ( set_ord_lessThan_nat @ I2 ) )
% 5.17/5.52 @ top_top_set_nat ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % suminf_eq_SUP_real
% 5.17/5.52 thf(fact_9598_UNIV__nat__eq,axiom,
% 5.17/5.52 ( top_top_set_nat
% 5.17/5.52 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % UNIV_nat_eq
% 5.17/5.52 thf(fact_9599_measure__function__int,axiom,
% 5.17/5.52 fun_is_measure_int @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) ).
% 5.17/5.52
% 5.17/5.52 % measure_function_int
% 5.17/5.52 thf(fact_9600_card__UNIV__bool,axiom,
% 5.17/5.52 ( ( finite_card_o @ top_top_set_o )
% 5.17/5.52 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_UNIV_bool
% 5.17/5.52 thf(fact_9601_range__mult,axiom,
% 5.17/5.52 ! [A: real] :
% 5.17/5.52 ( ( ( A = zero_zero_real )
% 5.17/5.52 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.17/5.52 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.17/5.52 & ( ( A != zero_zero_real )
% 5.17/5.52 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.17/5.52 = top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % range_mult
% 5.17/5.52 thf(fact_9602_infinite__UNIV__int,axiom,
% 5.17/5.52 ~ ( finite_finite_int @ top_top_set_int ) ).
% 5.17/5.52
% 5.17/5.52 % infinite_UNIV_int
% 5.17/5.52 thf(fact_9603_bij__prod__encode,axiom,
% 5.17/5.52 bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 5.17/5.52
% 5.17/5.52 % bij_prod_encode
% 5.17/5.52 thf(fact_9604_surj__prod__encode,axiom,
% 5.17/5.52 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 5.17/5.52 = top_top_set_nat ) ).
% 5.17/5.52
% 5.17/5.52 % surj_prod_encode
% 5.17/5.52 thf(fact_9605_int__in__range__abs,axiom,
% 5.17/5.52 ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_in_range_abs
% 5.17/5.52 thf(fact_9606_root__def,axiom,
% 5.17/5.52 ( root
% 5.17/5.52 = ( ^ [N4: nat,X3: real] :
% 5.17/5.52 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 5.17/5.52 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.17/5.52 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N4 ) )
% 5.17/5.52 @ X3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % root_def
% 5.17/5.52 thf(fact_9607_card__UNIV__char,axiom,
% 5.17/5.52 ( ( finite_card_char @ top_top_set_char )
% 5.17/5.52 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_UNIV_char
% 5.17/5.52 thf(fact_9608_UNIV__bool,axiom,
% 5.17/5.52 ( top_top_set_o
% 5.17/5.52 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % UNIV_bool
% 5.17/5.52 thf(fact_9609_UNIV__char__of__nat,axiom,
% 5.17/5.52 ( top_top_set_char
% 5.17/5.52 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % UNIV_char_of_nat
% 5.17/5.52 thf(fact_9610_char_Osize_I2_J,axiom,
% 5.17/5.52 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.17/5.52 ( ( size_size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.17/5.52 = zero_zero_nat ) ).
% 5.17/5.52
% 5.17/5.52 % char.size(2)
% 5.17/5.52 thf(fact_9611_nat__of__char__less__256,axiom,
% 5.17/5.52 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_of_char_less_256
% 5.17/5.52 thf(fact_9612_range__nat__of__char,axiom,
% 5.17/5.52 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.17/5.52 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % range_nat_of_char
% 5.17/5.52 thf(fact_9613_integer__of__char__code,axiom,
% 5.17/5.52 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.17/5.52 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.17/5.52 = ( 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 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % integer_of_char_code
% 5.17/5.52 thf(fact_9614_char_Osize__gen,axiom,
% 5.17/5.52 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.17/5.52 ( ( size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.17/5.52 = zero_zero_nat ) ).
% 5.17/5.52
% 5.17/5.52 % char.size_gen
% 5.17/5.52 thf(fact_9615_String_Ochar__of__ascii__of,axiom,
% 5.17/5.52 ! [C: char] :
% 5.17/5.52 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.17/5.52 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % String.char_of_ascii_of
% 5.17/5.52 thf(fact_9616_DERIV__real__root__generic,axiom,
% 5.17/5.52 ! [N: nat,X: real,D3: real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( X != zero_zero_real )
% 5.17/5.52 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( D3
% 5.17/5.52 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.17/5.52 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.52 => ( D3
% 5.17/5.52 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.17/5.52 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( D3
% 5.17/5.52 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_real_root_generic
% 5.17/5.52 thf(fact_9617_has__real__derivative__neg__dec__right,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,S: set_real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.17/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( member_real @ ( plus_plus_real @ X @ H2 ) @ S )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H2 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % has_real_derivative_neg_dec_right
% 5.17/5.52 thf(fact_9618_has__real__derivative__pos__inc__right,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,S: set_real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( member_real @ ( plus_plus_real @ X @ H2 ) @ S )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H2 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % has_real_derivative_pos_inc_right
% 5.17/5.52 thf(fact_9619_has__real__derivative__pos__inc__left,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,S: set_real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( member_real @ ( minus_minus_real @ X @ H2 ) @ S )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H2 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % has_real_derivative_pos_inc_left
% 5.17/5.52 thf(fact_9620_has__real__derivative__neg__dec__left,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,S: set_real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S ) )
% 5.17/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( member_real @ ( minus_minus_real @ X @ H2 ) @ S )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H2 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % has_real_derivative_neg_dec_left
% 5.17/5.52 thf(fact_9621_deriv__nonneg__imp__mono,axiom,
% 5.17/5.52 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.17/5.52 ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.17/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X4 ) ) )
% 5.17/5.52 => ( ( ord_less_eq_real @ A @ B )
% 5.17/5.52 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % deriv_nonneg_imp_mono
% 5.17/5.52 thf(fact_9622_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_eq_real @ zero_zero_real @ Y3 ) ) ) )
% 5.17/5.52 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_nonneg_imp_nondecreasing
% 5.17/5.52 thf(fact_9623_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_eq_real @ Y3 @ zero_zero_real ) ) ) )
% 5.17/5.52 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_nonpos_imp_nonincreasing
% 5.17/5.52 thf(fact_9624_DERIV__pos__imp__increasing,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 5.17/5.52 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_pos_imp_increasing
% 5.17/5.52 thf(fact_9625_DERIV__neg__imp__decreasing,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 5.17/5.52 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_neg_imp_decreasing
% 5.17/5.52 thf(fact_9626_DERIV__isconst__all,axiom,
% 5.17/5.52 ! [F: real > real,X: real,Y4: real] :
% 5.17/5.52 ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ( ( F @ X )
% 5.17/5.52 = ( F @ Y4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_isconst_all
% 5.17/5.52 thf(fact_9627_DERIV__pos__inc__right,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H2 ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_pos_inc_right
% 5.17/5.52 thf(fact_9628_DERIV__neg__dec__right,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H2 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_neg_dec_right
% 5.17/5.52 thf(fact_9629_DERIV__const__ratio__const2,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,K: real] :
% 5.17/5.52 ( ( A != B )
% 5.17/5.52 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.17/5.52 = K ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_const_ratio_const2
% 5.17/5.52 thf(fact_9630_DERIV__const__ratio__const,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,K: real] :
% 5.17/5.52 ( ( A != B )
% 5.17/5.52 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.17/5.52 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_const_ratio_const
% 5.17/5.52 thf(fact_9631_DERIV__pos__inc__left,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H2 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_pos_inc_left
% 5.17/5.52 thf(fact_9632_DERIV__neg__dec__left,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.17/5.52 => ? [D2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.17/5.52 & ! [H2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.17/5.52 => ( ( ord_less_real @ H2 @ D2 )
% 5.17/5.52 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H2 ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_neg_dec_left
% 5.17/5.52 thf(fact_9633_DERIV__isconst3,axiom,
% 5.17/5.52 ! [A: real,B: real,X: real,Y4: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ( F @ X )
% 5.17/5.52 = ( F @ Y4 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_isconst3
% 5.17/5.52 thf(fact_9634_MVT2,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,F2: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ F @ ( F2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ? [Z2: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.17/5.52 & ( ord_less_real @ Z2 @ B )
% 5.17/5.52 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.17/5.52 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F2 @ Z2 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % MVT2
% 5.17/5.52 thf(fact_9635_DERIV__local__const,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,D: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.17/5.52 => ( ! [Y: real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) @ D )
% 5.17/5.52 => ( ( F @ X )
% 5.17/5.52 = ( F @ Y ) ) )
% 5.17/5.52 => ( L = zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_local_const
% 5.17/5.52 thf(fact_9636_DERIV__ln,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_ln
% 5.17/5.52 thf(fact_9637_DERIV__const__average,axiom,
% 5.17/5.52 ! [A: real,B: real,V: real > real,K: real] :
% 5.17/5.52 ( ( A != B )
% 5.17/5.52 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.17/5.52 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_const_average
% 5.17/5.52 thf(fact_9638_DERIV__local__min,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,D: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.17/5.52 => ( ! [Y: real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) @ D )
% 5.17/5.52 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y ) ) )
% 5.17/5.52 => ( L = zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_local_min
% 5.17/5.52 thf(fact_9639_DERIV__local__max,axiom,
% 5.17/5.52 ! [F: real > real,L: real,X: real,D: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.17/5.52 => ( ! [Y: real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y ) ) @ D )
% 5.17/5.52 => ( ord_less_eq_real @ ( F @ Y ) @ ( F @ X ) ) )
% 5.17/5.52 => ( L = zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_local_max
% 5.17/5.52 thf(fact_9640_DERIV__ln__divide,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_ln_divide
% 5.17/5.52 thf(fact_9641_DERIV__pow,axiom,
% 5.17/5.52 ! [N: nat,X: real,S2: set_real] :
% 5.17/5.52 ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 5.17/5.52 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_pow
% 5.17/5.52 thf(fact_9642_DERIV__fun__pow,axiom,
% 5.17/5.52 ! [G: real > real,M: real,X: real,N: nat] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] : ( power_power_real @ ( G @ X3 ) @ N )
% 5.17/5.52 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_fun_pow
% 5.17/5.52 thf(fact_9643_has__real__derivative__powr,axiom,
% 5.17/5.52 ! [Z: real,R2: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [Z5: real] : ( powr_real @ Z5 @ R2 )
% 5.17/5.52 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % has_real_derivative_powr
% 5.17/5.52 thf(fact_9644_DERIV__series_H,axiom,
% 5.17/5.52 ! [F: real > nat > real,F2: real > nat > real,X0: real,A: real,B: real,L4: nat > real] :
% 5.17/5.52 ( ! [N2: nat] :
% 5.17/5.52 ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] : ( F @ X3 @ N2 )
% 5.17/5.52 @ ( F2 @ X0 @ N2 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( summable_real @ ( F @ X4 ) ) )
% 5.17/5.52 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( ( summable_real @ ( F2 @ X0 ) )
% 5.17/5.52 => ( ( summable_real @ L4 )
% 5.17/5.52 => ( ! [N2: nat,X4: real,Y: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.17/5.52 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N2 ) @ ( F @ Y @ N2 ) ) ) @ ( times_times_real @ ( L4 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y ) ) ) ) ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 5.17/5.52 @ ( suminf_real @ ( F2 @ X0 ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_series'
% 5.17/5.52 thf(fact_9645_DERIV__log,axiom,
% 5.17/5.52 ! [X: real,B: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_log
% 5.17/5.52 thf(fact_9646_DERIV__fun__powr,axiom,
% 5.17/5.52 ! [G: real > real,M: real,X: real,R2: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ R2 )
% 5.17/5.52 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_fun_powr
% 5.17/5.52 thf(fact_9647_DERIV__powr,axiom,
% 5.17/5.52 ! [G: real > real,M: real,X: real,F: real > real,R2: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.17/5.52 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) )
% 5.17/5.52 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_powr
% 5.17/5.52 thf(fact_9648_artanh__real__has__field__derivative,axiom,
% 5.17/5.52 ! [X: real,A2: set_real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % artanh_real_has_field_derivative
% 5.17/5.52 thf(fact_9649_DERIV__real__sqrt,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_real_sqrt
% 5.17/5.52 thf(fact_9650_DERIV__arctan,axiom,
% 5.17/5.52 ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_arctan
% 5.17/5.52 thf(fact_9651_arsinh__real__has__field__derivative,axiom,
% 5.17/5.52 ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 5.17/5.52
% 5.17/5.52 % arsinh_real_has_field_derivative
% 5.17/5.52 thf(fact_9652_DERIV__real__sqrt__generic,axiom,
% 5.17/5.52 ! [X: real,D3: real] :
% 5.17/5.52 ( ( X != zero_zero_real )
% 5.17/5.52 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( D3
% 5.17/5.52 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.52 => ( D3
% 5.17/5.52 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ sqrt @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_real_sqrt_generic
% 5.17/5.52 thf(fact_9653_arcosh__real__has__field__derivative,axiom,
% 5.17/5.52 ! [X: real,A2: set_real] :
% 5.17/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % arcosh_real_has_field_derivative
% 5.17/5.52 thf(fact_9654_DERIV__power__series_H,axiom,
% 5.17/5.52 ! [R: real,F: nat > real,X0: real] :
% 5.17/5.52 ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.17/5.52 => ( summable_real
% 5.17/5.52 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X4 @ N4 ) ) ) )
% 5.17/5.52 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( suminf_real
% 5.17/5.52 @ ^ [N4: nat] : ( times_times_real @ ( F @ N4 ) @ ( power_power_real @ X3 @ ( suc @ N4 ) ) ) )
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_power_series'
% 5.17/5.52 thf(fact_9655_DERIV__real__root,axiom,
% 5.17/5.52 ! [N: nat,X: real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_real_root
% 5.17/5.52 thf(fact_9656_DERIV__arccos,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_arccos
% 5.17/5.52 thf(fact_9657_DERIV__arcsin,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.17/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_arcsin
% 5.17/5.52 thf(fact_9658_Maclaurin__all__le__objl,axiom,
% 5.17/5.52 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.17/5.52 ( ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.52 & ( ( F @ X )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin_all_le_objl
% 5.17/5.52 thf(fact_9659_Maclaurin__all__le,axiom,
% 5.17/5.52 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.17/5.52 ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.52 & ( ( F @ X )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin_all_le
% 5.17/5.52 thf(fact_9660_DERIV__odd__real__root,axiom,
% 5.17/5.52 ! [N: nat,X: real] :
% 5.17/5.52 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( ( X != zero_zero_real )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_odd_real_root
% 5.17/5.52 thf(fact_9661_Maclaurin__minus,axiom,
% 5.17/5.52 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ H @ zero_zero_real )
% 5.17/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ H @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_real @ H @ T3 )
% 5.17/5.52 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.17/5.52 & ( ( F @ H )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin_minus
% 5.17/5.52 thf(fact_9662_Maclaurin2,axiom,
% 5.17/5.52 ! [H: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H )
% 5.17/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ H ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ H )
% 5.17/5.52 & ( ( F @ H )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin2
% 5.17/5.52 thf(fact_9663_Maclaurin,axiom,
% 5.17/5.52 ! [H: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ H )
% 5.17/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ H ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.17/5.52 & ( ord_less_real @ T3 @ H )
% 5.17/5.52 & ( ( F @ H )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin
% 5.17/5.52 thf(fact_9664_Maclaurin__all__lt,axiom,
% 5.17/5.52 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.17/5.52 ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( X != zero_zero_real )
% 5.17/5.52 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.17/5.52 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.52 & ( ( F @ X )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin_all_lt
% 5.17/5.52 thf(fact_9665_Maclaurin__bi__le,axiom,
% 5.17/5.52 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.17/5.52 ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X ) )
% 5.17/5.52 & ( ( F @ X )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin_bi_le
% 5.17/5.52 thf(fact_9666_Taylor__down,axiom,
% 5.17/5.52 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ A @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ B ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ( ord_less_real @ A @ C )
% 5.17/5.52 => ( ( ord_less_eq_real @ C @ B )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ T3 )
% 5.17/5.52 & ( ord_less_real @ T3 @ C )
% 5.17/5.52 & ( ( F @ A )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Taylor_down
% 5.17/5.52 thf(fact_9667_Taylor__up,axiom,
% 5.17/5.52 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ A @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ B ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ( ord_less_eq_real @ A @ C )
% 5.17/5.52 => ( ( ord_less_real @ C @ B )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ord_less_real @ C @ T3 )
% 5.17/5.52 & ( ord_less_real @ T3 @ B )
% 5.17/5.52 & ( ( F @ B )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Taylor_up
% 5.17/5.52 thf(fact_9668_Taylor,axiom,
% 5.17/5.52 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( ( Diff @ zero_zero_nat )
% 5.17/5.52 = F )
% 5.17/5.52 => ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ A @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ B ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ( ord_less_eq_real @ A @ C )
% 5.17/5.52 => ( ( ord_less_eq_real @ C @ B )
% 5.17/5.52 => ( ( ord_less_eq_real @ A @ X )
% 5.17/5.52 => ( ( ord_less_eq_real @ X @ B )
% 5.17/5.52 => ( ( X != C )
% 5.17/5.52 => ? [T3: real] :
% 5.17/5.52 ( ( ( ord_less_real @ X @ C )
% 5.17/5.52 => ( ( ord_less_real @ X @ T3 )
% 5.17/5.52 & ( ord_less_real @ T3 @ C ) ) )
% 5.17/5.52 & ( ~ ( ord_less_real @ X @ C )
% 5.17/5.52 => ( ( ord_less_real @ C @ T3 )
% 5.17/5.52 & ( ord_less_real @ T3 @ X ) ) )
% 5.17/5.52 & ( ( F @ X )
% 5.17/5.52 = ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M5 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ N ) )
% 5.17/5.52 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T3 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Taylor
% 5.17/5.52 thf(fact_9669_Maclaurin__lemma2,axiom,
% 5.17/5.52 ! [N: nat,H: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.17/5.52 ( ! [M4: nat,T3: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M4 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.17/5.52 & ( ord_less_eq_real @ T3 @ H ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ( N
% 5.17/5.52 = ( suc @ K ) )
% 5.17/5.52 => ! [M2: nat,T4: real] :
% 5.17/5.52 ( ( ( ord_less_nat @ M2 @ N )
% 5.17/5.52 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.17/5.52 & ( ord_less_eq_real @ T4 @ H ) )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [U3: real] :
% 5.17/5.52 ( minus_minus_real @ ( Diff @ M2 @ U3 )
% 5.17/5.52 @ ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U3 @ P6 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.17/5.52 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U3 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.17/5.52 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 5.17/5.52 @ ( plus_plus_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T4 @ P6 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.17/5.52 @ ( 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 ) ) ) ) ) ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Maclaurin_lemma2
% 5.17/5.52 thf(fact_9670_DERIV__arctan__series,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.52 => ( has_fi5821293074295781190e_real
% 5.17/5.52 @ ^ [X10: real] :
% 5.17/5.52 ( suminf_real
% 5.17/5.52 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_arctan_series
% 5.17/5.52 thf(fact_9671_DERIV__even__real__root,axiom,
% 5.17/5.52 ! [N: nat,X: real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_even_real_root
% 5.17/5.52 thf(fact_9672_isCont__Lb__Ub,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 & ( ord_less_eq_real @ X4 @ B ) )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.17/5.52 => ? [L5: real,M8: real] :
% 5.17/5.52 ( ! [X5: real] :
% 5.17/5.52 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.17/5.52 & ( ord_less_eq_real @ X5 @ B ) )
% 5.17/5.52 => ( ( ord_less_eq_real @ L5 @ ( F @ X5 ) )
% 5.17/5.52 & ( ord_less_eq_real @ ( F @ X5 ) @ M8 ) ) )
% 5.17/5.52 & ! [Y3: real] :
% 5.17/5.52 ( ( ( ord_less_eq_real @ L5 @ Y3 )
% 5.17/5.52 & ( ord_less_eq_real @ Y3 @ M8 ) )
% 5.17/5.52 => ? [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 & ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 & ( ( F @ X4 )
% 5.17/5.52 = Y3 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % isCont_Lb_Ub
% 5.17/5.52 thf(fact_9673_LIM__fun__less__zero,axiom,
% 5.17/5.52 ! [F: real > real,L: real,C: real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.17/5.52 => ? [R3: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.17/5.52 & ! [X5: real] :
% 5.17/5.52 ( ( ( X5 != C )
% 5.17/5.52 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.17/5.52 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIM_fun_less_zero
% 5.17/5.52 thf(fact_9674_LIM__fun__not__zero,axiom,
% 5.17/5.52 ! [F: real > real,L: real,C: real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.17/5.52 => ( ( L != zero_zero_real )
% 5.17/5.52 => ? [R3: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.17/5.52 & ! [X5: real] :
% 5.17/5.52 ( ( ( X5 != C )
% 5.17/5.52 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.17/5.52 => ( ( F @ X5 )
% 5.17/5.52 != zero_zero_real ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIM_fun_not_zero
% 5.17/5.52 thf(fact_9675_LIM__fun__gt__zero,axiom,
% 5.17/5.52 ! [F: real > real,L: real,C: real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.17/5.52 => ? [R3: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.17/5.52 & ! [X5: real] :
% 5.17/5.52 ( ( ( X5 != C )
% 5.17/5.52 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X5 ) ) @ R3 ) )
% 5.17/5.52 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIM_fun_gt_zero
% 5.17/5.52 thf(fact_9676_isCont__real__sqrt,axiom,
% 5.17/5.52 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 5.17/5.52
% 5.17/5.52 % isCont_real_sqrt
% 5.17/5.52 thf(fact_9677_isCont__real__root,axiom,
% 5.17/5.52 ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % isCont_real_root
% 5.17/5.52 thf(fact_9678_isCont__inverse__function2,axiom,
% 5.17/5.52 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X )
% 5.17/5.52 => ( ( ord_less_real @ X @ B )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.17/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.17/5.52 => ( ( G @ ( F @ Z2 ) )
% 5.17/5.52 = Z2 ) ) )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.17/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % isCont_inverse_function2
% 5.17/5.52 thf(fact_9679_isCont__ln,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( X != zero_zero_real )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ln_ln_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % isCont_ln
% 5.17/5.52 thf(fact_9680_LIM__cos__div__sin,axiom,
% 5.17/5.52 ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIM_cos_div_sin
% 5.17/5.52 thf(fact_9681_DERIV__inverse__function,axiom,
% 5.17/5.52 ! [F: real > real,D3: real,G: real > real,X: real,A: real,B: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ D3 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 5.17/5.52 => ( ( D3 != zero_zero_real )
% 5.17/5.52 => ( ( ord_less_real @ A @ X )
% 5.17/5.52 => ( ( ord_less_real @ X @ B )
% 5.17/5.52 => ( ! [Y: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Y )
% 5.17/5.52 => ( ( ord_less_real @ Y @ B )
% 5.17/5.52 => ( ( F @ ( G @ Y ) )
% 5.17/5.52 = Y ) ) )
% 5.17/5.52 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D3 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_inverse_function
% 5.17/5.52 thf(fact_9682_LIM__less__bound,axiom,
% 5.17/5.52 ! [B: real,X: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ B @ X )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 5.17/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.17/5.52 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 5.17/5.52 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIM_less_bound
% 5.17/5.52 thf(fact_9683_isCont__inverse__function,axiom,
% 5.17/5.52 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ D )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X ) ) @ D )
% 5.17/5.52 => ( ( G @ ( F @ Z2 ) )
% 5.17/5.52 = Z2 ) )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X ) ) @ D )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % isCont_inverse_function
% 5.17/5.52 thf(fact_9684_GMVT_H,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F2: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.17/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ Z2 )
% 5.17/5.52 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.17/5.52 => ( ( ord_less_real @ Z2 @ B )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ( ! [Z2: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.17/5.52 => ( ( ord_less_real @ Z2 @ B )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ F @ ( F2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ? [C3: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ C3 )
% 5.17/5.52 & ( ord_less_real @ C3 @ B )
% 5.17/5.52 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.17/5.52 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F2 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % GMVT'
% 5.17/5.52 thf(fact_9685_summable__Leibniz_I3_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.17/5.52 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.17/5.52 => ! [N6: nat] :
% 5.17/5.52 ( member_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.17/5.52 @ ( set_or1222579329274155063t_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz(3)
% 5.17/5.52 thf(fact_9686_summable__Leibniz_I2_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.17/5.52 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.17/5.52 => ! [N6: nat] :
% 5.17/5.52 ( member_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.17/5.52 @ ( set_or1222579329274155063t_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz(2)
% 5.17/5.52 thf(fact_9687_filterlim__Suc,axiom,
% 5.17/5.52 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.17/5.52
% 5.17/5.52 % filterlim_Suc
% 5.17/5.52 thf(fact_9688_mult__nat__right__at__top,axiom,
% 5.17/5.52 ! [C: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.52 => ( filterlim_nat_nat
% 5.17/5.52 @ ^ [X3: nat] : ( times_times_nat @ X3 @ C )
% 5.17/5.52 @ at_top_nat
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % mult_nat_right_at_top
% 5.17/5.52 thf(fact_9689_mult__nat__left__at__top,axiom,
% 5.17/5.52 ! [C: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.17/5.52 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % mult_nat_left_at_top
% 5.17/5.52 thf(fact_9690_monoseq__convergent,axiom,
% 5.17/5.52 ! [X9: nat > real,B4: real] :
% 5.17/5.52 ( ( topolo6980174941875973593q_real @ X9 )
% 5.17/5.52 => ( ! [I3: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X9 @ I3 ) ) @ B4 )
% 5.17/5.52 => ~ ! [L5: real] :
% 5.17/5.52 ~ ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L5 ) @ at_top_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % monoseq_convergent
% 5.17/5.52 thf(fact_9691_LIMSEQ__root,axiom,
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( root @ N4 @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_root
% 5.17/5.52 thf(fact_9692_nested__sequence__unique,axiom,
% 5.17/5.52 ! [F: nat > real,G: nat > real] :
% 5.17/5.52 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.17/5.52 => ( ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( minus_minus_real @ ( F @ N4 ) @ ( G @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat )
% 5.17/5.52 => ? [L2: real] :
% 5.17/5.52 ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L2 )
% 5.17/5.52 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat )
% 5.17/5.52 & ! [N6: nat] : ( ord_less_eq_real @ L2 @ ( G @ N6 ) )
% 5.17/5.52 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nested_sequence_unique
% 5.17/5.52 thf(fact_9693_LIMSEQ__inverse__zero,axiom,
% 5.17/5.52 ! [X9: nat > real] :
% 5.17/5.52 ( ! [R3: real] :
% 5.17/5.52 ? [N7: nat] :
% 5.17/5.52 ! [N2: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ N7 @ N2 )
% 5.17/5.52 => ( ord_less_real @ R3 @ ( X9 @ N2 ) ) )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X9 @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_inverse_zero
% 5.17/5.52 thf(fact_9694_lim__inverse__n_H,axiom,
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % lim_inverse_n'
% 5.17/5.52 thf(fact_9695_LIMSEQ__root__const,axiom,
% 5.17/5.52 ! [C: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ C )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( root @ N4 @ C )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_root_const
% 5.17/5.52 thf(fact_9696_LIMSEQ__inverse__real__of__nat,axiom,
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_inverse_real_of_nat
% 5.17/5.52 thf(fact_9697_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.17/5.52 ! [R2: real] :
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ R2 )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_inverse_real_of_nat_add
% 5.17/5.52 thf(fact_9698_increasing__LIMSEQ,axiom,
% 5.17/5.52 ! [F: nat > real,L: real] :
% 5.17/5.52 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 5.17/5.52 => ( ! [E: real] :
% 5.17/5.52 ( ( ord_less_real @ zero_zero_real @ E )
% 5.17/5.52 => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 5.17/5.52 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % increasing_LIMSEQ
% 5.17/5.52 thf(fact_9699_LIMSEQ__realpow__zero,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.52 => ( ( ord_less_real @ X @ one_one_real )
% 5.17/5.52 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_realpow_zero
% 5.17/5.52 thf(fact_9700_LIMSEQ__divide__realpow__zero,axiom,
% 5.17/5.52 ! [X: real,A: real] :
% 5.17/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_divide_realpow_zero
% 5.17/5.52 thf(fact_9701_LIMSEQ__abs__realpow__zero,axiom,
% 5.17/5.52 ! [C: real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.17/5.52 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_abs_realpow_zero
% 5.17/5.52 thf(fact_9702_LIMSEQ__abs__realpow__zero2,axiom,
% 5.17/5.52 ! [C: real] :
% 5.17/5.52 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.17/5.52 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_abs_realpow_zero2
% 5.17/5.52 thf(fact_9703_LIMSEQ__inverse__realpow__zero,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_real @ one_one_real @ X )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_inverse_realpow_zero
% 5.17/5.52 thf(fact_9704_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.17/5.52 ! [R2: real] :
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ R2 )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.17/5.52 thf(fact_9705_tendsto__exp__limit__sequentially,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N4 ) ) ) @ N4 )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % tendsto_exp_limit_sequentially
% 5.17/5.52 thf(fact_9706_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.17/5.52 ! [R2: real] :
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ R2 )
% 5.17/5.52 @ at_top_nat ) ).
% 5.17/5.52
% 5.17/5.52 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.17/5.52 thf(fact_9707_summable__Leibniz_I1_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.17/5.52 => ( summable_real
% 5.17/5.52 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz(1)
% 5.17/5.52 thf(fact_9708_summable,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.17/5.52 => ( summable_real
% 5.17/5.52 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable
% 5.17/5.52 thf(fact_9709_cos__diff__limit__1,axiom,
% 5.17/5.52 ! [Theta: nat > real,Theta2: real] :
% 5.17/5.52 ( ( filterlim_nat_real
% 5.17/5.52 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.17/5.52 @ at_top_nat )
% 5.17/5.52 => ~ ! [K2: nat > int] :
% 5.17/5.52 ~ ( filterlim_nat_real
% 5.17/5.52 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % cos_diff_limit_1
% 5.17/5.52 thf(fact_9710_cos__limit__1,axiom,
% 5.17/5.52 ! [Theta: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real
% 5.17/5.52 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.17/5.52 @ at_top_nat )
% 5.17/5.52 => ? [K2: nat > int] :
% 5.17/5.52 ( filterlim_nat_real
% 5.17/5.52 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K2 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % cos_limit_1
% 5.17/5.52 thf(fact_9711_summable__Leibniz_I4_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.17/5.52 @ at_top_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz(4)
% 5.17/5.52 thf(fact_9712_zeroseq__arctan__series,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [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 @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % zeroseq_arctan_series
% 5.17/5.52 thf(fact_9713_summable__Leibniz_H_I2_J,axiom,
% 5.17/5.52 ! [A: nat > real,N: nat] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.17/5.52 => ( ord_less_eq_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz'(2)
% 5.17/5.52 thf(fact_9714_summable__Leibniz_H_I3_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.17/5.52 @ at_top_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz'(3)
% 5.17/5.52 thf(fact_9715_sums__alternating__upper__lower,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.17/5.52 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ? [L2: real] :
% 5.17/5.52 ( ! [N6: nat] :
% 5.17/5.52 ( ord_less_eq_real
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.17/5.52 @ L2 )
% 5.17/5.52 & ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ L2 )
% 5.17/5.52 @ at_top_nat )
% 5.17/5.52 & ! [N6: nat] :
% 5.17/5.52 ( ord_less_eq_real @ L2
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 5.17/5.52 & ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ L2 )
% 5.17/5.52 @ at_top_nat ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sums_alternating_upper_lower
% 5.17/5.52 thf(fact_9716_summable__Leibniz_I5_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ( topolo6980174941875973593q_real @ A )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.17/5.52 @ at_top_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz(5)
% 5.17/5.52 thf(fact_9717_summable__Leibniz_H_I5_J,axiom,
% 5.17/5.52 ! [A: nat > real] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.17/5.52 => ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) ) )
% 5.17/5.52 @ at_top_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz'(5)
% 5.17/5.52 thf(fact_9718_summable__Leibniz_H_I4_J,axiom,
% 5.17/5.52 ! [A: nat > real,N: nat] :
% 5.17/5.52 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 5.17/5.52 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 5.17/5.52 => ( ord_less_eq_real
% 5.17/5.52 @ ( suminf_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) ) )
% 5.17/5.52 @ ( groups6591440286371151544t_real
% 5.17/5.52 @ ^ [I2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I2 ) @ ( A @ I2 ) )
% 5.17/5.52 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_Leibniz'(4)
% 5.17/5.52 thf(fact_9719_real__bounded__linear,axiom,
% 5.17/5.52 ( real_V5970128139526366754l_real
% 5.17/5.52 = ( ^ [F3: real > real] :
% 5.17/5.52 ? [C5: real] :
% 5.17/5.52 ( F3
% 5.17/5.52 = ( ^ [X3: real] : ( times_times_real @ X3 @ C5 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % real_bounded_linear
% 5.17/5.52 thf(fact_9720_tendsto__arctan__at__bot,axiom,
% 5.17/5.52 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.17/5.52
% 5.17/5.52 % tendsto_arctan_at_bot
% 5.17/5.52 thf(fact_9721_dist__real__def,axiom,
% 5.17/5.52 ( real_V975177566351809787t_real
% 5.17/5.52 = ( ^ [X3: real,Y6: real] : ( abs_abs_real @ ( minus_minus_real @ X3 @ Y6 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % dist_real_def
% 5.17/5.52 thf(fact_9722_dist__complex__def,axiom,
% 5.17/5.52 ( real_V3694042436643373181omplex
% 5.17/5.52 = ( ^ [X3: complex,Y6: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y6 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % dist_complex_def
% 5.17/5.52 thf(fact_9723_exp__at__bot,axiom,
% 5.17/5.52 filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 5.17/5.52
% 5.17/5.52 % exp_at_bot
% 5.17/5.52 thf(fact_9724_filterlim__inverse__at__bot__neg,axiom,
% 5.17/5.52 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % filterlim_inverse_at_bot_neg
% 5.17/5.52 thf(fact_9725_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.17/5.52 ! [B: real,F: real > real,Flim: real] :
% 5.17/5.52 ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ zero_zero_real @ Y3 ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.17/5.52 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_pos_imp_increasing_at_bot
% 5.17/5.52 thf(fact_9726_filterlim__pow__at__bot__odd,axiom,
% 5.17/5.52 ! [N: nat,F: real > real,F4: filter_real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 5.17/5.52 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ F4 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % filterlim_pow_at_bot_odd
% 5.17/5.52 thf(fact_9727_tendsto__exp__limit__at__right,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( filterlim_real_real
% 5.17/5.52 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y6 ) ) @ ( divide_divide_real @ one_one_real @ Y6 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % tendsto_exp_limit_at_right
% 5.17/5.52 thf(fact_9728_ln__at__0,axiom,
% 5.17/5.52 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % ln_at_0
% 5.17/5.52 thf(fact_9729_tendsto__arcosh__at__left__1,axiom,
% 5.17/5.52 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % tendsto_arcosh_at_left_1
% 5.17/5.52 thf(fact_9730_filterlim__tan__at__right,axiom,
% 5.17/5.52 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 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % filterlim_tan_at_right
% 5.17/5.52 thf(fact_9731_atLeast__0,axiom,
% 5.17/5.52 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.17/5.52 = top_top_set_nat ) ).
% 5.17/5.52
% 5.17/5.52 % atLeast_0
% 5.17/5.52 thf(fact_9732_atLeast__Suc__greaterThan,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.17/5.52 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeast_Suc_greaterThan
% 5.17/5.52 thf(fact_9733_greaterThan__0,axiom,
% 5.17/5.52 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.17/5.52 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % greaterThan_0
% 5.17/5.52 thf(fact_9734_greaterThan__Suc,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.17/5.52 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % greaterThan_Suc
% 5.17/5.52 thf(fact_9735_atLeast__Suc,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.17/5.52 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeast_Suc
% 5.17/5.52 thf(fact_9736_filterlim__pow__at__bot__even,axiom,
% 5.17/5.52 ! [N: nat,F: real > real,F4: filter_real] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( filterlim_real_real @ F @ at_bot_real @ F4 )
% 5.17/5.52 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ F4 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % filterlim_pow_at_bot_even
% 5.17/5.52 thf(fact_9737_filterlim__tan__at__left,axiom,
% 5.17/5.52 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 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % filterlim_tan_at_left
% 5.17/5.52 thf(fact_9738_sqrt__at__top,axiom,
% 5.17/5.52 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.17/5.52
% 5.17/5.52 % sqrt_at_top
% 5.17/5.52 thf(fact_9739_filterlim__real__sequentially,axiom,
% 5.17/5.52 filterlim_nat_real @ semiri5074537144036343181t_real @ at_top_real @ at_top_nat ).
% 5.17/5.52
% 5.17/5.52 % filterlim_real_sequentially
% 5.17/5.52 thf(fact_9740_ln__x__over__x__tendsto__0,axiom,
% 5.17/5.52 ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_real ) ).
% 5.17/5.52
% 5.17/5.52 % ln_x_over_x_tendsto_0
% 5.17/5.52 thf(fact_9741_filterlim__inverse__at__right__top,axiom,
% 5.17/5.52 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 5.17/5.52
% 5.17/5.52 % filterlim_inverse_at_right_top
% 5.17/5.52 thf(fact_9742_filterlim__inverse__at__top__right,axiom,
% 5.17/5.52 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % filterlim_inverse_at_top_right
% 5.17/5.52 thf(fact_9743_tendsto__power__div__exp__0,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( power_power_real @ X3 @ K ) @ ( exp_real @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.17/5.52 @ at_top_real ) ).
% 5.17/5.52
% 5.17/5.52 % tendsto_power_div_exp_0
% 5.17/5.52 thf(fact_9744_tendsto__exp__limit__at__top,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( filterlim_real_real
% 5.17/5.52 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y6 ) ) @ Y6 )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.17/5.52 @ at_top_real ) ).
% 5.17/5.52
% 5.17/5.52 % tendsto_exp_limit_at_top
% 5.17/5.52 thf(fact_9745_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.17/5.52 ! [B: real,F: real > real,Flim: real] :
% 5.17/5.52 ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ B @ X4 )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ Y3 @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.17/5.52 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_neg_imp_decreasing_at_top
% 5.17/5.52 thf(fact_9746_tendsto__arctan__at__top,axiom,
% 5.17/5.52 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.17/5.52
% 5.17/5.52 % tendsto_arctan_at_top
% 5.17/5.52 thf(fact_9747_lhopital__left__at__top,axiom,
% 5.17/5.52 ! [G: real > real,X: real,G2: real > real,F: real > real,F2: real > real,Y4: real] :
% 5.17/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_left_at_top
% 5.17/5.52 thf(fact_9748_at__top__le__at__infinity,axiom,
% 5.17/5.52 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.17/5.52
% 5.17/5.52 % at_top_le_at_infinity
% 5.17/5.52 thf(fact_9749_at__bot__le__at__infinity,axiom,
% 5.17/5.52 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.17/5.52
% 5.17/5.52 % at_bot_le_at_infinity
% 5.17/5.52 thf(fact_9750_filterlim__real__at__infinity__sequentially,axiom,
% 5.17/5.52 filterlim_nat_real @ semiri5074537144036343181t_real @ at_infinity_real @ at_top_nat ).
% 5.17/5.52
% 5.17/5.52 % filterlim_real_at_infinity_sequentially
% 5.17/5.52 thf(fact_9751_eventually__at__right__to__0,axiom,
% 5.17/5.52 ! [P: real > $o,A: real] :
% 5.17/5.52 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 = ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( P @ ( plus_plus_real @ X3 @ A ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % eventually_at_right_to_0
% 5.17/5.52 thf(fact_9752_eventually__at__top__to__right,axiom,
% 5.17/5.52 ! [P: real > $o] :
% 5.17/5.52 ( ( eventually_real @ P @ at_top_real )
% 5.17/5.52 = ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % eventually_at_top_to_right
% 5.17/5.52 thf(fact_9753_eventually__at__right__to__top,axiom,
% 5.17/5.52 ! [P: real > $o] :
% 5.17/5.52 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 = ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.17/5.52 @ at_top_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % eventually_at_right_to_top
% 5.17/5.52 thf(fact_9754_lhopital__at__top__at__top,axiom,
% 5.17/5.52 ! [F: real > real,A: real,G: real > real,F2: real > real,G2: real > real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_at_top_at_top
% 5.17/5.52 thf(fact_9755_lhopital,axiom,
% 5.17/5.52 ! [F: real > real,X: real,G: real > real,G2: real > real,F2: real > real,F4: filter_real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital
% 5.17/5.52 thf(fact_9756_lhopital__right__at__top__at__top,axiom,
% 5.17/5.52 ! [F: real > real,A: real,G: real > real,F2: real > real,G2: real > real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_right_at_top_at_top
% 5.17/5.52 thf(fact_9757_lhopital__at__top__at__bot,axiom,
% 5.17/5.52 ! [F: real > real,A: real,G: real > real,F2: real > real,G2: real > real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_at_top_at_bot
% 5.17/5.52 thf(fact_9758_lhopital__left__at__top__at__top,axiom,
% 5.17/5.52 ! [F: real > real,A: real,G: real > real,F2: real > real,G2: real > real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ at_top_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_left_at_top_at_top
% 5.17/5.52 thf(fact_9759_lhospital__at__top__at__top,axiom,
% 5.17/5.52 ! [G: real > real,G2: real > real,F: real > real,F2: real > real,X: real] :
% 5.17/5.52 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ at_top_real )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ at_top_real )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ at_top_real )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.17/5.52 @ at_top_real )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.17/5.52 @ at_top_real ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhospital_at_top_at_top
% 5.17/5.52 thf(fact_9760_lhopital__at__top,axiom,
% 5.17/5.52 ! [G: real > real,X: real,G2: real > real,F: real > real,F2: real > real,Y4: real] :
% 5.17/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_at_top
% 5.17/5.52 thf(fact_9761_lhopital__right__0,axiom,
% 5.17/5.52 ! [F0: real > real,G0: real > real,G2: real > real,F2: real > real,F4: filter_real] :
% 5.17/5.52 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G0 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F0 @ X3 ) @ ( G0 @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_right_0
% 5.17/5.52 thf(fact_9762_lhopital__right,axiom,
% 5.17/5.52 ! [F: real > real,X: real,G: real > real,G2: real > real,F2: real > real,F4: filter_real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_right
% 5.17/5.52 thf(fact_9763_lhopital__left,axiom,
% 5.17/5.52 ! [F: real > real,X: real,G: real > real,G2: real > real,F2: real > real,F4: filter_real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ F4
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_left
% 5.17/5.52 thf(fact_9764_lhopital__right__at__top__at__bot,axiom,
% 5.17/5.52 ! [F: real > real,A: real,G: real > real,F2: real > real,G2: real > real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_right_at_top_at_bot
% 5.17/5.52 thf(fact_9765_lhopital__left__at__top__at__bot,axiom,
% 5.17/5.52 ! [F: real > real,A: real,G: real > real,F2: real > real,G2: real > real] :
% 5.17/5.52 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ at_bot_real
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_left_at_top_at_bot
% 5.17/5.52 thf(fact_9766_lhopital__right__at__top,axiom,
% 5.17/5.52 ! [G: real > real,X: real,G2: real > real,F: real > real,F2: real > real,Y4: real] :
% 5.17/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_right_at_top
% 5.17/5.52 thf(fact_9767_lhopital__right__0__at__top,axiom,
% 5.17/5.52 ! [G: real > real,G2: real > real,F: real > real,F2: real > real,X: real] :
% 5.17/5.52 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] :
% 5.17/5.52 ( ( G2 @ X3 )
% 5.17/5.52 != zero_zero_real )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( eventually_real
% 5.17/5.52 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.52 => ( filterlim_real_real
% 5.17/5.52 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ X )
% 5.17/5.52 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % lhopital_right_0_at_top
% 5.17/5.52 thf(fact_9768_eventually__sequentially__Suc,axiom,
% 5.17/5.52 ! [P: nat > $o] :
% 5.17/5.52 ( ( eventually_nat
% 5.17/5.52 @ ^ [I2: nat] : ( P @ ( suc @ I2 ) )
% 5.17/5.52 @ at_top_nat )
% 5.17/5.52 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % eventually_sequentially_Suc
% 5.17/5.52 thf(fact_9769_le__sequentially,axiom,
% 5.17/5.52 ! [F4: filter_nat] :
% 5.17/5.52 ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 5.17/5.52 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % le_sequentially
% 5.17/5.52 thf(fact_9770_eventually__sequentially,axiom,
% 5.17/5.52 ! [P: nat > $o] :
% 5.17/5.52 ( ( eventually_nat @ P @ at_top_nat )
% 5.17/5.52 = ( ? [N8: nat] :
% 5.17/5.52 ! [N4: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ N8 @ N4 )
% 5.17/5.52 => ( P @ N4 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % eventually_sequentially
% 5.17/5.52 thf(fact_9771_eventually__sequentiallyI,axiom,
% 5.17/5.52 ! [C: nat,P: nat > $o] :
% 5.17/5.52 ( ! [X4: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ C @ X4 )
% 5.17/5.52 => ( P @ X4 ) )
% 5.17/5.52 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % eventually_sequentiallyI
% 5.17/5.52 thf(fact_9772_filterlim__int__sequentially,axiom,
% 5.17/5.52 filterlim_nat_int @ semiri1314217659103216013at_int @ at_top_int @ at_top_nat ).
% 5.17/5.52
% 5.17/5.52 % filterlim_int_sequentially
% 5.17/5.52 thf(fact_9773_Bseq__eq__bounded,axiom,
% 5.17/5.52 ! [F: nat > real,A: real,B: real] :
% 5.17/5.52 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.17/5.52 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % Bseq_eq_bounded
% 5.17/5.52 thf(fact_9774_Bseq__realpow,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.52 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.52 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Bseq_realpow
% 5.17/5.52 thf(fact_9775_GreatestI__nat,axiom,
% 5.17/5.52 ! [P: nat > $o,K: nat,B: nat] :
% 5.17/5.52 ( ( P @ K )
% 5.17/5.52 => ( ! [Y: nat] :
% 5.17/5.52 ( ( P @ Y )
% 5.17/5.52 => ( ord_less_eq_nat @ Y @ B ) )
% 5.17/5.52 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % GreatestI_nat
% 5.17/5.52 thf(fact_9776_Greatest__le__nat,axiom,
% 5.17/5.52 ! [P: nat > $o,K: nat,B: nat] :
% 5.17/5.52 ( ( P @ K )
% 5.17/5.52 => ( ! [Y: nat] :
% 5.17/5.52 ( ( P @ Y )
% 5.17/5.52 => ( ord_less_eq_nat @ Y @ B ) )
% 5.17/5.52 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Greatest_le_nat
% 5.17/5.52 thf(fact_9777_GreatestI__ex__nat,axiom,
% 5.17/5.52 ! [P: nat > $o,B: nat] :
% 5.17/5.52 ( ? [X_12: nat] : ( P @ X_12 )
% 5.17/5.52 => ( ! [Y: nat] :
% 5.17/5.52 ( ( P @ Y )
% 5.17/5.52 => ( ord_less_eq_nat @ Y @ B ) )
% 5.17/5.52 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % GreatestI_ex_nat
% 5.17/5.52 thf(fact_9778_GMVT,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 & ( ord_less_eq_real @ X4 @ B ) )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 & ( ord_less_real @ X4 @ B ) )
% 5.17/5.52 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.17/5.52 & ( ord_less_eq_real @ X4 @ B ) )
% 5.17/5.52 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 & ( ord_less_real @ X4 @ B ) )
% 5.17/5.52 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.17/5.52 => ? [G_c: real,F_c: real,C3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.17/5.52 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ A @ C3 )
% 5.17/5.52 & ( ord_less_real @ C3 @ B )
% 5.17/5.52 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.17/5.52 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % GMVT
% 5.17/5.52 thf(fact_9779_MVT,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ? [L2: real,Z2: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.17/5.52 & ( ord_less_real @ Z2 @ B )
% 5.17/5.52 & ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.17/5.52 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.17/5.52 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L2 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % MVT
% 5.17/5.52 thf(fact_9780_continuous__on__arcosh_H,axiom,
% 5.17/5.52 ! [A2: set_real,F: real > real] :
% 5.17/5.52 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ A2 )
% 5.17/5.52 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.17/5.52 => ( topolo5044208981011980120l_real @ A2
% 5.17/5.52 @ ^ [X3: real] : ( arcosh_real @ ( F @ X3 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % continuous_on_arcosh'
% 5.17/5.52 thf(fact_9781_continuous__image__closed__interval,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_eq_real @ A @ B )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ? [C3: real,D2: real] :
% 5.17/5.52 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.17/5.52 = ( set_or1222579329274155063t_real @ C3 @ D2 ) )
% 5.17/5.52 & ( ord_less_eq_real @ C3 @ D2 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % continuous_image_closed_interval
% 5.17/5.52 thf(fact_9782_continuous__on__arcosh,axiom,
% 5.17/5.52 ! [A2: set_real] :
% 5.17/5.52 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.17/5.52 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % continuous_on_arcosh
% 5.17/5.52 thf(fact_9783_Rolle__deriv,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,F2: real > real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( ( F @ A )
% 5.17/5.52 = ( F @ B ) )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ( has_de1759254742604945161l_real @ F @ ( F2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ? [Z2: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.17/5.52 & ( ord_less_real @ Z2 @ B )
% 5.17/5.52 & ( ( F2 @ Z2 )
% 5.17/5.52 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rolle_deriv
% 5.17/5.52 thf(fact_9784_mvt,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,F2: real > real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ( has_de1759254742604945161l_real @ F @ ( F2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ~ ! [Xi: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Xi )
% 5.17/5.52 => ( ( ord_less_real @ Xi @ B )
% 5.17/5.52 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.17/5.52 != ( F2 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % mvt
% 5.17/5.52 thf(fact_9785_DERIV__pos__imp__increasing__open,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ zero_zero_real @ Y3 ) ) ) )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_pos_imp_increasing_open
% 5.17/5.52 thf(fact_9786_DERIV__neg__imp__decreasing__open,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ? [Y3: real] :
% 5.17/5.52 ( ( has_fi5821293074295781190e_real @ F @ Y3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 & ( ord_less_real @ Y3 @ zero_zero_real ) ) ) )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_neg_imp_decreasing_open
% 5.17/5.52 thf(fact_9787_DERIV__isconst__end,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ( ( F @ B )
% 5.17/5.52 = ( F @ A ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_isconst_end
% 5.17/5.52 thf(fact_9788_continuous__on__artanh,axiom,
% 5.17/5.52 ! [A2: set_real] :
% 5.17/5.52 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.17/5.52 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % continuous_on_artanh
% 5.17/5.52 thf(fact_9789_DERIV__isconst2,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real,X: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ( ( ord_less_eq_real @ A @ X )
% 5.17/5.52 => ( ( ord_less_eq_real @ X @ B )
% 5.17/5.52 => ( ( F @ X )
% 5.17/5.52 = ( F @ A ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % DERIV_isconst2
% 5.17/5.52 thf(fact_9790_Rolle,axiom,
% 5.17/5.52 ! [A: real,B: real,F: real > real] :
% 5.17/5.52 ( ( ord_less_real @ A @ B )
% 5.17/5.52 => ( ( ( F @ A )
% 5.17/5.52 = ( F @ B ) )
% 5.17/5.52 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.17/5.52 => ( ! [X4: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ X4 )
% 5.17/5.52 => ( ( ord_less_real @ X4 @ B )
% 5.17/5.52 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.17/5.52 => ? [Z2: real] :
% 5.17/5.52 ( ( ord_less_real @ A @ Z2 )
% 5.17/5.52 & ( ord_less_real @ Z2 @ B )
% 5.17/5.52 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rolle
% 5.17/5.52 thf(fact_9791_surj__int__encode,axiom,
% 5.17/5.52 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 5.17/5.52 = top_top_set_nat ) ).
% 5.17/5.52
% 5.17/5.52 % surj_int_encode
% 5.17/5.52 thf(fact_9792_int__encode__eq,axiom,
% 5.17/5.52 ! [X: int,Y4: int] :
% 5.17/5.52 ( ( ( nat_int_encode @ X )
% 5.17/5.52 = ( nat_int_encode @ Y4 ) )
% 5.17/5.52 = ( X = Y4 ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_encode_eq
% 5.17/5.52 thf(fact_9793_bij__int__encode,axiom,
% 5.17/5.52 bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 5.17/5.52
% 5.17/5.52 % bij_int_encode
% 5.17/5.52 thf(fact_9794_uniformity__real__def,axiom,
% 5.17/5.52 ( topolo1511823702728130853y_real
% 5.17/5.52 = ( comple2936214249959783750l_real
% 5.17/5.52 @ ( image_2178119161166701260l_real
% 5.17/5.52 @ ^ [E3: real] :
% 5.17/5.52 ( princi6114159922880469582l_real
% 5.17/5.52 @ ( collec3799799289383736868l_real
% 5.17/5.52 @ ( produc5414030515140494994real_o
% 5.17/5.52 @ ^ [X3: real,Y6: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X3 @ Y6 ) @ E3 ) ) ) )
% 5.17/5.52 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % uniformity_real_def
% 5.17/5.52 thf(fact_9795_uniformity__complex__def,axiom,
% 5.17/5.52 ( topolo896644834953643431omplex
% 5.17/5.52 = ( comple8358262395181532106omplex
% 5.17/5.52 @ ( image_5971271580939081552omplex
% 5.17/5.52 @ ^ [E3: real] :
% 5.17/5.52 ( princi3496590319149328850omplex
% 5.17/5.52 @ ( collec8663557070575231912omplex
% 5.17/5.52 @ ( produc6771430404735790350plex_o
% 5.17/5.52 @ ^ [X3: complex,Y6: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X3 @ Y6 ) @ E3 ) ) ) )
% 5.17/5.52 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % uniformity_complex_def
% 5.17/5.52 thf(fact_9796_range__abs__Nats,axiom,
% 5.17/5.52 ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 5.17/5.52 = semiring_1_Nats_int ) ).
% 5.17/5.52
% 5.17/5.52 % range_abs_Nats
% 5.17/5.52 thf(fact_9797_inj__sgn__power,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( inj_on_real_real
% 5.17/5.52 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N ) )
% 5.17/5.52 @ top_top_set_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % inj_sgn_power
% 5.17/5.52 thf(fact_9798_surj__int__decode,axiom,
% 5.17/5.52 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 5.17/5.52 = top_top_set_int ) ).
% 5.17/5.52
% 5.17/5.52 % surj_int_decode
% 5.17/5.52 thf(fact_9799_int__decode__inverse,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( nat_int_encode @ ( nat_int_decode @ N ) )
% 5.17/5.52 = N ) ).
% 5.17/5.52
% 5.17/5.52 % int_decode_inverse
% 5.17/5.52 thf(fact_9800_int__encode__inverse,axiom,
% 5.17/5.52 ! [X: int] :
% 5.17/5.52 ( ( nat_int_decode @ ( nat_int_encode @ X ) )
% 5.17/5.52 = X ) ).
% 5.17/5.52
% 5.17/5.52 % int_encode_inverse
% 5.17/5.52 thf(fact_9801_int__decode__eq,axiom,
% 5.17/5.52 ! [X: nat,Y4: nat] :
% 5.17/5.52 ( ( ( nat_int_decode @ X )
% 5.17/5.52 = ( nat_int_decode @ Y4 ) )
% 5.17/5.52 = ( X = Y4 ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_decode_eq
% 5.17/5.52 thf(fact_9802_bij__int__decode,axiom,
% 5.17/5.52 bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 5.17/5.52
% 5.17/5.52 % bij_int_decode
% 5.17/5.52 thf(fact_9803_log__inj,axiom,
% 5.17/5.52 ! [B: real] :
% 5.17/5.52 ( ( ord_less_real @ one_one_real @ B )
% 5.17/5.52 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % log_inj
% 5.17/5.52 thf(fact_9804_complex__is__Nat__iff,axiom,
% 5.17/5.52 ! [Z: complex] :
% 5.17/5.52 ( ( member_complex @ Z @ semiri3842193898606819883omplex )
% 5.17/5.52 = ( ( ( im @ Z )
% 5.17/5.52 = zero_zero_real )
% 5.17/5.52 & ? [I2: nat] :
% 5.17/5.52 ( ( re @ Z )
% 5.17/5.52 = ( semiri5074537144036343181t_real @ I2 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % complex_is_Nat_iff
% 5.17/5.52 thf(fact_9805_inj__int__encode,axiom,
% 5.17/5.52 ! [A2: set_int] : ( inj_on_int_nat @ nat_int_encode @ A2 ) ).
% 5.17/5.52
% 5.17/5.52 % inj_int_encode
% 5.17/5.52 thf(fact_9806_inj__on__set__encode,axiom,
% 5.17/5.52 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 5.17/5.52
% 5.17/5.52 % inj_on_set_encode
% 5.17/5.52 thf(fact_9807_inj__prod__encode,axiom,
% 5.17/5.52 ! [A2: set_Pr1261947904930325089at_nat] : ( inj_on2178005380612969504at_nat @ nat_prod_encode @ A2 ) ).
% 5.17/5.52
% 5.17/5.52 % inj_prod_encode
% 5.17/5.52 thf(fact_9808_inj__Suc,axiom,
% 5.17/5.52 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 5.17/5.52
% 5.17/5.52 % inj_Suc
% 5.17/5.52 thf(fact_9809_inj__int__decode,axiom,
% 5.17/5.52 ! [A2: set_nat] : ( inj_on_nat_int @ nat_int_decode @ A2 ) ).
% 5.17/5.52
% 5.17/5.52 % inj_int_decode
% 5.17/5.52 thf(fact_9810_inj__on__diff__nat,axiom,
% 5.17/5.52 ! [N5: set_nat,K: nat] :
% 5.17/5.52 ( ! [N2: nat] :
% 5.17/5.52 ( ( member_nat @ N2 @ N5 )
% 5.17/5.52 => ( ord_less_eq_nat @ K @ N2 ) )
% 5.17/5.52 => ( inj_on_nat_nat
% 5.17/5.52 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K )
% 5.17/5.52 @ N5 ) ) ).
% 5.17/5.52
% 5.17/5.52 % inj_on_diff_nat
% 5.17/5.52 thf(fact_9811_summable__reindex,axiom,
% 5.17/5.52 ! [F: nat > real,G: nat > nat] :
% 5.17/5.52 ( ( summable_real @ F )
% 5.17/5.52 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.17/5.52 => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.17/5.52 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % summable_reindex
% 5.17/5.52 thf(fact_9812_suminf__reindex__mono,axiom,
% 5.17/5.52 ! [F: nat > real,G: nat > nat] :
% 5.17/5.52 ( ( summable_real @ F )
% 5.17/5.52 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.17/5.52 => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.17/5.52 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % suminf_reindex_mono
% 5.17/5.52 thf(fact_9813_inj__on__char__of__nat,axiom,
% 5.17/5.52 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % inj_on_char_of_nat
% 5.17/5.52 thf(fact_9814_suminf__reindex,axiom,
% 5.17/5.52 ! [F: nat > real,G: nat > nat] :
% 5.17/5.52 ( ( summable_real @ F )
% 5.17/5.52 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.17/5.52 => ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.17/5.52 => ( ! [X4: nat] :
% 5.17/5.52 ( ~ ( member_nat @ X4 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.17/5.52 => ( ( F @ X4 )
% 5.17/5.52 = zero_zero_real ) )
% 5.17/5.52 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.17/5.52 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % suminf_reindex
% 5.17/5.52 thf(fact_9815_powr__real__of__int_H,axiom,
% 5.17/5.52 ! [X: real,N: int] :
% 5.17/5.52 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.52 => ( ( ( X != zero_zero_real )
% 5.17/5.52 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.17/5.52 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.17/5.52 = ( power_int_real @ X @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % powr_real_of_int'
% 5.17/5.52 thf(fact_9816_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.17/5.52 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.52 ( ~ ( vEBT_VEBT_valid @ X @ Xa )
% 5.17/5.52 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.17/5.52 ( X
% 5.17/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.52 => ( Xa = one_one_nat ) )
% 5.17/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.52 => ( ( Deg2 = Xa )
% 5.17/5.52 & ! [X4: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.elims(3)
% 5.17/5.52 thf(fact_9817_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.17/5.52 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.52 ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.17/5.52 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.17/5.52 ( X
% 5.17/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.52 => ( Xa != one_one_nat ) )
% 5.17/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.52 => ~ ( ( Deg2 = Xa )
% 5.17/5.52 & ! [X5: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.elims(2)
% 5.17/5.52 thf(fact_9818_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.17/5.52 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.17/5.52 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.17/5.52 = ( ( Deg = Deg4 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.simps(2)
% 5.17/5.52 thf(fact_9819_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.17/5.52 ! [X: vEBT_VEBT,Xa: nat,Y4: $o] :
% 5.17/5.52 ( ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.17/5.52 ( X
% 5.17/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 = ( Xa != one_one_nat ) ) )
% 5.17/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 = ( ~ ( ( Deg2 = Xa )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.elims(1)
% 5.17/5.52 thf(fact_9820_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.17/5.52 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.52 ( ~ ( vEBT_VEBT_valid @ X @ Xa )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.52 => ( ! [Uu2: $o,Uv2: $o] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 5.17/5.52 => ( Xa = one_one_nat ) ) )
% 5.17/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.17/5.52 => ( ( Deg2 = Xa )
% 5.17/5.52 & ! [X4: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.pelims(3)
% 5.17/5.52 thf(fact_9821_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.17/5.52 ! [X: vEBT_VEBT,Xa: nat] :
% 5.17/5.52 ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.52 => ( ! [Uu2: $o,Uv2: $o] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 5.17/5.52 => ( Xa != one_one_nat ) ) )
% 5.17/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) )
% 5.17/5.52 => ~ ( ( Deg2 = Xa )
% 5.17/5.52 & ! [X5: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.pelims(2)
% 5.17/5.52 thf(fact_9822_Sup__int__def,axiom,
% 5.17/5.52 ( complete_Sup_Sup_int
% 5.17/5.52 = ( ^ [X8: set_int] :
% 5.17/5.52 ( the_int
% 5.17/5.52 @ ^ [X3: int] :
% 5.17/5.52 ( ( member_int @ X3 @ X8 )
% 5.17/5.52 & ! [Y6: int] :
% 5.17/5.52 ( ( member_int @ Y6 @ X8 )
% 5.17/5.52 => ( ord_less_eq_int @ Y6 @ X3 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Sup_int_def
% 5.17/5.52 thf(fact_9823_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.17/5.52 ! [X: vEBT_VEBT,Xa: nat,Y4: $o] :
% 5.17/5.52 ( ( ( vEBT_VEBT_valid @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa ) )
% 5.17/5.52 => ( ! [Uu2: $o,Uv2: $o] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( Xa = one_one_nat ) )
% 5.17/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.17/5.52 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( ( Deg2 = Xa )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.17/5.52 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.17/5.52 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 & ( case_o184042715313410164at_nat
% 5.17/5.52 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 5.17/5.52 & ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 @ ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [Mi3: nat,Ma3: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.17/5.52 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 & ! [I2: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.17/5.52 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X8 ) )
% 5.17/5.52 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.17/5.52 & ( ( Mi3 = Ma3 )
% 5.17/5.52 => ! [X3: vEBT_VEBT] :
% 5.17/5.52 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.17/5.52 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X8 ) ) )
% 5.17/5.52 & ( ( Mi3 != Ma3 )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.17/5.52 & ! [X3: nat] :
% 5.17/5.52 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.17/5.52 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.17/5.52 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.17/5.52 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.17/5.52 @ Mima ) ) )
% 5.17/5.52 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % VEBT_internal.valid'.pelims(1)
% 5.17/5.52 thf(fact_9824_Rats__eq__int__div__nat,axiom,
% 5.17/5.52 ( field_5140801741446780682s_real
% 5.17/5.52 = ( collect_real
% 5.17/5.52 @ ^ [Uu3: real] :
% 5.17/5.52 ? [I2: int,N4: nat] :
% 5.17/5.52 ( ( Uu3
% 5.17/5.52 = ( divide_divide_real @ ( ring_1_of_int_real @ I2 ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 5.17/5.52 & ( N4 != zero_zero_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rats_eq_int_div_nat
% 5.17/5.52 thf(fact_9825_Rats__abs__iff,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ( ( member_real @ ( abs_abs_real @ X ) @ field_5140801741446780682s_real )
% 5.17/5.52 = ( member_real @ X @ field_5140801741446780682s_real ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rats_abs_iff
% 5.17/5.52 thf(fact_9826_Rats__dense__in__real,axiom,
% 5.17/5.52 ! [X: real,Y4: real] :
% 5.17/5.52 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.52 => ? [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.17/5.52 & ( ord_less_real @ X @ X4 )
% 5.17/5.52 & ( ord_less_real @ X4 @ Y4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rats_dense_in_real
% 5.17/5.52 thf(fact_9827_Rats__no__bot__less,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ? [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.17/5.52 & ( ord_less_real @ X4 @ X ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rats_no_bot_less
% 5.17/5.52 thf(fact_9828_Rats__no__top__le,axiom,
% 5.17/5.52 ! [X: real] :
% 5.17/5.52 ? [X4: real] :
% 5.17/5.52 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.17/5.52 & ( ord_less_eq_real @ X @ X4 ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rats_no_top_le
% 5.17/5.52 thf(fact_9829_Rats__eq__int__div__int,axiom,
% 5.17/5.52 ( field_5140801741446780682s_real
% 5.17/5.52 = ( collect_real
% 5.17/5.52 @ ^ [Uu3: real] :
% 5.17/5.52 ? [I2: int,J3: int] :
% 5.17/5.52 ( ( Uu3
% 5.17/5.52 = ( divide_divide_real @ ( ring_1_of_int_real @ I2 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.17/5.52 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rats_eq_int_div_int
% 5.17/5.52 thf(fact_9830_rat__floor__lemma,axiom,
% 5.17/5.52 ! [A: int,B: int] :
% 5.17/5.52 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.17/5.52 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % rat_floor_lemma
% 5.17/5.52 thf(fact_9831_mult__rat,axiom,
% 5.17/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.52 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.17/5.52 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % mult_rat
% 5.17/5.52 thf(fact_9832_divide__rat,axiom,
% 5.17/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.17/5.52 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.17/5.52 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % divide_rat
% 5.17/5.52 thf(fact_9833_floor__Fract,axiom,
% 5.17/5.52 ! [A: int,B: int] :
% 5.17/5.52 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.17/5.52 = ( divide_divide_int @ A @ B ) ) ).
% 5.17/5.52
% 5.17/5.52 % floor_Fract
% 5.17/5.52 thf(fact_9834_less__rat,axiom,
% 5.17/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.17/5.52 ( ( B != zero_zero_int )
% 5.17/5.52 => ( ( D != zero_zero_int )
% 5.17/5.52 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.17/5.52 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_rat
% 5.17/5.52 thf(fact_9835_add__rat,axiom,
% 5.17/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.17/5.52 ( ( B != zero_zero_int )
% 5.17/5.52 => ( ( D != zero_zero_int )
% 5.17/5.52 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.17/5.52 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % add_rat
% 5.17/5.52 thf(fact_9836_le__rat,axiom,
% 5.17/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.17/5.52 ( ( B != zero_zero_int )
% 5.17/5.52 => ( ( D != zero_zero_int )
% 5.17/5.52 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.17/5.52 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % le_rat
% 5.17/5.52 thf(fact_9837_diff__rat,axiom,
% 5.17/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.17/5.52 ( ( B != zero_zero_int )
% 5.17/5.52 => ( ( D != zero_zero_int )
% 5.17/5.52 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.17/5.52 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % diff_rat
% 5.17/5.52 thf(fact_9838_sgn__rat,axiom,
% 5.17/5.52 ! [A: int,B: int] :
% 5.17/5.52 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.17/5.52 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sgn_rat
% 5.17/5.52 thf(fact_9839_Rat__induct__pos,axiom,
% 5.17/5.52 ! [P: rat > $o,Q2: rat] :
% 5.17/5.52 ( ! [A4: int,B3: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.17/5.52 => ( P @ ( fract @ A4 @ B3 ) ) )
% 5.17/5.52 => ( P @ Q2 ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat_induct_pos
% 5.17/5.52 thf(fact_9840_Fract__coprime,axiom,
% 5.17/5.52 ! [A: int,B: int] :
% 5.17/5.52 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.17/5.52 = ( fract @ A @ B ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_coprime
% 5.17/5.52 thf(fact_9841_rat__number__collapse_I1_J,axiom,
% 5.17/5.52 ! [K: int] :
% 5.17/5.52 ( ( fract @ zero_zero_int @ K )
% 5.17/5.52 = zero_zero_rat ) ).
% 5.17/5.52
% 5.17/5.52 % rat_number_collapse(1)
% 5.17/5.52 thf(fact_9842_rat__number__collapse_I6_J,axiom,
% 5.17/5.52 ! [K: int] :
% 5.17/5.52 ( ( fract @ K @ zero_zero_int )
% 5.17/5.52 = zero_zero_rat ) ).
% 5.17/5.52
% 5.17/5.52 % rat_number_collapse(6)
% 5.17/5.52 thf(fact_9843_eq__rat_I2_J,axiom,
% 5.17/5.52 ! [A: int] :
% 5.17/5.52 ( ( fract @ A @ zero_zero_int )
% 5.17/5.52 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.17/5.52
% 5.17/5.52 % eq_rat(2)
% 5.17/5.52 thf(fact_9844_mult__rat__cancel,axiom,
% 5.17/5.52 ! [C: int,A: int,B: int] :
% 5.17/5.52 ( ( C != zero_zero_int )
% 5.17/5.52 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.17/5.52 = ( fract @ A @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % mult_rat_cancel
% 5.17/5.52 thf(fact_9845_eq__rat_I1_J,axiom,
% 5.17/5.52 ! [B: int,D: int,A: int,C: int] :
% 5.17/5.52 ( ( B != zero_zero_int )
% 5.17/5.52 => ( ( D != zero_zero_int )
% 5.17/5.52 => ( ( ( fract @ A @ B )
% 5.17/5.52 = ( fract @ C @ D ) )
% 5.17/5.52 = ( ( times_times_int @ A @ D )
% 5.17/5.52 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % eq_rat(1)
% 5.17/5.52 thf(fact_9846_eq__rat_I3_J,axiom,
% 5.17/5.52 ! [A: int,C: int] :
% 5.17/5.52 ( ( fract @ zero_zero_int @ A )
% 5.17/5.52 = ( fract @ zero_zero_int @ C ) ) ).
% 5.17/5.52
% 5.17/5.52 % eq_rat(3)
% 5.17/5.52 thf(fact_9847_Fract__of__nat__eq,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 5.17/5.52 = ( semiri681578069525770553at_rat @ K ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_of_nat_eq
% 5.17/5.52 thf(fact_9848_Zero__rat__def,axiom,
% 5.17/5.52 ( zero_zero_rat
% 5.17/5.52 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.17/5.52
% 5.17/5.52 % Zero_rat_def
% 5.17/5.52 thf(fact_9849_atLeastLessThan__add__Un,axiom,
% 5.17/5.52 ! [I: nat,J: nat,K: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.52 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.17/5.52 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeastLessThan_add_Un
% 5.17/5.52 thf(fact_9850_rat__number__collapse_I3_J,axiom,
% 5.17/5.52 ! [W: num] :
% 5.17/5.52 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.17/5.52 = ( numeral_numeral_rat @ W ) ) ).
% 5.17/5.52
% 5.17/5.52 % rat_number_collapse(3)
% 5.17/5.52 thf(fact_9851_rat__number__expand_I3_J,axiom,
% 5.17/5.52 ( numeral_numeral_rat
% 5.17/5.52 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % rat_number_expand(3)
% 5.17/5.52 thf(fact_9852_zero__less__Fract__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.17/5.52 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % zero_less_Fract_iff
% 5.17/5.52 thf(fact_9853_Fract__less__zero__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.17/5.52 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_less_zero_iff
% 5.17/5.52 thf(fact_9854_Fract__less__one__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.17/5.52 = ( ord_less_int @ A @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_less_one_iff
% 5.17/5.52 thf(fact_9855_one__less__Fract__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.17/5.52 = ( ord_less_int @ B @ A ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % one_less_Fract_iff
% 5.17/5.52 thf(fact_9856_Fract__add__one,axiom,
% 5.17/5.52 ! [N: int,M: int] :
% 5.17/5.52 ( ( N != zero_zero_int )
% 5.17/5.52 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 5.17/5.52 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_add_one
% 5.17/5.52 thf(fact_9857_Fract__le__zero__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.17/5.52 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_le_zero_iff
% 5.17/5.52 thf(fact_9858_zero__le__Fract__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.17/5.52 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % zero_le_Fract_iff
% 5.17/5.52 thf(fact_9859_one__le__Fract__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.17/5.52 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % one_le_Fract_iff
% 5.17/5.52 thf(fact_9860_Fract__le__one__iff,axiom,
% 5.17/5.52 ! [B: int,A: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B )
% 5.17/5.52 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.17/5.52 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract_le_one_iff
% 5.17/5.52 thf(fact_9861_rat__number__expand_I5_J,axiom,
% 5.17/5.52 ! [K: num] :
% 5.17/5.52 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.17/5.52 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.17/5.52
% 5.17/5.52 % rat_number_expand(5)
% 5.17/5.52 thf(fact_9862_rat__number__collapse_I4_J,axiom,
% 5.17/5.52 ! [W: num] :
% 5.17/5.52 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.17/5.52 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % rat_number_collapse(4)
% 5.17/5.52 thf(fact_9863_sup__int__def,axiom,
% 5.17/5.52 sup_sup_int = ord_max_int ).
% 5.17/5.52
% 5.17/5.52 % sup_int_def
% 5.17/5.52 thf(fact_9864_sup__enat__def,axiom,
% 5.17/5.52 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.17/5.52
% 5.17/5.52 % sup_enat_def
% 5.17/5.52 thf(fact_9865_sup__nat__def,axiom,
% 5.17/5.52 sup_sup_nat = ord_max_nat ).
% 5.17/5.52
% 5.17/5.52 % sup_nat_def
% 5.17/5.52 thf(fact_9866_pos__deriv__imp__strict__mono,axiom,
% 5.17/5.52 ! [F: real > real,F2: real > real] :
% 5.17/5.52 ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F2 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.17/5.52 => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F2 @ X4 ) )
% 5.17/5.52 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % pos_deriv_imp_strict_mono
% 5.17/5.52 thf(fact_9867_take__bit__numeral__minus__numeral__int,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int
% 5.17/5.52 @ ^ [Q3: 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 @ Q3 ) ) )
% 5.17/5.52 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_numeral_minus_numeral_int
% 5.17/5.52 thf(fact_9868_of__nat__eq__id,axiom,
% 5.17/5.52 semiri1316708129612266289at_nat = id_nat ).
% 5.17/5.52
% 5.17/5.52 % of_nat_eq_id
% 5.17/5.52 thf(fact_9869_take__bit__num__simps_I1_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.17/5.52 = none_num ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(1)
% 5.17/5.52 thf(fact_9870_take__bit__num__simps_I2_J,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.17/5.52 = ( some_num @ one ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(2)
% 5.17/5.52 thf(fact_9871_take__bit__num__simps_I5_J,axiom,
% 5.17/5.52 ! [R2: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.17/5.52 = ( some_num @ one ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(5)
% 5.17/5.52 thf(fact_9872_strict__mono__imp__increasing,axiom,
% 5.17/5.52 ! [F: nat > nat,N: nat] :
% 5.17/5.52 ( ( order_5726023648592871131at_nat @ F )
% 5.17/5.52 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % strict_mono_imp_increasing
% 5.17/5.52 thf(fact_9873_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( bit_take_bit_num @ N @ one )
% 5.17/5.52 = ( case_nat_option_num @ none_num
% 5.17/5.52 @ ^ [N4: nat] : ( some_num @ one )
% 5.17/5.52 @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.17/5.52 thf(fact_9874_less__int__def,axiom,
% 5.17/5.52 ( ord_less_int
% 5.17/5.52 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.17/5.52 @ ( produc8739625826339149834_nat_o
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_int_def
% 5.17/5.52 thf(fact_9875_nat__def,axiom,
% 5.17/5.52 ( nat2
% 5.17/5.52 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_def
% 5.17/5.52 thf(fact_9876_less__eq__int__def,axiom,
% 5.17/5.52 ( ord_less_eq_int
% 5.17/5.52 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.17/5.52 @ ( produc8739625826339149834_nat_o
% 5.17/5.52 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.52 ( produc6081775807080527818_nat_o
% 5.17/5.52 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_eq_int_def
% 5.17/5.52 thf(fact_9877_take__bit__num__def,axiom,
% 5.17/5.52 ( bit_take_bit_num
% 5.17/5.52 = ( ^ [N4: nat,M5: num] :
% 5.17/5.52 ( if_option_num
% 5.17/5.52 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M5 ) )
% 5.17/5.52 = zero_zero_nat )
% 5.17/5.52 @ none_num
% 5.17/5.52 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M5 ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_def
% 5.17/5.52 thf(fact_9878_and__minus__numerals_I3_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_minus_numerals(3)
% 5.17/5.52 thf(fact_9879_and__minus__numerals_I7_J,axiom,
% 5.17/5.52 ! [N: num,M: num] :
% 5.17/5.52 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_minus_numerals(7)
% 5.17/5.52 thf(fact_9880_take__bit__num__simps_I4_J,axiom,
% 5.17/5.52 ! [N: nat,M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.17/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(4)
% 5.17/5.52 thf(fact_9881_take__bit__num__simps_I3_J,axiom,
% 5.17/5.52 ! [N: nat,M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.17/5.52 = ( case_o6005452278849405969um_num @ none_num
% 5.17/5.52 @ ^ [Q3: num] : ( some_num @ ( bit0 @ Q3 ) )
% 5.17/5.52 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(3)
% 5.17/5.52 thf(fact_9882_take__bit__num__simps_I7_J,axiom,
% 5.17/5.52 ! [R2: num,M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.17/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(7)
% 5.17/5.52 thf(fact_9883_take__bit__num__simps_I6_J,axiom,
% 5.17/5.52 ! [R2: num,M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.17/5.52 = ( case_o6005452278849405969um_num @ none_num
% 5.17/5.52 @ ^ [Q3: num] : ( some_num @ ( bit0 @ Q3 ) )
% 5.17/5.52 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_num_simps(6)
% 5.17/5.52 thf(fact_9884_and__minus__numerals_I8_J,axiom,
% 5.17/5.52 ! [N: num,M: num] :
% 5.17/5.52 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_minus_numerals(8)
% 5.17/5.52 thf(fact_9885_and__minus__numerals_I4_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_minus_numerals(4)
% 5.17/5.52 thf(fact_9886_and__not__num_Osimps_I8_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.52 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.17/5.52 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(8)
% 5.17/5.52 thf(fact_9887_and__not__num_Osimps_I1_J,axiom,
% 5.17/5.52 ( ( bit_and_not_num @ one @ one )
% 5.17/5.52 = none_num ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(1)
% 5.17/5.52 thf(fact_9888_and__not__num_Osimps_I3_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.17/5.52 = none_num ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(3)
% 5.17/5.52 thf(fact_9889_and__not__num_Osimps_I4_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.17/5.52 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(4)
% 5.17/5.52 thf(fact_9890_and__not__num_Osimps_I2_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.17/5.52 = ( some_num @ one ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(2)
% 5.17/5.52 thf(fact_9891_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.17/5.52 ! [N: nat,M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.17/5.52 = ( case_nat_option_num @ none_num
% 5.17/5.52 @ ^ [N4: nat] :
% 5.17/5.52 ( case_o6005452278849405969um_num @ none_num
% 5.17/5.52 @ ^ [Q3: num] : ( some_num @ ( bit0 @ Q3 ) )
% 5.17/5.52 @ ( bit_take_bit_num @ N4 @ M ) )
% 5.17/5.52 @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.17/5.52 thf(fact_9892_and__not__num_Osimps_I7_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.17/5.52 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(7)
% 5.17/5.52 thf(fact_9893_and__not__num__eq__Some__iff,axiom,
% 5.17/5.52 ! [M: num,N: num,Q2: num] :
% 5.17/5.52 ( ( ( bit_and_not_num @ M @ N )
% 5.17/5.52 = ( some_num @ Q2 ) )
% 5.17/5.52 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num_eq_Some_iff
% 5.17/5.52 thf(fact_9894_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.17/5.52 ! [N: nat,M: num] :
% 5.17/5.52 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.17/5.52 = ( case_nat_option_num @ none_num
% 5.17/5.52 @ ^ [N4: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N4 @ M ) ) )
% 5.17/5.52 @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.17/5.52 thf(fact_9895_and__not__num__eq__None__iff,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( ( bit_and_not_num @ M @ N )
% 5.17/5.52 = none_num )
% 5.17/5.52 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = zero_zero_int ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num_eq_None_iff
% 5.17/5.52 thf(fact_9896_int__numeral__and__not__num,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_numeral_and_not_num
% 5.17/5.52 thf(fact_9897_int__numeral__not__and__num,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % int_numeral_not_and_num
% 5.17/5.52 thf(fact_9898_positive__rat,axiom,
% 5.17/5.52 ! [A: int,B: int] :
% 5.17/5.52 ( ( positive @ ( fract @ A @ B ) )
% 5.17/5.52 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % positive_rat
% 5.17/5.52 thf(fact_9899_Rat_Opositive__zero,axiom,
% 5.17/5.52 ~ ( positive @ zero_zero_rat ) ).
% 5.17/5.52
% 5.17/5.52 % Rat.positive_zero
% 5.17/5.52 thf(fact_9900_Rat_Opositive__minus,axiom,
% 5.17/5.52 ! [X: rat] :
% 5.17/5.52 ( ~ ( positive @ X )
% 5.17/5.52 => ( ( X != zero_zero_rat )
% 5.17/5.52 => ( positive @ ( uminus_uminus_rat @ X ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat.positive_minus
% 5.17/5.52 thf(fact_9901_less__rat__def,axiom,
% 5.17/5.52 ( ord_less_rat
% 5.17/5.52 = ( ^ [X3: rat,Y6: rat] : ( positive @ ( minus_minus_rat @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % less_rat_def
% 5.17/5.52 thf(fact_9902_Rat_Opositive_Orep__eq,axiom,
% 5.17/5.52 ( positive
% 5.17/5.52 = ( ^ [X3: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X3 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X3 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat.positive.rep_eq
% 5.17/5.52 thf(fact_9903_and__not__num_Oelims,axiom,
% 5.17/5.52 ! [X: num,Xa: num,Y4: option_num] :
% 5.17/5.52 ( ( ( bit_and_not_num @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4 != none_num ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ? [N2: num] :
% 5.17/5.52 ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ one ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ? [N2: num] :
% 5.17/5.52 ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4 != none_num ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.17/5.52 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ~ ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.elims
% 5.17/5.52 thf(fact_9904_and__not__num_Osimps_I5_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(5)
% 5.17/5.52 thf(fact_9905_and__not__num_Osimps_I9_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(9)
% 5.17/5.52 thf(fact_9906_and__not__num_Osimps_I6_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.simps(6)
% 5.17/5.52 thf(fact_9907_and__not__num_Opelims,axiom,
% 5.17/5.52 ! [X: num,Xa: num,Y4: option_num] :
% 5.17/5.52 ( ( ( bit_and_not_num @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4 = none_num )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ one ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4 = none_num )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.17/5.52 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ~ ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_not_num.pelims
% 5.17/5.52 thf(fact_9908_Rat_Opositive__def,axiom,
% 5.17/5.52 ( positive
% 5.17/5.52 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.17/5.52 @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat.positive_def
% 5.17/5.52 thf(fact_9909_and__num_Oelims,axiom,
% 5.17/5.52 ! [X: num,Xa: num,Y4: option_num] :
% 5.17/5.52 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ one ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ? [N2: num] :
% 5.17/5.52 ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4 != none_num ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ? [N2: num] :
% 5.17/5.52 ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ one ) ) ) )
% 5.17/5.52 => ( ( ? [M4: num] :
% 5.17/5.52 ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4 != none_num ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ( ? [M4: num] :
% 5.17/5.52 ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ one ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ~ ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.17/5.52 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.elims
% 5.17/5.52 thf(fact_9910_xor__num_Oelims,axiom,
% 5.17/5.52 ! [X: num,Xa: num,Y4: option_num] :
% 5.17/5.52 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4 != none_num ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( bit1 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( bit0 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ~ ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.elims
% 5.17/5.52 thf(fact_9911_and__num_Osimps_I1_J,axiom,
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.17/5.52 = ( some_num @ one ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(1)
% 5.17/5.52 thf(fact_9912_xor__num_Osimps_I1_J,axiom,
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.17/5.52 = none_num ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(1)
% 5.17/5.52 thf(fact_9913_xor__num_Osimps_I5_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(5)
% 5.17/5.52 thf(fact_9914_and__num_Osimps_I5_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(5)
% 5.17/5.52 thf(fact_9915_and__num_Osimps_I7_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.17/5.52 = ( some_num @ one ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(7)
% 5.17/5.52 thf(fact_9916_and__num_Osimps_I3_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.17/5.52 = ( some_num @ one ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(3)
% 5.17/5.52 thf(fact_9917_and__num_Osimps_I4_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.17/5.52 = none_num ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(4)
% 5.17/5.52 thf(fact_9918_and__num_Osimps_I2_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.17/5.52 = none_num ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(2)
% 5.17/5.52 thf(fact_9919_and__num_Osimps_I8_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(8)
% 5.17/5.52 thf(fact_9920_and__num_Osimps_I6_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(6)
% 5.17/5.52 thf(fact_9921_xor__num_Osimps_I9_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(9)
% 5.17/5.52 thf(fact_9922_xor__num_Osimps_I2_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.17/5.52 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(2)
% 5.17/5.52 thf(fact_9923_xor__num_Osimps_I3_J,axiom,
% 5.17/5.52 ! [N: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.17/5.52 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(3)
% 5.17/5.52 thf(fact_9924_xor__num_Osimps_I4_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.17/5.52 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(4)
% 5.17/5.52 thf(fact_9925_xor__num_Osimps_I7_J,axiom,
% 5.17/5.52 ! [M: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.17/5.52 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(7)
% 5.17/5.52 thf(fact_9926_and__num_Osimps_I9_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.17/5.52 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.17/5.52 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.simps(9)
% 5.17/5.52 thf(fact_9927_xor__num_Osimps_I8_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.17/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(8)
% 5.17/5.52 thf(fact_9928_xor__num_Osimps_I6_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.17/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.simps(6)
% 5.17/5.52 thf(fact_9929_and__num_Opelims,axiom,
% 5.17/5.52 ! [X: num,Xa: num,Y4: option_num] :
% 5.17/5.52 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ one ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4 = none_num )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ one ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4 = none_num )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ one ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ~ ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.17/5.52 @ ( bit_un7362597486090784418nd_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % and_num.pelims
% 5.17/5.52 thf(fact_9930_xor__num_Opelims,axiom,
% 5.17/5.52 ! [X: num,Xa: num,Y4: option_num] :
% 5.17/5.52 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4 = none_num )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( bit1 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ( ( X = one )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( bit0 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( bit1 @ M4 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit0 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ( ( Xa = one )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.17/5.52 => ( ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit0 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N2 ) ) ) ) ) )
% 5.17/5.52 => ~ ! [M4: num] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( bit1 @ M4 ) )
% 5.17/5.52 => ! [N2: num] :
% 5.17/5.52 ( ( Xa
% 5.17/5.52 = ( bit1 @ N2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N2 ) ) )
% 5.17/5.52 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % xor_num.pelims
% 5.17/5.52 thf(fact_9931_and__num__rel__dict,axiom,
% 5.17/5.52 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.17/5.52
% 5.17/5.52 % and_num_rel_dict
% 5.17/5.52 thf(fact_9932_xor__num__rel__dict,axiom,
% 5.17/5.52 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.17/5.52
% 5.17/5.52 % xor_num_rel_dict
% 5.17/5.52 thf(fact_9933_xor__num__dict,axiom,
% 5.17/5.52 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.17/5.52
% 5.17/5.52 % xor_num_dict
% 5.17/5.52 thf(fact_9934_and__num__dict,axiom,
% 5.17/5.52 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.17/5.52
% 5.17/5.52 % and_num_dict
% 5.17/5.52 thf(fact_9935_Bit__Operations_Otake__bit__num__code,axiom,
% 5.17/5.52 ( bit_take_bit_num
% 5.17/5.52 = ( ^ [N4: nat,M5: num] :
% 5.17/5.52 ( produc478579273971653890on_num
% 5.17/5.52 @ ^ [A3: nat,X3: num] :
% 5.17/5.52 ( case_nat_option_num @ none_num
% 5.17/5.52 @ ^ [O: nat] :
% 5.17/5.52 ( case_num_option_num @ ( some_num @ one )
% 5.17/5.52 @ ^ [P6: num] :
% 5.17/5.52 ( case_o6005452278849405969um_num @ none_num
% 5.17/5.52 @ ^ [Q3: num] : ( some_num @ ( bit0 @ Q3 ) )
% 5.17/5.52 @ ( bit_take_bit_num @ O @ P6 ) )
% 5.17/5.52 @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 5.17/5.52 @ X3 )
% 5.17/5.52 @ A3 )
% 5.17/5.52 @ ( product_Pair_nat_num @ N4 @ M5 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Bit_Operations.take_bit_num_code
% 5.17/5.52 thf(fact_9936_of__rat__dense,axiom,
% 5.17/5.52 ! [X: real,Y4: real] :
% 5.17/5.52 ( ( ord_less_real @ X @ Y4 )
% 5.17/5.52 => ? [Q4: rat] :
% 5.17/5.52 ( ( ord_less_real @ X @ ( field_7254667332652039916t_real @ Q4 ) )
% 5.17/5.52 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q4 ) @ Y4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % of_rat_dense
% 5.17/5.52 thf(fact_9937_plus__rat__def,axiom,
% 5.17/5.52 ( plus_plus_rat
% 5.17/5.52 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.17/5.52 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % plus_rat_def
% 5.17/5.52 thf(fact_9938_inverse__rat__def,axiom,
% 5.17/5.52 ( inverse_inverse_rat
% 5.17/5.52 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.17/5.52 @ ^ [X3: product_prod_int_int] :
% 5.17/5.52 ( if_Pro3027730157355071871nt_int
% 5.17/5.52 @ ( ( product_fst_int_int @ X3 )
% 5.17/5.52 = zero_zero_int )
% 5.17/5.52 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.17/5.52 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % inverse_rat_def
% 5.17/5.52 thf(fact_9939_Fract_Oabs__eq,axiom,
% 5.17/5.52 ( fract
% 5.17/5.52 = ( ^ [Xa4: int,X3: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X3 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Fract.abs_eq
% 5.17/5.52 thf(fact_9940_zero__rat__def,axiom,
% 5.17/5.52 ( zero_zero_rat
% 5.17/5.52 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % zero_rat_def
% 5.17/5.52 thf(fact_9941_times__rat__def,axiom,
% 5.17/5.52 ( times_times_rat
% 5.17/5.52 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.17/5.52 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y6 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % times_rat_def
% 5.17/5.52 thf(fact_9942_plus__rat_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 5.17/5.52 ( ( ratrel @ Xa @ Xa )
% 5.17/5.52 => ( ( ratrel @ X @ X )
% 5.17/5.52 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 5.17/5.52 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % plus_rat.abs_eq
% 5.17/5.52 thf(fact_9943_inverse__rat_Oabs__eq,axiom,
% 5.17/5.52 ! [X: product_prod_int_int] :
% 5.17/5.52 ( ( ratrel @ X @ X )
% 5.17/5.52 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 5.17/5.52 = ( abs_Rat
% 5.17/5.52 @ ( if_Pro3027730157355071871nt_int
% 5.17/5.52 @ ( ( product_fst_int_int @ X )
% 5.17/5.52 = zero_zero_int )
% 5.17/5.52 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.17/5.52 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % inverse_rat.abs_eq
% 5.17/5.52 thf(fact_9944_ratrel__iff,axiom,
% 5.17/5.52 ( ratrel
% 5.17/5.52 = ( ^ [X3: product_prod_int_int,Y6: product_prod_int_int] :
% 5.17/5.52 ( ( ( product_snd_int_int @ X3 )
% 5.17/5.52 != zero_zero_int )
% 5.17/5.52 & ( ( product_snd_int_int @ Y6 )
% 5.17/5.52 != zero_zero_int )
% 5.17/5.52 & ( ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) )
% 5.17/5.52 = ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % ratrel_iff
% 5.17/5.52 thf(fact_9945_zero__rat_Orsp,axiom,
% 5.17/5.52 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 5.17/5.52
% 5.17/5.52 % zero_rat.rsp
% 5.17/5.52 thf(fact_9946_ratrel__def,axiom,
% 5.17/5.52 ( ratrel
% 5.17/5.52 = ( ^ [X3: product_prod_int_int,Y6: product_prod_int_int] :
% 5.17/5.52 ( ( ( product_snd_int_int @ X3 )
% 5.17/5.52 != zero_zero_int )
% 5.17/5.52 & ( ( product_snd_int_int @ Y6 )
% 5.17/5.52 != zero_zero_int )
% 5.17/5.52 & ( ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) )
% 5.17/5.52 = ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % ratrel_def
% 5.17/5.52 thf(fact_9947_times__rat_Oabs__eq,axiom,
% 5.17/5.52 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 5.17/5.52 ( ( ratrel @ Xa @ Xa )
% 5.17/5.52 => ( ( ratrel @ X @ X )
% 5.17/5.52 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 5.17/5.52 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % times_rat.abs_eq
% 5.17/5.52 thf(fact_9948_Rat_Opositive_Oabs__eq,axiom,
% 5.17/5.52 ! [X: product_prod_int_int] :
% 5.17/5.52 ( ( ratrel @ X @ X )
% 5.17/5.52 => ( ( positive @ ( abs_Rat @ X ) )
% 5.17/5.52 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat.positive.abs_eq
% 5.17/5.52 thf(fact_9949_num__of__integer__code,axiom,
% 5.17/5.52 ( code_num_of_integer
% 5.17/5.52 = ( ^ [K3: code_integer] :
% 5.17/5.52 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.17/5.52 @ ( produc7336495610019696514er_num
% 5.17/5.52 @ ^ [L3: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L3 ) @ ( code_num_of_integer @ L3 ) ) @ one ) )
% 5.17/5.52 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % num_of_integer_code
% 5.17/5.52 thf(fact_9950_take__upt,axiom,
% 5.17/5.52 ! [I: nat,M: nat,N: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 5.17/5.52 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 5.17/5.52 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_upt
% 5.17/5.52 thf(fact_9951_min__Suc__Suc,axiom,
% 5.17/5.52 ! [M: nat,N: nat] :
% 5.17/5.52 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.17/5.52 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % min_Suc_Suc
% 5.17/5.52 thf(fact_9952_min__0R,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.17/5.52 = zero_zero_nat ) ).
% 5.17/5.52
% 5.17/5.52 % min_0R
% 5.17/5.52 thf(fact_9953_min__0L,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.17/5.52 = zero_zero_nat ) ).
% 5.17/5.52
% 5.17/5.52 % min_0L
% 5.17/5.52 thf(fact_9954_min__Suc__numeral,axiom,
% 5.17/5.52 ! [N: nat,K: num] :
% 5.17/5.52 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.17/5.52 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % min_Suc_numeral
% 5.17/5.52 thf(fact_9955_min__numeral__Suc,axiom,
% 5.17/5.52 ! [K: num,N: nat] :
% 5.17/5.52 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.17/5.52 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % min_numeral_Suc
% 5.17/5.52 thf(fact_9956_inf__nat__def,axiom,
% 5.17/5.52 inf_inf_nat = ord_min_nat ).
% 5.17/5.52
% 5.17/5.52 % inf_nat_def
% 5.17/5.52 thf(fact_9957_concat__bit__assoc__sym,axiom,
% 5.17/5.52 ! [M: nat,N: nat,K: int,L: int,R2: int] :
% 5.17/5.52 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N @ K @ L ) @ R2 )
% 5.17/5.52 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N ) @ L @ R2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % concat_bit_assoc_sym
% 5.17/5.52 thf(fact_9958_min__diff,axiom,
% 5.17/5.52 ! [M: nat,I: nat,N: nat] :
% 5.17/5.52 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.17/5.52 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.17/5.52
% 5.17/5.52 % min_diff
% 5.17/5.52 thf(fact_9959_nat__mult__min__right,axiom,
% 5.17/5.52 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.52 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q2 ) )
% 5.17/5.52 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_mult_min_right
% 5.17/5.52 thf(fact_9960_nat__mult__min__left,axiom,
% 5.17/5.52 ! [M: nat,N: nat,Q2: nat] :
% 5.17/5.52 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q2 )
% 5.17/5.52 = ( ord_min_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nat_mult_min_left
% 5.17/5.52 thf(fact_9961_take__bit__concat__bit__eq,axiom,
% 5.17/5.52 ! [M: nat,N: nat,K: int,L: int] :
% 5.17/5.52 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N @ K @ L ) )
% 5.17/5.52 = ( bit_concat_bit @ ( ord_min_nat @ M @ N ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N ) @ L ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % take_bit_concat_bit_eq
% 5.17/5.52 thf(fact_9962_min__Suc2,axiom,
% 5.17/5.52 ! [M: nat,N: nat] :
% 5.17/5.52 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.17/5.52 = ( case_nat_nat @ zero_zero_nat
% 5.17/5.52 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ M6 @ N ) )
% 5.17/5.52 @ M ) ) ).
% 5.17/5.52
% 5.17/5.52 % min_Suc2
% 5.17/5.52 thf(fact_9963_min__Suc1,axiom,
% 5.17/5.52 ! [N: nat,M: nat] :
% 5.17/5.52 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.17/5.52 = ( case_nat_nat @ zero_zero_nat
% 5.17/5.52 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ N @ M6 ) )
% 5.17/5.52 @ M ) ) ).
% 5.17/5.52
% 5.17/5.52 % min_Suc1
% 5.17/5.52 thf(fact_9964_min__enat__simps_I2_J,axiom,
% 5.17/5.52 ! [Q2: extended_enat] :
% 5.17/5.52 ( ( ord_mi8085742599997312461d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.17/5.52 = zero_z5237406670263579293d_enat ) ).
% 5.17/5.52
% 5.17/5.52 % min_enat_simps(2)
% 5.17/5.52 thf(fact_9965_min__enat__simps_I3_J,axiom,
% 5.17/5.52 ! [Q2: extended_enat] :
% 5.17/5.52 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.17/5.52 = zero_z5237406670263579293d_enat ) ).
% 5.17/5.52
% 5.17/5.52 % min_enat_simps(3)
% 5.17/5.52 thf(fact_9966_inf__int__def,axiom,
% 5.17/5.52 inf_inf_int = ord_min_int ).
% 5.17/5.52
% 5.17/5.52 % inf_int_def
% 5.17/5.52 thf(fact_9967_Max__divisors__self__nat,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( N != zero_zero_nat )
% 5.17/5.52 => ( ( lattic8265883725875713057ax_nat
% 5.17/5.52 @ ( collect_nat
% 5.17/5.52 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 5.17/5.52 = N ) ) ).
% 5.17/5.52
% 5.17/5.52 % Max_divisors_self_nat
% 5.17/5.52 thf(fact_9968_inf__enat__def,axiom,
% 5.17/5.52 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.17/5.52
% 5.17/5.52 % inf_enat_def
% 5.17/5.52 thf(fact_9969_card__le__Suc__Max,axiom,
% 5.17/5.52 ! [S: set_nat] :
% 5.17/5.52 ( ( finite_finite_nat @ S )
% 5.17/5.52 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % card_le_Suc_Max
% 5.17/5.52 thf(fact_9970_Sup__nat__def,axiom,
% 5.17/5.52 ( complete_Sup_Sup_nat
% 5.17/5.52 = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Sup_nat_def
% 5.17/5.52 thf(fact_9971_divide__nat__def,axiom,
% 5.17/5.52 ( divide_divide_nat
% 5.17/5.52 = ( ^ [M5: nat,N4: nat] :
% 5.17/5.52 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 5.17/5.52 @ ( lattic8265883725875713057ax_nat
% 5.17/5.52 @ ( collect_nat
% 5.17/5.52 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M5 ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % divide_nat_def
% 5.17/5.52 thf(fact_9972_gcd__is__Max__divisors__nat,axiom,
% 5.17/5.52 ! [N: nat,M: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( ( gcd_gcd_nat @ M @ N )
% 5.17/5.52 = ( lattic8265883725875713057ax_nat
% 5.17/5.52 @ ( collect_nat
% 5.17/5.52 @ ^ [D4: nat] :
% 5.17/5.52 ( ( dvd_dvd_nat @ D4 @ M )
% 5.17/5.52 & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % gcd_is_Max_divisors_nat
% 5.17/5.52 thf(fact_9973_Gcd__eq__Max,axiom,
% 5.17/5.52 ! [M10: set_nat] :
% 5.17/5.52 ( ( finite_finite_nat @ M10 )
% 5.17/5.52 => ( ( M10 != bot_bot_set_nat )
% 5.17/5.52 => ( ~ ( member_nat @ zero_zero_nat @ M10 )
% 5.17/5.52 => ( ( gcd_Gcd_nat @ M10 )
% 5.17/5.52 = ( lattic8265883725875713057ax_nat
% 5.17/5.52 @ ( comple7806235888213564991et_nat
% 5.17/5.52 @ ( image_nat_set_nat
% 5.17/5.52 @ ^ [M5: nat] :
% 5.17/5.52 ( collect_nat
% 5.17/5.52 @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M5 ) )
% 5.17/5.52 @ M10 ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Gcd_eq_Max
% 5.17/5.52 thf(fact_9974_Max__divisors__self__int,axiom,
% 5.17/5.52 ! [N: int] :
% 5.17/5.52 ( ( N != zero_zero_int )
% 5.17/5.52 => ( ( lattic8263393255366662781ax_int
% 5.17/5.52 @ ( collect_int
% 5.17/5.52 @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 5.17/5.52 = ( abs_abs_int @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Max_divisors_self_int
% 5.17/5.52 thf(fact_9975_upt__conv__Cons__Cons,axiom,
% 5.17/5.52 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.17/5.52 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.17/5.52 = ( upt @ M @ Q2 ) )
% 5.17/5.52 = ( ( cons_nat @ N @ Ns )
% 5.17/5.52 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_conv_Cons_Cons
% 5.17/5.52 thf(fact_9976_upt__conv__Cons,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( ord_less_nat @ I @ J )
% 5.17/5.52 => ( ( upt @ I @ J )
% 5.17/5.52 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_conv_Cons
% 5.17/5.52 thf(fact_9977_gcd__is__Max__divisors__int,axiom,
% 5.17/5.52 ! [N: int,M: int] :
% 5.17/5.52 ( ( N != zero_zero_int )
% 5.17/5.52 => ( ( gcd_gcd_int @ M @ N )
% 5.17/5.52 = ( lattic8263393255366662781ax_int
% 5.17/5.52 @ ( collect_int
% 5.17/5.52 @ ^ [D4: int] :
% 5.17/5.52 ( ( dvd_dvd_int @ D4 @ M )
% 5.17/5.52 & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % gcd_is_Max_divisors_int
% 5.17/5.52 thf(fact_9978_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.17/5.52 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.17/5.52 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sorted_list_of_set_greaterThanAtMost
% 5.17/5.52 thf(fact_9979_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.17/5.52 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.17/5.52 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sorted_list_of_set_greaterThanLessThan
% 5.17/5.52 thf(fact_9980_upto__aux__rec,axiom,
% 5.17/5.52 ( upto_aux
% 5.17/5.52 = ( ^ [I2: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I2 ) @ Js @ ( upto_aux @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_aux_rec
% 5.17/5.52 thf(fact_9981_list__encode_Osimps_I2_J,axiom,
% 5.17/5.52 ! [X: nat,Xs: list_nat] :
% 5.17/5.52 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 5.17/5.52 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % list_encode.simps(2)
% 5.17/5.52 thf(fact_9982_upt__conv__Nil,axiom,
% 5.17/5.52 ! [J: nat,I: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ J @ I )
% 5.17/5.52 => ( ( upt @ I @ J )
% 5.17/5.52 = nil_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_conv_Nil
% 5.17/5.52 thf(fact_9983_upt__eq__Nil__conv,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( ( upt @ I @ J )
% 5.17/5.52 = nil_nat )
% 5.17/5.52 = ( ( J = zero_zero_nat )
% 5.17/5.52 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_eq_Nil_conv
% 5.17/5.52 thf(fact_9984_sorted__list__of__set__lessThan__Suc,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.17/5.52 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sorted_list_of_set_lessThan_Suc
% 5.17/5.52 thf(fact_9985_sorted__list__of__set__atMost__Suc,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.17/5.52 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % sorted_list_of_set_atMost_Suc
% 5.17/5.52 thf(fact_9986_upt__rec__numeral,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.52 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.52 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.52 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.17/5.52 = nil_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_rec_numeral
% 5.17/5.52 thf(fact_9987_upt__Suc,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.52 => ( ( upt @ I @ ( suc @ J ) )
% 5.17/5.52 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.17/5.52 => ( ( upt @ I @ ( suc @ J ) )
% 5.17/5.52 = nil_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_Suc
% 5.17/5.52 thf(fact_9988_upt__Suc__append,axiom,
% 5.17/5.52 ! [I: nat,J: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.52 => ( ( upt @ I @ ( suc @ J ) )
% 5.17/5.52 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_Suc_append
% 5.17/5.52 thf(fact_9989_list__encode_Ocases,axiom,
% 5.17/5.52 ! [X: list_nat] :
% 5.17/5.52 ( ( X != nil_nat )
% 5.17/5.52 => ~ ! [X4: nat,Xs2: list_nat] :
% 5.17/5.52 ( X
% 5.17/5.52 != ( cons_nat @ X4 @ Xs2 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % list_encode.cases
% 5.17/5.52 thf(fact_9990_list__encode_Osimps_I1_J,axiom,
% 5.17/5.52 ( ( nat_list_encode @ nil_nat )
% 5.17/5.52 = zero_zero_nat ) ).
% 5.17/5.52
% 5.17/5.52 % list_encode.simps(1)
% 5.17/5.52 thf(fact_9991_upt__0,axiom,
% 5.17/5.52 ! [I: nat] :
% 5.17/5.52 ( ( upt @ I @ zero_zero_nat )
% 5.17/5.52 = nil_nat ) ).
% 5.17/5.52
% 5.17/5.52 % upt_0
% 5.17/5.52 thf(fact_9992_inj__list__encode,axiom,
% 5.17/5.52 ! [A2: set_list_nat] : ( inj_on_list_nat_nat @ nat_list_encode @ A2 ) ).
% 5.17/5.52
% 5.17/5.52 % inj_list_encode
% 5.17/5.52 thf(fact_9993_list__encode__eq,axiom,
% 5.17/5.52 ! [X: list_nat,Y4: list_nat] :
% 5.17/5.52 ( ( ( nat_list_encode @ X )
% 5.17/5.52 = ( nat_list_encode @ Y4 ) )
% 5.17/5.52 = ( X = Y4 ) ) ).
% 5.17/5.52
% 5.17/5.52 % list_encode_eq
% 5.17/5.52 thf(fact_9994_bij__list__encode,axiom,
% 5.17/5.52 bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 5.17/5.52
% 5.17/5.52 % bij_list_encode
% 5.17/5.52 thf(fact_9995_surj__list__encode,axiom,
% 5.17/5.52 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 5.17/5.52 = top_top_set_nat ) ).
% 5.17/5.52
% 5.17/5.52 % surj_list_encode
% 5.17/5.52 thf(fact_9996_upt__add__eq__append,axiom,
% 5.17/5.52 ! [I: nat,J: nat,K: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ I @ J )
% 5.17/5.52 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.17/5.52 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_add_eq_append
% 5.17/5.52 thf(fact_9997_list__encode_Oelims,axiom,
% 5.17/5.52 ! [X: list_nat,Y4: nat] :
% 5.17/5.52 ( ( ( nat_list_encode @ X )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( ( X = nil_nat )
% 5.17/5.52 => ( Y4 != zero_zero_nat ) )
% 5.17/5.52 => ~ ! [X4: nat,Xs2: list_nat] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( cons_nat @ X4 @ Xs2 ) )
% 5.17/5.52 => ( Y4
% 5.17/5.52 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % list_encode.elims
% 5.17/5.52 thf(fact_9998_upt__rec,axiom,
% 5.17/5.52 ( upt
% 5.17/5.52 = ( ^ [I2: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I2 @ J3 ) @ ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upt_rec
% 5.17/5.52 thf(fact_9999_list__encode_Opelims,axiom,
% 5.17/5.52 ! [X: list_nat,Y4: nat] :
% 5.17/5.52 ( ( ( nat_list_encode @ X )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.17/5.52 => ( ( ( X = nil_nat )
% 5.17/5.52 => ( ( Y4 = zero_zero_nat )
% 5.17/5.52 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.17/5.52 => ~ ! [X4: nat,Xs2: list_nat] :
% 5.17/5.52 ( ( X
% 5.17/5.52 = ( cons_nat @ X4 @ Xs2 ) )
% 5.17/5.52 => ( ( Y4
% 5.17/5.52 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 5.17/5.52 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs2 ) ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % list_encode.pelims
% 5.17/5.52 thf(fact_10000_upto_Opelims,axiom,
% 5.17/5.52 ! [X: int,Xa: int,Y4: list_int] :
% 5.17/5.52 ( ( ( upto @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 5.17/5.52 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 5.17/5.52 => ( Y4
% 5.17/5.52 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 5.17/5.52 => ( Y4 = nil_int ) ) )
% 5.17/5.52 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto.pelims
% 5.17/5.52 thf(fact_10001_nth__upto,axiom,
% 5.17/5.52 ! [I: int,K: nat,J: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.17/5.52 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.17/5.52 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % nth_upto
% 5.17/5.52 thf(fact_10002_length__upto,axiom,
% 5.17/5.52 ! [I: int,J: int] :
% 5.17/5.52 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.17/5.52 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % length_upto
% 5.17/5.52 thf(fact_10003_upto__rec__numeral_I1_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 = nil_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_rec_numeral(1)
% 5.17/5.52 thf(fact_10004_upto__rec__numeral_I4_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = ( 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 ) ) ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = nil_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_rec_numeral(4)
% 5.17/5.52 thf(fact_10005_upto__rec__numeral_I3_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 = ( 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 ) ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.17/5.52 = nil_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_rec_numeral(3)
% 5.17/5.52 thf(fact_10006_upto__rec__numeral_I2_J,axiom,
% 5.17/5.52 ! [M: num,N: num] :
% 5.17/5.52 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.17/5.52 = nil_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_rec_numeral(2)
% 5.17/5.52 thf(fact_10007_sorted__upto,axiom,
% 5.17/5.52 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % sorted_upto
% 5.17/5.52 thf(fact_10008_upto__split2,axiom,
% 5.17/5.52 ! [I: int,J: int,K: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( ord_less_eq_int @ J @ K )
% 5.17/5.52 => ( ( upto @ I @ K )
% 5.17/5.52 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_split2
% 5.17/5.52 thf(fact_10009_upto__split1,axiom,
% 5.17/5.52 ! [I: int,J: int,K: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( ord_less_eq_int @ J @ K )
% 5.17/5.52 => ( ( upto @ I @ K )
% 5.17/5.52 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_split1
% 5.17/5.52 thf(fact_10010_atLeastLessThan__upto,axiom,
% 5.17/5.52 ( set_or4662586982721622107an_int
% 5.17/5.52 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ I2 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % atLeastLessThan_upto
% 5.17/5.52 thf(fact_10011_upto_Osimps,axiom,
% 5.17/5.52 ( upto
% 5.17/5.52 = ( ^ [I2: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I2 @ J3 ) @ ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto.simps
% 5.17/5.52 thf(fact_10012_upto_Oelims,axiom,
% 5.17/5.52 ! [X: int,Xa: int,Y4: list_int] :
% 5.17/5.52 ( ( ( upto @ X @ Xa )
% 5.17/5.52 = Y4 )
% 5.17/5.52 => ( ( ( ord_less_eq_int @ X @ Xa )
% 5.17/5.52 => ( Y4
% 5.17/5.52 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 5.17/5.52 => ( Y4 = nil_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto.elims
% 5.17/5.52 thf(fact_10013_upto__rec1,axiom,
% 5.17/5.52 ! [I: int,J: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( upto @ I @ J )
% 5.17/5.52 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_rec1
% 5.17/5.52 thf(fact_10014_upto__rec2,axiom,
% 5.17/5.52 ! [I: int,J: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( upto @ I @ J )
% 5.17/5.52 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_rec2
% 5.17/5.52 thf(fact_10015_greaterThanLessThan__upto,axiom,
% 5.17/5.52 ( set_or5832277885323065728an_int
% 5.17/5.52 = ( ^ [I2: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % greaterThanLessThan_upto
% 5.17/5.52 thf(fact_10016_upto__split3,axiom,
% 5.17/5.52 ! [I: int,J: int,K: int] :
% 5.17/5.52 ( ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( ord_less_eq_int @ J @ K )
% 5.17/5.52 => ( ( upto @ I @ K )
% 5.17/5.52 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto_split3
% 5.17/5.52 thf(fact_10017_upto_Opsimps,axiom,
% 5.17/5.52 ! [I: int,J: int] :
% 5.17/5.52 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.17/5.52 => ( ( ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( upto @ I @ J )
% 5.17/5.52 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.17/5.52 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.17/5.52 => ( ( upto @ I @ J )
% 5.17/5.52 = nil_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % upto.psimps
% 5.17/5.52 thf(fact_10018_tl__upt,axiom,
% 5.17/5.52 ! [M: nat,N: nat] :
% 5.17/5.52 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.17/5.52 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % tl_upt
% 5.17/5.52 thf(fact_10019_quotient__of__def,axiom,
% 5.17/5.52 ( quotient_of
% 5.17/5.52 = ( ^ [X3: rat] :
% 5.17/5.52 ( the_Pr4378521158711661632nt_int
% 5.17/5.52 @ ^ [Pair: product_prod_int_int] :
% 5.17/5.52 ( ( X3
% 5.17/5.52 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.17/5.52 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.17/5.52 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % quotient_of_def
% 5.17/5.52 thf(fact_10020_coprime__abs__left__iff,axiom,
% 5.17/5.52 ! [K: int,L: int] :
% 5.17/5.52 ( ( algebr932160517623751201me_int @ ( abs_abs_int @ K ) @ L )
% 5.17/5.52 = ( algebr932160517623751201me_int @ K @ L ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_abs_left_iff
% 5.17/5.52 thf(fact_10021_coprime__abs__right__iff,axiom,
% 5.17/5.52 ! [K: int,L: int] :
% 5.17/5.52 ( ( algebr932160517623751201me_int @ K @ ( abs_abs_int @ L ) )
% 5.17/5.52 = ( algebr932160517623751201me_int @ K @ L ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_abs_right_iff
% 5.17/5.52 thf(fact_10022_normalize__stable,axiom,
% 5.17/5.52 ! [Q2: int,P5: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ Q2 )
% 5.17/5.52 => ( ( algebr932160517623751201me_int @ P5 @ Q2 )
% 5.17/5.52 => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.17/5.52 = ( product_Pair_int_int @ P5 @ Q2 ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % normalize_stable
% 5.17/5.52 thf(fact_10023_mono__Suc,axiom,
% 5.17/5.52 order_mono_nat_nat @ suc ).
% 5.17/5.52
% 5.17/5.52 % mono_Suc
% 5.17/5.52 thf(fact_10024_coprime__crossproduct__int,axiom,
% 5.17/5.52 ! [A: int,D: int,B: int,C: int] :
% 5.17/5.52 ( ( algebr932160517623751201me_int @ A @ D )
% 5.17/5.52 => ( ( algebr932160517623751201me_int @ B @ C )
% 5.17/5.52 => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C ) )
% 5.17/5.52 = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 5.17/5.52 = ( ( ( abs_abs_int @ A )
% 5.17/5.52 = ( abs_abs_int @ B ) )
% 5.17/5.52 & ( ( abs_abs_int @ C )
% 5.17/5.52 = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_crossproduct_int
% 5.17/5.52 thf(fact_10025_mono__times__nat,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % mono_times_nat
% 5.17/5.52 thf(fact_10026_coprime__common__divisor__int,axiom,
% 5.17/5.52 ! [A: int,B: int,X: int] :
% 5.17/5.52 ( ( algebr932160517623751201me_int @ A @ B )
% 5.17/5.52 => ( ( dvd_dvd_int @ X @ A )
% 5.17/5.52 => ( ( dvd_dvd_int @ X @ B )
% 5.17/5.52 => ( ( abs_abs_int @ X )
% 5.17/5.52 = one_one_int ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_common_divisor_int
% 5.17/5.52 thf(fact_10027_Rat__cases,axiom,
% 5.17/5.52 ! [Q2: rat] :
% 5.17/5.52 ~ ! [A4: int,B3: int] :
% 5.17/5.52 ( ( Q2
% 5.17/5.52 = ( fract @ A4 @ B3 ) )
% 5.17/5.52 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.17/5.52 => ~ ( algebr932160517623751201me_int @ A4 @ B3 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat_cases
% 5.17/5.52 thf(fact_10028_Rat__induct,axiom,
% 5.17/5.52 ! [P: rat > $o,Q2: rat] :
% 5.17/5.52 ( ! [A4: int,B3: int] :
% 5.17/5.52 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.17/5.52 => ( ( algebr932160517623751201me_int @ A4 @ B3 )
% 5.17/5.52 => ( P @ ( fract @ A4 @ B3 ) ) ) )
% 5.17/5.52 => ( P @ Q2 ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat_induct
% 5.17/5.52 thf(fact_10029_Rat__cases__nonzero,axiom,
% 5.17/5.52 ! [Q2: rat] :
% 5.17/5.52 ( ! [A4: int,B3: int] :
% 5.17/5.52 ( ( Q2
% 5.17/5.52 = ( fract @ A4 @ B3 ) )
% 5.17/5.52 => ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.17/5.52 => ( ( A4 != zero_zero_int )
% 5.17/5.52 => ~ ( algebr932160517623751201me_int @ A4 @ B3 ) ) ) )
% 5.17/5.52 => ( Q2 = zero_zero_rat ) ) ).
% 5.17/5.52
% 5.17/5.52 % Rat_cases_nonzero
% 5.17/5.52 thf(fact_10030_quotient__of__unique,axiom,
% 5.17/5.52 ! [R2: rat] :
% 5.17/5.52 ? [X4: product_prod_int_int] :
% 5.17/5.52 ( ( R2
% 5.17/5.52 = ( fract @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.17/5.52 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X4 ) )
% 5.17/5.52 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) )
% 5.17/5.52 & ! [Y3: product_prod_int_int] :
% 5.17/5.52 ( ( ( R2
% 5.17/5.52 = ( fract @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 5.17/5.52 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y3 ) )
% 5.17/5.52 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 5.17/5.52 => ( Y3 = X4 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % quotient_of_unique
% 5.17/5.52 thf(fact_10031_mono__ge2__power__minus__self,axiom,
% 5.17/5.52 ! [K: nat] :
% 5.17/5.52 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.17/5.52 => ( order_mono_nat_nat
% 5.17/5.52 @ ^ [M5: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M5 ) @ M5 ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % mono_ge2_power_minus_self
% 5.17/5.52 thf(fact_10032_tendsto__at__topI__sequentially__real,axiom,
% 5.17/5.52 ! [F: real > real,Y4: real] :
% 5.17/5.52 ( ( order_mono_real_real @ F )
% 5.17/5.52 => ( ( filterlim_nat_real
% 5.17/5.52 @ ^ [N4: nat] : ( F @ ( semiri5074537144036343181t_real @ N4 ) )
% 5.17/5.52 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.17/5.52 @ at_top_nat )
% 5.17/5.52 => ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Y4 ) @ at_top_real ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % tendsto_at_topI_sequentially_real
% 5.17/5.52 thf(fact_10033_coprime__int__iff,axiom,
% 5.17/5.52 ! [M: nat,N: nat] :
% 5.17/5.52 ( ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.17/5.52 = ( algebr934650988132801477me_nat @ M @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_int_iff
% 5.17/5.52 thf(fact_10034_coprime__nat__abs__left__iff,axiom,
% 5.17/5.52 ! [K: int,N: nat] :
% 5.17/5.52 ( ( algebr934650988132801477me_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N )
% 5.17/5.52 = ( algebr932160517623751201me_int @ K @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_nat_abs_left_iff
% 5.17/5.52 thf(fact_10035_coprime__nat__abs__right__iff,axiom,
% 5.17/5.52 ! [N: nat,K: int] :
% 5.17/5.52 ( ( algebr934650988132801477me_nat @ N @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.17/5.52 = ( algebr932160517623751201me_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_nat_abs_right_iff
% 5.17/5.52 thf(fact_10036_coprime__Suc__0__right,axiom,
% 5.17/5.52 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_Suc_0_right
% 5.17/5.52 thf(fact_10037_coprime__Suc__0__left,axiom,
% 5.17/5.52 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_Suc_0_left
% 5.17/5.52 thf(fact_10038_coprime__crossproduct__nat,axiom,
% 5.17/5.52 ! [A: nat,D: nat,B: nat,C: nat] :
% 5.17/5.52 ( ( algebr934650988132801477me_nat @ A @ D )
% 5.17/5.52 => ( ( algebr934650988132801477me_nat @ B @ C )
% 5.17/5.52 => ( ( ( times_times_nat @ A @ C )
% 5.17/5.52 = ( times_times_nat @ B @ D ) )
% 5.17/5.52 = ( ( A = B )
% 5.17/5.52 & ( C = D ) ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_crossproduct_nat
% 5.17/5.52 thf(fact_10039_coprime__Suc__left__nat,axiom,
% 5.17/5.52 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_Suc_left_nat
% 5.17/5.52 thf(fact_10040_coprime__Suc__right__nat,axiom,
% 5.17/5.52 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_Suc_right_nat
% 5.17/5.52 thf(fact_10041_coprime__common__divisor__nat,axiom,
% 5.17/5.52 ! [A: nat,B: nat,X: nat] :
% 5.17/5.52 ( ( algebr934650988132801477me_nat @ A @ B )
% 5.17/5.52 => ( ( dvd_dvd_nat @ X @ A )
% 5.17/5.52 => ( ( dvd_dvd_nat @ X @ B )
% 5.17/5.52 => ( X = one_one_nat ) ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_common_divisor_nat
% 5.17/5.52 thf(fact_10042_incseq__bounded,axiom,
% 5.17/5.52 ! [X9: nat > real,B4: real] :
% 5.17/5.52 ( ( order_mono_nat_real @ X9 )
% 5.17/5.52 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X9 @ I3 ) @ B4 )
% 5.17/5.52 => ( bfun_nat_real @ X9 @ at_top_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % incseq_bounded
% 5.17/5.52 thf(fact_10043_coprime__diff__one__right__nat,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_diff_one_right_nat
% 5.17/5.52 thf(fact_10044_coprime__diff__one__left__nat,axiom,
% 5.17/5.52 ! [N: nat] :
% 5.17/5.52 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.17/5.52 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.17/5.52
% 5.17/5.52 % coprime_diff_one_left_nat
% 5.17/5.52 thf(fact_10045_incseq__convergent,axiom,
% 5.17/5.52 ! [X9: nat > real,B4: real] :
% 5.17/5.52 ( ( order_mono_nat_real @ X9 )
% 5.17/5.52 => ( ! [I3: nat] : ( ord_less_eq_real @ ( X9 @ I3 ) @ B4 )
% 5.17/5.52 => ~ ! [L5: real] :
% 5.17/5.52 ( ( filterlim_nat_real @ X9 @ ( topolo2815343760600316023s_real @ L5 ) @ at_top_nat )
% 5.17/5.53 => ~ ! [I4: nat] : ( ord_less_eq_real @ ( X9 @ I4 ) @ L5 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % incseq_convergent
% 5.17/5.53 thf(fact_10046_Rats__abs__nat__div__natE,axiom,
% 5.17/5.53 ! [X: real] :
% 5.17/5.53 ( ( member_real @ X @ field_5140801741446780682s_real )
% 5.17/5.53 => ~ ! [M4: nat,N2: nat] :
% 5.17/5.53 ( ( N2 != zero_zero_nat )
% 5.17/5.53 => ( ( ( abs_abs_real @ X )
% 5.17/5.53 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.17/5.53 => ~ ( algebr934650988132801477me_nat @ M4 @ N2 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Rats_abs_nat_div_natE
% 5.17/5.53 thf(fact_10047_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.17/5.53 ! [F: nat > real,G: nat > nat] :
% 5.17/5.53 ( ! [X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.17/5.53 => ( ( order_mono_nat_real @ F )
% 5.17/5.53 => ( ( order_5726023648592871131at_nat @ G )
% 5.17/5.53 => ( ( bfun_nat_real
% 5.17/5.53 @ ^ [X3: nat] : ( F @ ( G @ X3 ) )
% 5.17/5.53 @ at_top_nat )
% 5.17/5.53 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % nonneg_incseq_Bseq_subseq_iff
% 5.17/5.53 thf(fact_10048_Rat_Opositive_Orsp,axiom,
% 5.17/5.53 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 5.17/5.53 @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Rat.positive.rsp
% 5.17/5.53 thf(fact_10049_vanishes__mult__bounded,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ? [A7: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ A7 )
% 5.17/5.53 & ! [N2: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N2 ) ) @ A7 ) )
% 5.17/5.53 => ( ( vanishes @ Y7 )
% 5.17/5.53 => ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( times_times_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_mult_bounded
% 5.17/5.53 thf(fact_10050_vanishes__const,axiom,
% 5.17/5.53 ! [C: rat] :
% 5.17/5.53 ( ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : C )
% 5.17/5.53 = ( C = zero_zero_rat ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_const
% 5.17/5.53 thf(fact_10051_vanishes__diff,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( vanishes @ X9 )
% 5.17/5.53 => ( ( vanishes @ Y7 )
% 5.17/5.53 => ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_diff
% 5.17/5.53 thf(fact_10052_vanishes__add,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( vanishes @ X9 )
% 5.17/5.53 => ( ( vanishes @ Y7 )
% 5.17/5.53 => ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( plus_plus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_add
% 5.17/5.53 thf(fact_10053_vanishes__minus,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( vanishes @ X9 )
% 5.17/5.53 => ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X9 @ N4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_minus
% 5.17/5.53 thf(fact_10054_vanishes__def,axiom,
% 5.17/5.53 ( vanishes
% 5.17/5.53 = ( ^ [X8: nat > rat] :
% 5.17/5.53 ! [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 => ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N4 ) ) @ R5 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_def
% 5.17/5.53 thf(fact_10055_vanishesI,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ! [R3: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.17/5.53 => ? [K4: nat] :
% 5.17/5.53 ! [N2: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K4 @ N2 )
% 5.17/5.53 => ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N2 ) ) @ R3 ) ) )
% 5.17/5.53 => ( vanishes @ X9 ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishesI
% 5.17/5.53 thf(fact_10056_vanishesD,axiom,
% 5.17/5.53 ! [X9: nat > rat,R2: rat] :
% 5.17/5.53 ( ( vanishes @ X9 )
% 5.17/5.53 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.17/5.53 => ? [K2: nat] :
% 5.17/5.53 ! [N6: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.17/5.53 => ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N6 ) ) @ R2 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishesD
% 5.17/5.53 thf(fact_10057_Fract_Orsp,axiom,
% 5.17/5.53 ( bNF_re157797125943740599nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re6250860962936578807nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ratrel )
% 5.17/5.53 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.17/5.53 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B2 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Fract.rsp
% 5.17/5.53 thf(fact_10058_integer__of__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re6650684261131312217nt_int
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ semiri1314217659103216013at_int
% 5.17/5.53 @ semiri1314217659103216013at_int ) ).
% 5.17/5.53
% 5.17/5.53 % integer_of_natural.rsp
% 5.17/5.53 thf(fact_10059_less__eq__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re3403563459893282935_int_o
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5089333283451836215nt_o_o
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ord_less_eq_int
% 5.17/5.53 @ ord_less_eq_int ) ).
% 5.17/5.53
% 5.17/5.53 % less_eq_integer.rsp
% 5.17/5.53 thf(fact_10060_less__eq__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re578469030762574527_nat_o
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4705727531993890431at_o_o
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ord_less_eq_nat
% 5.17/5.53 @ ord_less_eq_nat ) ).
% 5.17/5.53
% 5.17/5.53 % less_eq_natural.rsp
% 5.17/5.53 thf(fact_10061_times__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re1345281282404953727at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.53 @ times_times_nat
% 5.17/5.53 @ times_times_nat ) ).
% 5.17/5.53
% 5.17/5.53 % times_natural.rsp
% 5.17/5.53 thf(fact_10062_times__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re711492959462206631nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4712519889275205905nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ times_times_int
% 5.17/5.53 @ times_times_int ) ).
% 5.17/5.53
% 5.17/5.53 % times_integer.rsp
% 5.17/5.53 thf(fact_10063_divide__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re711492959462206631nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4712519889275205905nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ divide_divide_int
% 5.17/5.53 @ divide_divide_int ) ).
% 5.17/5.53
% 5.17/5.53 % divide_integer.rsp
% 5.17/5.53 thf(fact_10064_divide__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re1345281282404953727at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.53 @ divide_divide_nat
% 5.17/5.53 @ divide_divide_nat ) ).
% 5.17/5.53
% 5.17/5.53 % divide_natural.rsp
% 5.17/5.53 thf(fact_10065_set__bit__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re1345281282404953727at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.53 @ bit_se7882103937844011126it_nat
% 5.17/5.53 @ bit_se7882103937844011126it_nat ) ).
% 5.17/5.53
% 5.17/5.53 % set_bit_natural.rsp
% 5.17/5.53 thf(fact_10066_set__bit__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re4785983289428654063nt_int
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4712519889275205905nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ bit_se7879613467334960850it_int
% 5.17/5.53 @ bit_se7879613467334960850it_int ) ).
% 5.17/5.53
% 5.17/5.53 % set_bit_integer.rsp
% 5.17/5.53 thf(fact_10067_unset__bit__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re1345281282404953727at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.53 @ bit_se4205575877204974255it_nat
% 5.17/5.53 @ bit_se4205575877204974255it_nat ) ).
% 5.17/5.53
% 5.17/5.53 % unset_bit_natural.rsp
% 5.17/5.53 thf(fact_10068_unset__bit__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re4785983289428654063nt_int
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4712519889275205905nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ bit_se4203085406695923979it_int
% 5.17/5.53 @ bit_se4203085406695923979it_int ) ).
% 5.17/5.53
% 5.17/5.53 % unset_bit_integer.rsp
% 5.17/5.53 thf(fact_10069_flip__bit__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re1345281282404953727at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.53 @ bit_se2161824704523386999it_nat
% 5.17/5.53 @ bit_se2161824704523386999it_nat ) ).
% 5.17/5.53
% 5.17/5.53 % flip_bit_natural.rsp
% 5.17/5.53 thf(fact_10070_flip__bit__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re4785983289428654063nt_int
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4712519889275205905nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ bit_se2159334234014336723it_int
% 5.17/5.53 @ bit_se2159334234014336723it_int ) ).
% 5.17/5.53
% 5.17/5.53 % flip_bit_integer.rsp
% 5.17/5.53 thf(fact_10071_Suc_Orsp,axiom,
% 5.17/5.53 ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ suc
% 5.17/5.53 @ suc ) ).
% 5.17/5.53
% 5.17/5.53 % Suc.rsp
% 5.17/5.53 thf(fact_10072_minus__integer_Orsp,axiom,
% 5.17/5.53 ( bNF_re711492959462206631nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re4712519889275205905nt_int
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ minus_minus_int
% 5.17/5.53 @ minus_minus_int ) ).
% 5.17/5.53
% 5.17/5.53 % minus_integer.rsp
% 5.17/5.53 thf(fact_10073_minus__natural_Orsp,axiom,
% 5.17/5.53 ( bNF_re1345281282404953727at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re5653821019739307937at_nat
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 ) )
% 5.17/5.53 @ minus_minus_nat
% 5.17/5.53 @ minus_minus_nat ) ).
% 5.17/5.53
% 5.17/5.53 % minus_natural.rsp
% 5.17/5.53 thf(fact_10074_sub_Orsp,axiom,
% 5.17/5.53 ( bNF_re8402795839162346335um_int
% 5.17/5.53 @ ^ [Y5: num,Z4: num] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re1822329894187522285nt_int
% 5.17/5.53 @ ^ [Y5: num,Z4: num] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ^ [M5: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) )
% 5.17/5.53 @ ^ [M5: num,N4: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N4 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % sub.rsp
% 5.17/5.53 thf(fact_10075_times__rat_Orsp,axiom,
% 5.17/5.53 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.17/5.53 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y6 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) )
% 5.17/5.53 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y6 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % times_rat.rsp
% 5.17/5.53 thf(fact_10076_plus__rat_Orsp,axiom,
% 5.17/5.53 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.17/5.53 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) )
% 5.17/5.53 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % plus_rat.rsp
% 5.17/5.53 thf(fact_10077_inverse__rat_Orsp,axiom,
% 5.17/5.53 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.17/5.53 @ ^ [X3: product_prod_int_int] :
% 5.17/5.53 ( if_Pro3027730157355071871nt_int
% 5.17/5.53 @ ( ( product_fst_int_int @ X3 )
% 5.17/5.53 = zero_zero_int )
% 5.17/5.53 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.17/5.53 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 5.17/5.53 @ ^ [X3: product_prod_int_int] :
% 5.17/5.53 ( if_Pro3027730157355071871nt_int
% 5.17/5.53 @ ( ( product_fst_int_int @ X3 )
% 5.17/5.53 = zero_zero_int )
% 5.17/5.53 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.17/5.53 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_rat.rsp
% 5.17/5.53 thf(fact_10078_plus__rat_Otransfer,axiom,
% 5.17/5.53 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.17/5.53 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) )
% 5.17/5.53 @ plus_plus_rat ) ).
% 5.17/5.53
% 5.17/5.53 % plus_rat.transfer
% 5.17/5.53 thf(fact_10079_inverse__rat_Otransfer,axiom,
% 5.17/5.53 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.17/5.53 @ ^ [X3: product_prod_int_int] :
% 5.17/5.53 ( if_Pro3027730157355071871nt_int
% 5.17/5.53 @ ( ( product_fst_int_int @ X3 )
% 5.17/5.53 = zero_zero_int )
% 5.17/5.53 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.17/5.53 @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 5.17/5.53 @ inverse_inverse_rat ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_rat.transfer
% 5.17/5.53 thf(fact_10080_zero__rat_Otransfer,axiom,
% 5.17/5.53 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 5.17/5.53
% 5.17/5.53 % zero_rat.transfer
% 5.17/5.53 thf(fact_10081_Fract_Otransfer,axiom,
% 5.17/5.53 ( bNF_re3461391660133120880nt_rat
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ ( bNF_re2214769303045360666nt_rat
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 )
% 5.17/5.53 @ pcr_rat )
% 5.17/5.53 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( B2 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B2 ) )
% 5.17/5.53 @ fract ) ).
% 5.17/5.53
% 5.17/5.53 % Fract.transfer
% 5.17/5.53 thf(fact_10082_times__rat_Otransfer,axiom,
% 5.17/5.53 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.17/5.53 @ ^ [X3: product_prod_int_int,Y6: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y6 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y6 ) ) )
% 5.17/5.53 @ times_times_rat ) ).
% 5.17/5.53
% 5.17/5.53 % times_rat.transfer
% 5.17/5.53 thf(fact_10083_Rat_Opositive_Otransfer,axiom,
% 5.17/5.53 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 5.17/5.53 @ positive ) ).
% 5.17/5.53
% 5.17/5.53 % Rat.positive.transfer
% 5.17/5.53 thf(fact_10084_times__int_Otransfer,axiom,
% 5.17/5.53 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y6 @ U3 ) ) ) ) )
% 5.17/5.53 @ times_times_int ) ).
% 5.17/5.53
% 5.17/5.53 % times_int.transfer
% 5.17/5.53 thf(fact_10085_zero__int_Otransfer,axiom,
% 5.17/5.53 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.17/5.53
% 5.17/5.53 % zero_int.transfer
% 5.17/5.53 thf(fact_10086_int__transfer,axiom,
% 5.17/5.53 ( bNF_re6830278522597306478at_int
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ pcr_int
% 5.17/5.53 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 5.17/5.53 @ semiri1314217659103216013at_int ) ).
% 5.17/5.53
% 5.17/5.53 % int_transfer
% 5.17/5.53 thf(fact_10087_uminus__int_Otransfer,axiom,
% 5.17/5.53 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.17/5.53 @ ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X3 ) )
% 5.17/5.53 @ uminus_uminus_int ) ).
% 5.17/5.53
% 5.17/5.53 % uminus_int.transfer
% 5.17/5.53 thf(fact_10088_nat_Otransfer,axiom,
% 5.17/5.53 ( bNF_re4555766996558763186at_nat @ pcr_int
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.17/5.53 @ nat2 ) ).
% 5.17/5.53
% 5.17/5.53 % nat.transfer
% 5.17/5.53 thf(fact_10089_one__int_Otransfer,axiom,
% 5.17/5.53 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.17/5.53
% 5.17/5.53 % one_int.transfer
% 5.17/5.53 thf(fact_10090_less__int_Otransfer,axiom,
% 5.17/5.53 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.17/5.53 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) )
% 5.17/5.53 @ ord_less_int ) ).
% 5.17/5.53
% 5.17/5.53 % less_int.transfer
% 5.17/5.53 thf(fact_10091_less__eq__int_Otransfer,axiom,
% 5.17/5.53 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.17/5.53 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) )
% 5.17/5.53 @ ord_less_eq_int ) ).
% 5.17/5.53
% 5.17/5.53 % less_eq_int.transfer
% 5.17/5.53 thf(fact_10092_plus__int_Otransfer,axiom,
% 5.17/5.53 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) )
% 5.17/5.53 @ plus_plus_int ) ).
% 5.17/5.53
% 5.17/5.53 % plus_int.transfer
% 5.17/5.53 thf(fact_10093_minus__int_Otransfer,axiom,
% 5.17/5.53 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y6 @ U3 ) ) ) )
% 5.17/5.53 @ minus_minus_int ) ).
% 5.17/5.53
% 5.17/5.53 % minus_int.transfer
% 5.17/5.53 thf(fact_10094_product__atMost__eq__Un,axiom,
% 5.17/5.53 ! [A2: set_nat,M: nat] :
% 5.17/5.53 ( ( produc457027306803732586at_nat @ A2
% 5.17/5.53 @ ^ [Uu3: nat] : ( set_ord_atMost_nat @ M ) )
% 5.17/5.53 = ( sup_su6327502436637775413at_nat
% 5.17/5.53 @ ( produc457027306803732586at_nat @ A2
% 5.17/5.53 @ ^ [I2: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ I2 ) ) )
% 5.17/5.53 @ ( produc457027306803732586at_nat @ A2
% 5.17/5.53 @ ^ [I2: nat] : ( set_or6659071591806873216st_nat @ ( minus_minus_nat @ M @ I2 ) @ M ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % product_atMost_eq_Un
% 5.17/5.53 thf(fact_10095_pairs__le__eq__Sigma,axiom,
% 5.17/5.53 ! [M: nat] :
% 5.17/5.53 ( ( collec3392354462482085612at_nat
% 5.17/5.53 @ ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [I2: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ J3 ) @ M ) ) )
% 5.17/5.53 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.17/5.53 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % pairs_le_eq_Sigma
% 5.17/5.53 thf(fact_10096_inverse__real_Otransfer,axiom,
% 5.17/5.53 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ( if_nat_rat @ ( vanishes @ X8 )
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) )
% 5.17/5.53 @ inverse_inverse_real ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_real.transfer
% 5.17/5.53 thf(fact_10097_zero__real_Otransfer,axiom,
% 5.17/5.53 ( pcr_real
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ zero_zero_real ) ).
% 5.17/5.53
% 5.17/5.53 % zero_real.transfer
% 5.17/5.53 thf(fact_10098_one__real_Otransfer,axiom,
% 5.17/5.53 ( pcr_real
% 5.17/5.53 @ ^ [N4: nat] : one_one_rat
% 5.17/5.53 @ one_one_real ) ).
% 5.17/5.53
% 5.17/5.53 % one_real.transfer
% 5.17/5.53 thf(fact_10099_uminus__real_Otransfer,axiom,
% 5.17/5.53 ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real
% 5.17/5.53 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) )
% 5.17/5.53 @ uminus_uminus_real ) ).
% 5.17/5.53
% 5.17/5.53 % uminus_real.transfer
% 5.17/5.53 thf(fact_10100_plus__real_Otransfer,axiom,
% 5.17/5.53 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) )
% 5.17/5.53 @ plus_plus_real ) ).
% 5.17/5.53
% 5.17/5.53 % plus_real.transfer
% 5.17/5.53 thf(fact_10101_times__real_Otransfer,axiom,
% 5.17/5.53 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) )
% 5.17/5.53 @ times_times_real ) ).
% 5.17/5.53
% 5.17/5.53 % times_real.transfer
% 5.17/5.53 thf(fact_10102_rat__floor__code,axiom,
% 5.17/5.53 ( archim3151403230148437115or_rat
% 5.17/5.53 = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % rat_floor_code
% 5.17/5.53 thf(fact_10103_Divides_Oadjust__div__def,axiom,
% 5.17/5.53 ( adjust_div
% 5.17/5.53 = ( produc8211389475949308722nt_int
% 5.17/5.53 @ ^ [Q3: int,R5: int] : ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Divides.adjust_div_def
% 5.17/5.53 thf(fact_10104_Real_Opositive_Otransfer,axiom,
% 5.17/5.53 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) )
% 5.17/5.53 @ positive2 ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive.transfer
% 5.17/5.53 thf(fact_10105_times__int_Orsp,axiom,
% 5.17/5.53 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y6 @ U3 ) ) ) ) )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U3 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y6 @ U3 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % times_int.rsp
% 5.17/5.53 thf(fact_10106_intrel__iff,axiom,
% 5.17/5.53 ! [X: nat,Y4: nat,U: nat,V: nat] :
% 5.17/5.53 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y4 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.17/5.53 = ( ( plus_plus_nat @ X @ V )
% 5.17/5.53 = ( plus_plus_nat @ U @ Y4 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % intrel_iff
% 5.17/5.53 thf(fact_10107_uminus__int_Orsp,axiom,
% 5.17/5.53 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.17/5.53 @ ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X3 ) )
% 5.17/5.53 @ ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X3 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % uminus_int.rsp
% 5.17/5.53 thf(fact_10108_zero__int_Orsp,axiom,
% 5.17/5.53 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.17/5.53
% 5.17/5.53 % zero_int.rsp
% 5.17/5.53 thf(fact_10109_int_Oabs__eq__iff,axiom,
% 5.17/5.53 ! [X: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.17/5.53 ( ( ( abs_Integ @ X )
% 5.17/5.53 = ( abs_Integ @ Y4 ) )
% 5.17/5.53 = ( intrel @ X @ Y4 ) ) ).
% 5.17/5.53
% 5.17/5.53 % int.abs_eq_iff
% 5.17/5.53 thf(fact_10110_Real_Opositive__mult,axiom,
% 5.17/5.53 ! [X: real,Y4: real] :
% 5.17/5.53 ( ( positive2 @ X )
% 5.17/5.53 => ( ( positive2 @ Y4 )
% 5.17/5.53 => ( positive2 @ ( times_times_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive_mult
% 5.17/5.53 thf(fact_10111_Real_Opositive__zero,axiom,
% 5.17/5.53 ~ ( positive2 @ zero_zero_real ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive_zero
% 5.17/5.53 thf(fact_10112_Real_Opositive__add,axiom,
% 5.17/5.53 ! [X: real,Y4: real] :
% 5.17/5.53 ( ( positive2 @ X )
% 5.17/5.53 => ( ( positive2 @ Y4 )
% 5.17/5.53 => ( positive2 @ ( plus_plus_real @ X @ Y4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive_add
% 5.17/5.53 thf(fact_10113_Real_Opositive__minus,axiom,
% 5.17/5.53 ! [X: real] :
% 5.17/5.53 ( ~ ( positive2 @ X )
% 5.17/5.53 => ( ( X != zero_zero_real )
% 5.17/5.53 => ( positive2 @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive_minus
% 5.17/5.53 thf(fact_10114_nat_Orsp,axiom,
% 5.17/5.53 ( bNF_re8246922863344978751at_nat @ intrel
% 5.17/5.53 @ ^ [Y5: nat,Z4: nat] : ( Y5 = Z4 )
% 5.17/5.53 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.17/5.53 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 5.17/5.53
% 5.17/5.53 % nat.rsp
% 5.17/5.53 thf(fact_10115_less__real__def,axiom,
% 5.17/5.53 ( ord_less_real
% 5.17/5.53 = ( ^ [X3: real,Y6: real] : ( positive2 @ ( minus_minus_real @ Y6 @ X3 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % less_real_def
% 5.17/5.53 thf(fact_10116_one__int_Orsp,axiom,
% 5.17/5.53 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.17/5.53
% 5.17/5.53 % one_int.rsp
% 5.17/5.53 thf(fact_10117_intrel__def,axiom,
% 5.17/5.53 ( intrel
% 5.17/5.53 = ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] :
% 5.17/5.53 ( ( plus_plus_nat @ X3 @ V4 )
% 5.17/5.53 = ( plus_plus_nat @ U3 @ Y6 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % intrel_def
% 5.17/5.53 thf(fact_10118_less__int_Orsp,axiom,
% 5.17/5.53 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.17/5.53 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) )
% 5.17/5.53 @ ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % less_int.rsp
% 5.17/5.53 thf(fact_10119_less__eq__int_Orsp,axiom,
% 5.17/5.53 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.17/5.53 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) )
% 5.17/5.53 @ ( produc8739625826339149834_nat_o
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc6081775807080527818_nat_o
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U3 @ Y6 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % less_eq_int.rsp
% 5.17/5.53 thf(fact_10120_int_Orel__eq__transfer,axiom,
% 5.17/5.53 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.17/5.53 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ intrel
% 5.17/5.53 @ ^ [Y5: int,Z4: int] : ( Y5 = Z4 ) ) ).
% 5.17/5.53
% 5.17/5.53 % int.rel_eq_transfer
% 5.17/5.53 thf(fact_10121_plus__int_Orsp,axiom,
% 5.17/5.53 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U3 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % plus_int.rsp
% 5.17/5.53 thf(fact_10122_minus__int_Orsp,axiom,
% 5.17/5.53 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y6 @ U3 ) ) ) )
% 5.17/5.53 @ ( produc27273713700761075at_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] :
% 5.17/5.53 ( produc2626176000494625587at_nat
% 5.17/5.53 @ ^ [U3: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y6 @ U3 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % minus_int.rsp
% 5.17/5.53 thf(fact_10123_Real_Opositive_Orep__eq,axiom,
% 5.17/5.53 ( positive2
% 5.17/5.53 = ( ^ [X3: real] :
% 5.17/5.53 ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( rep_real @ X3 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive.rep_eq
% 5.17/5.53 thf(fact_10124_Real_Opositive_Orsp,axiom,
% 5.17/5.53 ( bNF_re728719798268516973at_o_o @ realrel
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 )
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) )
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive.rsp
% 5.17/5.53 thf(fact_10125_times__real_Orsp,axiom,
% 5.17/5.53 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % times_real.rsp
% 5.17/5.53 thf(fact_10126_plus__real_Orsp,axiom,
% 5.17/5.53 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % plus_real.rsp
% 5.17/5.53 thf(fact_10127_uminus__real_Orsp,axiom,
% 5.17/5.53 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.17/5.53 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) )
% 5.17/5.53 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % uminus_real.rsp
% 5.17/5.53 thf(fact_10128_zero__real_Orsp,axiom,
% 5.17/5.53 ( realrel
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat ) ).
% 5.17/5.53
% 5.17/5.53 % zero_real.rsp
% 5.17/5.53 thf(fact_10129_one__real_Orsp,axiom,
% 5.17/5.53 ( realrel
% 5.17/5.53 @ ^ [N4: nat] : one_one_rat
% 5.17/5.53 @ ^ [N4: nat] : one_one_rat ) ).
% 5.17/5.53
% 5.17/5.53 % one_real.rsp
% 5.17/5.53 thf(fact_10130_real_Orel__eq__transfer,axiom,
% 5.17/5.53 ( bNF_re4521903465945308077real_o @ pcr_real
% 5.17/5.53 @ ( bNF_re4297313714947099218al_o_o @ pcr_real
% 5.17/5.53 @ ^ [Y5: $o,Z4: $o] : ( Y5 = Z4 ) )
% 5.17/5.53 @ realrel
% 5.17/5.53 @ ^ [Y5: real,Z4: real] : ( Y5 = Z4 ) ) ).
% 5.17/5.53
% 5.17/5.53 % real.rel_eq_transfer
% 5.17/5.53 thf(fact_10131_inverse__real_Orsp,axiom,
% 5.17/5.53 ( bNF_re895249473297799549at_rat @ realrel @ realrel
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ( if_nat_rat @ ( vanishes @ X8 )
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) )
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ( if_nat_rat @ ( vanishes @ X8 )
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_real.rsp
% 5.17/5.53 thf(fact_10132_Real_Opositive__def,axiom,
% 5.17/5.53 ( positive2
% 5.17/5.53 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( X8 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive_def
% 5.17/5.53 thf(fact_10133_inverse__real_Oabs__eq,axiom,
% 5.17/5.53 ! [X: nat > rat] :
% 5.17/5.53 ( ( realrel @ X @ X )
% 5.17/5.53 => ( ( inverse_inverse_real @ ( real2 @ X ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ( if_nat_rat @ ( vanishes @ X )
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_real.abs_eq
% 5.17/5.53 thf(fact_10134_real_Oabs__induct,axiom,
% 5.17/5.53 ! [P: real > $o,X: real] :
% 5.17/5.53 ( ! [Y: nat > rat] :
% 5.17/5.53 ( ( realrel @ Y @ Y )
% 5.17/5.53 => ( P @ ( real2 @ Y ) ) )
% 5.17/5.53 => ( P @ X ) ) ).
% 5.17/5.53
% 5.17/5.53 % real.abs_induct
% 5.17/5.53 thf(fact_10135_of__int__Real,axiom,
% 5.17/5.53 ( ring_1_of_int_real
% 5.17/5.53 = ( ^ [X3: int] :
% 5.17/5.53 ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( ring_1_of_int_rat @ X3 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % of_int_Real
% 5.17/5.53 thf(fact_10136_of__rat__Real,axiom,
% 5.17/5.53 ( field_7254667332652039916t_real
% 5.17/5.53 = ( ^ [X3: rat] :
% 5.17/5.53 ( real2
% 5.17/5.53 @ ^ [N4: nat] : X3 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % of_rat_Real
% 5.17/5.53 thf(fact_10137_one__real__def,axiom,
% 5.17/5.53 ( one_one_real
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : one_one_rat ) ) ).
% 5.17/5.53
% 5.17/5.53 % one_real_def
% 5.17/5.53 thf(fact_10138_zero__real__def,axiom,
% 5.17/5.53 ( zero_zero_real
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat ) ) ).
% 5.17/5.53
% 5.17/5.53 % zero_real_def
% 5.17/5.53 thf(fact_10139_of__nat__Real,axiom,
% 5.17/5.53 ( semiri5074537144036343181t_real
% 5.17/5.53 = ( ^ [X3: nat] :
% 5.17/5.53 ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( semiri681578069525770553at_rat @ X3 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % of_nat_Real
% 5.17/5.53 thf(fact_10140_uminus__real_Oabs__eq,axiom,
% 5.17/5.53 ! [X: nat > rat] :
% 5.17/5.53 ( ( realrel @ X @ X )
% 5.17/5.53 => ( ( uminus_uminus_real @ ( real2 @ X ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % uminus_real.abs_eq
% 5.17/5.53 thf(fact_10141_plus__real_Oabs__eq,axiom,
% 5.17/5.53 ! [Xa: nat > rat,X: nat > rat] :
% 5.17/5.53 ( ( realrel @ Xa @ Xa )
% 5.17/5.53 => ( ( realrel @ X @ X )
% 5.17/5.53 => ( ( plus_plus_real @ ( real2 @ Xa ) @ ( real2 @ X ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( plus_plus_rat @ ( Xa @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % plus_real.abs_eq
% 5.17/5.53 thf(fact_10142_times__real_Oabs__eq,axiom,
% 5.17/5.53 ! [Xa: nat > rat,X: nat > rat] :
% 5.17/5.53 ( ( realrel @ Xa @ Xa )
% 5.17/5.53 => ( ( realrel @ X @ X )
% 5.17/5.53 => ( ( times_times_real @ ( real2 @ Xa ) @ ( real2 @ X ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( times_times_rat @ ( Xa @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % times_real.abs_eq
% 5.17/5.53 thf(fact_10143_Real_Opositive_Oabs__eq,axiom,
% 5.17/5.53 ! [X: nat > rat] :
% 5.17/5.53 ( ( realrel @ X @ X )
% 5.17/5.53 => ( ( positive2 @ ( real2 @ X ) )
% 5.17/5.53 = ( ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( X @ N4 ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real.positive.abs_eq
% 5.17/5.53 thf(fact_10144_inverse__real__def,axiom,
% 5.17/5.53 ( inverse_inverse_real
% 5.17/5.53 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.17/5.53 @ ^ [X8: nat > rat] :
% 5.17/5.53 ( if_nat_rat @ ( vanishes @ X8 )
% 5.17/5.53 @ ^ [N4: nat] : zero_zero_rat
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X8 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_real_def
% 5.17/5.53 thf(fact_10145_le__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( ord_less_eq_real @ ( real2 @ X9 ) @ ( real2 @ Y7 ) )
% 5.17/5.53 = ( ! [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 => ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_eq_rat @ ( X9 @ N4 ) @ ( plus_plus_rat @ ( Y7 @ N4 ) @ R5 ) ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % le_Real
% 5.17/5.53 thf(fact_10146_cr__real__eq,axiom,
% 5.17/5.53 ( pcr_real
% 5.17/5.53 = ( ^ [X3: nat > rat,Y6: real] :
% 5.17/5.53 ( ( cauchy @ X3 )
% 5.17/5.53 & ( ( real2 @ X3 )
% 5.17/5.53 = Y6 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cr_real_eq
% 5.17/5.53 thf(fact_10147_Real__induct,axiom,
% 5.17/5.53 ! [P: real > $o,X: real] :
% 5.17/5.53 ( ! [X15: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X15 )
% 5.17/5.53 => ( P @ ( real2 @ X15 ) ) )
% 5.17/5.53 => ( P @ X ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real_induct
% 5.17/5.53 thf(fact_10148_cauchy__inverse,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ~ ( vanishes @ X9 )
% 5.17/5.53 => ( cauchy
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X9 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_inverse
% 5.17/5.53 thf(fact_10149_cauchy__add,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( cauchy
% 5.17/5.53 @ ^ [N4: nat] : ( plus_plus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_add
% 5.17/5.53 thf(fact_10150_cauchy__minus,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( cauchy
% 5.17/5.53 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X9 @ N4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_minus
% 5.17/5.53 thf(fact_10151_cauchy__const,axiom,
% 5.17/5.53 ! [X: rat] :
% 5.17/5.53 ( cauchy
% 5.17/5.53 @ ^ [N4: nat] : X ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_const
% 5.17/5.53 thf(fact_10152_cauchy__mult,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( cauchy
% 5.17/5.53 @ ^ [N4: nat] : ( times_times_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_mult
% 5.17/5.53 thf(fact_10153_cauchy__diff,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( cauchy
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_diff
% 5.17/5.53 thf(fact_10154_realrel__refl,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( realrel @ X9 @ X9 ) ) ).
% 5.17/5.53
% 5.17/5.53 % realrel_refl
% 5.17/5.53 thf(fact_10155_cauchy__imp__bounded,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ? [B3: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.17/5.53 & ! [N6: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X9 @ N6 ) ) @ B3 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_imp_bounded
% 5.17/5.53 thf(fact_10156_less__RealD,axiom,
% 5.17/5.53 ! [Y7: nat > rat,X: real] :
% 5.17/5.53 ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( ord_less_real @ X @ ( real2 @ Y7 ) )
% 5.17/5.53 => ? [N2: nat] : ( ord_less_real @ X @ ( field_7254667332652039916t_real @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % less_RealD
% 5.17/5.53 thf(fact_10157_Real__leI,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y4: real] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ! [N2: nat] : ( ord_less_eq_real @ ( field_7254667332652039916t_real @ ( X9 @ N2 ) ) @ Y4 )
% 5.17/5.53 => ( ord_less_eq_real @ ( real2 @ X9 ) @ Y4 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Real_leI
% 5.17/5.53 thf(fact_10158_le__RealI,axiom,
% 5.17/5.53 ! [Y7: nat > rat,X: real] :
% 5.17/5.53 ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ! [N2: nat] : ( ord_less_eq_real @ X @ ( field_7254667332652039916t_real @ ( Y7 @ N2 ) ) )
% 5.17/5.53 => ( ord_less_eq_real @ X @ ( real2 @ Y7 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % le_RealI
% 5.17/5.53 thf(fact_10159_minus__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( uminus_uminus_real @ ( real2 @ X9 ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( uminus_uminus_rat @ ( X9 @ N4 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % minus_Real
% 5.17/5.53 thf(fact_10160_add__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( plus_plus_real @ ( real2 @ X9 ) @ ( real2 @ Y7 ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( plus_plus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % add_Real
% 5.17/5.53 thf(fact_10161_mult__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( times_times_real @ ( real2 @ X9 ) @ ( real2 @ Y7 ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( times_times_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % mult_Real
% 5.17/5.53 thf(fact_10162_diff__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( minus_minus_real @ ( real2 @ X9 ) @ ( real2 @ Y7 ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % diff_Real
% 5.17/5.53 thf(fact_10163_realrelI,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) )
% 5.17/5.53 => ( realrel @ X9 @ Y7 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % realrelI
% 5.17/5.53 thf(fact_10164_eq__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ( ( real2 @ X9 )
% 5.17/5.53 = ( real2 @ Y7 ) )
% 5.17/5.53 = ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % eq_Real
% 5.17/5.53 thf(fact_10165_vanishes__diff__inverse,axiom,
% 5.17/5.53 ! [X9: nat > rat,Y7: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ~ ( vanishes @ X9 )
% 5.17/5.53 => ( ( cauchy @ Y7 )
% 5.17/5.53 => ( ~ ( vanishes @ Y7 )
% 5.17/5.53 => ( ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X9 @ N4 ) @ ( Y7 @ N4 ) ) )
% 5.17/5.53 => ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( inverse_inverse_rat @ ( X9 @ N4 ) ) @ ( inverse_inverse_rat @ ( Y7 @ N4 ) ) ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vanishes_diff_inverse
% 5.17/5.53 thf(fact_10166_realrel__def,axiom,
% 5.17/5.53 ( realrel
% 5.17/5.53 = ( ^ [X8: nat > rat,Y8: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X8 )
% 5.17/5.53 & ( cauchy @ Y8 )
% 5.17/5.53 & ( vanishes
% 5.17/5.53 @ ^ [N4: nat] : ( minus_minus_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % realrel_def
% 5.17/5.53 thf(fact_10167_cauchy__not__vanishes__cases,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ~ ( vanishes @ X9 )
% 5.17/5.53 => ? [B3: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.17/5.53 & ? [K2: nat] :
% 5.17/5.53 ( ! [N6: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.17/5.53 => ( ord_less_rat @ B3 @ ( uminus_uminus_rat @ ( X9 @ N6 ) ) ) )
% 5.17/5.53 | ! [N6: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.17/5.53 => ( ord_less_rat @ B3 @ ( X9 @ N6 ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_not_vanishes_cases
% 5.17/5.53 thf(fact_10168_positive__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( positive2 @ ( real2 @ X9 ) )
% 5.17/5.53 = ( ? [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 & ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ R5 @ ( X9 @ N4 ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % positive_Real
% 5.17/5.53 thf(fact_10169_uminus__real__def,axiom,
% 5.17/5.53 ( uminus_uminus_real
% 5.17/5.53 = ( map_fu7146612038024189824t_real @ rep_real @ real2
% 5.17/5.53 @ ^ [X8: nat > rat,N4: nat] : ( uminus_uminus_rat @ ( X8 @ N4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % uminus_real_def
% 5.17/5.53 thf(fact_10170_cauchy__not__vanishes,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ~ ( vanishes @ X9 )
% 5.17/5.53 => ? [B3: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 5.17/5.53 & ? [K2: nat] :
% 5.17/5.53 ! [N6: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.17/5.53 => ( ord_less_rat @ B3 @ ( abs_abs_rat @ ( X9 @ N6 ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_not_vanishes
% 5.17/5.53 thf(fact_10171_cauchyD,axiom,
% 5.17/5.53 ! [X9: nat > rat,R2: rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.17/5.53 => ? [K2: nat] :
% 5.17/5.53 ! [M2: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K2 @ M2 )
% 5.17/5.53 => ! [N6: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K2 @ N6 )
% 5.17/5.53 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X9 @ M2 ) @ ( X9 @ N6 ) ) ) @ R2 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchyD
% 5.17/5.53 thf(fact_10172_cauchyI,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ! [R3: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.17/5.53 => ? [K4: nat] :
% 5.17/5.53 ! [M4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K4 @ M4 )
% 5.17/5.53 => ! [N2: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K4 @ N2 )
% 5.17/5.53 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) ) @ R3 ) ) ) )
% 5.17/5.53 => ( cauchy @ X9 ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchyI
% 5.17/5.53 thf(fact_10173_cauchy__def,axiom,
% 5.17/5.53 ( cauchy
% 5.17/5.53 = ( ^ [X8: nat > rat] :
% 5.17/5.53 ! [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 => ? [K3: nat] :
% 5.17/5.53 ! [M5: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ M5 )
% 5.17/5.53 => ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M5 ) @ ( X8 @ N4 ) ) ) @ R5 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cauchy_def
% 5.17/5.53 thf(fact_10174_inverse__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( ( vanishes @ X9 )
% 5.17/5.53 => ( ( inverse_inverse_real @ ( real2 @ X9 ) )
% 5.17/5.53 = zero_zero_real ) )
% 5.17/5.53 & ( ~ ( vanishes @ X9 )
% 5.17/5.53 => ( ( inverse_inverse_real @ ( real2 @ X9 ) )
% 5.17/5.53 = ( real2
% 5.17/5.53 @ ^ [N4: nat] : ( inverse_inverse_rat @ ( X9 @ N4 ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % inverse_Real
% 5.17/5.53 thf(fact_10175_not__positive__Real,axiom,
% 5.17/5.53 ! [X9: nat > rat] :
% 5.17/5.53 ( ( cauchy @ X9 )
% 5.17/5.53 => ( ( ~ ( positive2 @ ( real2 @ X9 ) ) )
% 5.17/5.53 = ( ! [R5: rat] :
% 5.17/5.53 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.17/5.53 => ? [K3: nat] :
% 5.17/5.53 ! [N4: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ K3 @ N4 )
% 5.17/5.53 => ( ord_less_eq_rat @ ( X9 @ N4 ) @ R5 ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % not_positive_Real
% 5.17/5.53 thf(fact_10176_times__real__def,axiom,
% 5.17/5.53 ( times_times_real
% 5.17/5.53 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % times_real_def
% 5.17/5.53 thf(fact_10177_plus__real__def,axiom,
% 5.17/5.53 ( plus_plus_real
% 5.17/5.53 = ( map_fu1532550112467129777l_real @ rep_real @ ( map_fu7146612038024189824t_real @ rep_real @ real2 )
% 5.17/5.53 @ ^ [X8: nat > rat,Y8: nat > rat,N4: nat] : ( plus_plus_rat @ ( X8 @ N4 ) @ ( Y8 @ N4 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % plus_real_def
% 5.17/5.53 thf(fact_10178_cr__real__def,axiom,
% 5.17/5.53 ( cr_real
% 5.17/5.53 = ( ^ [X3: nat > rat,Y6: real] :
% 5.17/5.53 ( ( realrel @ X3 @ X3 )
% 5.17/5.53 & ( ( real2 @ X3 )
% 5.17/5.53 = Y6 ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % cr_real_def
% 5.17/5.53 thf(fact_10179_int_Obi__total,axiom,
% 5.17/5.53 bi_tot896582865486249351at_int @ pcr_int ).
% 5.17/5.53
% 5.17/5.53 % int.bi_total
% 5.17/5.53 thf(fact_10180_real_Opcr__cr__eq,axiom,
% 5.17/5.53 pcr_real = cr_real ).
% 5.17/5.53
% 5.17/5.53 % real.pcr_cr_eq
% 5.17/5.53 thf(fact_10181_rcis__inverse,axiom,
% 5.17/5.53 ! [R2: real,A: real] :
% 5.17/5.53 ( ( invers8013647133539491842omplex @ ( rcis @ R2 @ A ) )
% 5.17/5.53 = ( rcis @ ( divide_divide_real @ one_one_real @ R2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % rcis_inverse
% 5.17/5.53 thf(fact_10182_rcis__zero__arg,axiom,
% 5.17/5.53 ! [R2: real] :
% 5.17/5.53 ( ( rcis @ R2 @ zero_zero_real )
% 5.17/5.53 = ( real_V4546457046886955230omplex @ R2 ) ) ).
% 5.17/5.53
% 5.17/5.53 % rcis_zero_arg
% 5.17/5.53 thf(fact_10183_rcis__eq__zero__iff,axiom,
% 5.17/5.53 ! [R2: real,A: real] :
% 5.17/5.53 ( ( ( rcis @ R2 @ A )
% 5.17/5.53 = zero_zero_complex )
% 5.17/5.53 = ( R2 = zero_zero_real ) ) ).
% 5.17/5.53
% 5.17/5.53 % rcis_eq_zero_iff
% 5.17/5.53 thf(fact_10184_rcis__zero__mod,axiom,
% 5.17/5.53 ! [A: real] :
% 5.17/5.53 ( ( rcis @ zero_zero_real @ A )
% 5.17/5.53 = zero_zero_complex ) ).
% 5.17/5.53
% 5.17/5.53 % rcis_zero_mod
% 5.17/5.53 thf(fact_10185_Re__rcis,axiom,
% 5.17/5.53 ! [R2: real,A: real] :
% 5.17/5.53 ( ( re @ ( rcis @ R2 @ A ) )
% 5.17/5.53 = ( times_times_real @ R2 @ ( cos_real @ A ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Re_rcis
% 5.17/5.53 thf(fact_10186_Im__rcis,axiom,
% 5.17/5.53 ! [R2: real,A: real] :
% 5.17/5.53 ( ( im @ ( rcis @ R2 @ A ) )
% 5.17/5.53 = ( times_times_real @ R2 @ ( sin_real @ A ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Im_rcis
% 5.17/5.53 thf(fact_10187_rcis__mult,axiom,
% 5.17/5.53 ! [R1: real,A: real,R22: real,B: real] :
% 5.17/5.53 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.17/5.53 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % rcis_mult
% 5.17/5.53 thf(fact_10188_rcis__divide,axiom,
% 5.17/5.53 ! [R1: real,A: real,R22: real,B: real] :
% 5.17/5.53 ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.17/5.53 = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % rcis_divide
% 5.17/5.53 thf(fact_10189_DeMoivre2,axiom,
% 5.17/5.53 ! [R2: real,A: real,N: nat] :
% 5.17/5.53 ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 5.17/5.53 = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % DeMoivre2
% 5.17/5.53 thf(fact_10190_pred__nat__trancl__eq__le,axiom,
% 5.17/5.53 ! [M: nat,N: nat] :
% 5.17/5.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.17/5.53 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.17/5.53
% 5.17/5.53 % pred_nat_trancl_eq_le
% 5.17/5.53 thf(fact_10191_le__enumerate,axiom,
% 5.17/5.53 ! [S: set_nat,N: nat] :
% 5.17/5.53 ( ~ ( finite_finite_nat @ S )
% 5.17/5.53 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % le_enumerate
% 5.17/5.53 thf(fact_10192_finite__le__enumerate,axiom,
% 5.17/5.53 ! [S: set_nat,N: nat] :
% 5.17/5.53 ( ( finite_finite_nat @ S )
% 5.17/5.53 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S ) )
% 5.17/5.53 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S @ N ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % finite_le_enumerate
% 5.17/5.53 thf(fact_10193_Least__eq__0,axiom,
% 5.17/5.53 ! [P: nat > $o] :
% 5.17/5.53 ( ( P @ zero_zero_nat )
% 5.17/5.53 => ( ( ord_Least_nat @ P )
% 5.17/5.53 = zero_zero_nat ) ) ).
% 5.17/5.53
% 5.17/5.53 % Least_eq_0
% 5.17/5.53 thf(fact_10194_Least__Suc2,axiom,
% 5.17/5.53 ! [P: nat > $o,N: nat,Q: nat > $o,M: nat] :
% 5.17/5.53 ( ( P @ N )
% 5.17/5.53 => ( ( Q @ M )
% 5.17/5.53 => ( ~ ( P @ zero_zero_nat )
% 5.17/5.53 => ( ! [K2: nat] :
% 5.17/5.53 ( ( P @ ( suc @ K2 ) )
% 5.17/5.53 = ( Q @ K2 ) )
% 5.17/5.53 => ( ( ord_Least_nat @ P )
% 5.17/5.53 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Least_Suc2
% 5.17/5.53 thf(fact_10195_Least__Suc,axiom,
% 5.17/5.53 ! [P: nat > $o,N: nat] :
% 5.17/5.53 ( ( P @ N )
% 5.17/5.53 => ( ~ ( P @ zero_zero_nat )
% 5.17/5.53 => ( ( ord_Least_nat @ P )
% 5.17/5.53 = ( suc
% 5.17/5.53 @ ( ord_Least_nat
% 5.17/5.53 @ ^ [M5: nat] : ( P @ ( suc @ M5 ) ) ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Least_Suc
% 5.17/5.53 thf(fact_10196_Sup__real__def,axiom,
% 5.17/5.53 ( comple1385675409528146559p_real
% 5.17/5.53 = ( ^ [X8: set_real] :
% 5.17/5.53 ( ord_Least_real
% 5.17/5.53 @ ^ [Z5: real] :
% 5.17/5.53 ! [X3: real] :
% 5.17/5.53 ( ( member_real @ X3 @ X8 )
% 5.17/5.53 => ( ord_less_eq_real @ X3 @ Z5 ) ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Sup_real_def
% 5.17/5.53 thf(fact_10197_last__upt,axiom,
% 5.17/5.53 ! [I: nat,J: nat] :
% 5.17/5.53 ( ( ord_less_nat @ I @ J )
% 5.17/5.53 => ( ( last_nat @ ( upt @ I @ J ) )
% 5.17/5.53 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % last_upt
% 5.17/5.53 thf(fact_10198_vimage__Suc__insert__0,axiom,
% 5.17/5.53 ! [A2: set_nat] :
% 5.17/5.53 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A2 ) )
% 5.17/5.53 = ( vimage_nat_nat @ suc @ A2 ) ) ).
% 5.17/5.53
% 5.17/5.53 % vimage_Suc_insert_0
% 5.17/5.53 thf(fact_10199_vimage__Suc__insert__Suc,axiom,
% 5.17/5.53 ! [N: nat,A2: set_nat] :
% 5.17/5.53 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A2 ) )
% 5.17/5.53 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A2 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % vimage_Suc_insert_Suc
% 5.17/5.53 thf(fact_10200_finite__vimage__Suc__iff,axiom,
% 5.17/5.53 ! [F4: set_nat] :
% 5.17/5.53 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F4 ) )
% 5.17/5.53 = ( finite_finite_nat @ F4 ) ) ).
% 5.17/5.53
% 5.17/5.53 % finite_vimage_Suc_iff
% 5.17/5.53 thf(fact_10201_set__decode__div__2,axiom,
% 5.17/5.53 ! [X: nat] :
% 5.17/5.53 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.17/5.53 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % set_decode_div_2
% 5.17/5.53 thf(fact_10202_set__encode__vimage__Suc,axiom,
% 5.17/5.53 ! [A2: set_nat] :
% 5.17/5.53 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A2 ) )
% 5.17/5.53 = ( divide_divide_nat @ ( nat_set_encode @ A2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % set_encode_vimage_Suc
% 5.17/5.53 thf(fact_10203_Bseq__monoseq__convergent_H__dec,axiom,
% 5.17/5.53 ! [F: nat > real,M10: nat] :
% 5.17/5.53 ( ( bfun_nat_real
% 5.17/5.53 @ ^ [N4: nat] : ( F @ ( plus_plus_nat @ N4 @ M10 ) )
% 5.17/5.53 @ at_top_nat )
% 5.17/5.53 => ( ! [M4: nat,N2: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ M10 @ M4 )
% 5.17/5.53 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.17/5.53 => ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ M4 ) ) ) )
% 5.17/5.53 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Bseq_monoseq_convergent'_dec
% 5.17/5.53 thf(fact_10204_Bseq__mono__convergent,axiom,
% 5.17/5.53 ! [X9: nat > real] :
% 5.17/5.53 ( ( bfun_nat_real @ X9 @ at_top_nat )
% 5.17/5.53 => ( ! [M4: nat,N2: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.17/5.53 => ( ord_less_eq_real @ ( X9 @ M4 ) @ ( X9 @ N2 ) ) )
% 5.17/5.53 => ( topolo7531315842566124627t_real @ X9 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Bseq_mono_convergent
% 5.17/5.53 thf(fact_10205_convergent__realpow,axiom,
% 5.17/5.53 ! [X: real] :
% 5.17/5.53 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.17/5.53 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.17/5.53 => ( topolo7531315842566124627t_real @ ( power_power_real @ X ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % convergent_realpow
% 5.17/5.53 thf(fact_10206_Bseq__monoseq__convergent_H__inc,axiom,
% 5.17/5.53 ! [F: nat > real,M10: nat] :
% 5.17/5.53 ( ( bfun_nat_real
% 5.17/5.53 @ ^ [N4: nat] : ( F @ ( plus_plus_nat @ N4 @ M10 ) )
% 5.17/5.53 @ at_top_nat )
% 5.17/5.53 => ( ! [M4: nat,N2: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ M10 @ M4 )
% 5.17/5.53 => ( ( ord_less_eq_nat @ M4 @ N2 )
% 5.17/5.53 => ( ord_less_eq_real @ ( F @ M4 ) @ ( F @ N2 ) ) ) )
% 5.17/5.53 => ( topolo7531315842566124627t_real @ F ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % Bseq_monoseq_convergent'_inc
% 5.17/5.53 thf(fact_10207_pair__lessI2,axiom,
% 5.17/5.53 ! [A: nat,B: nat,S2: nat,T: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.53 => ( ( ord_less_nat @ S2 @ T )
% 5.17/5.53 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % pair_lessI2
% 5.17/5.53 thf(fact_10208_pair__leqI2,axiom,
% 5.17/5.53 ! [A: nat,B: nat,S2: nat,T: nat] :
% 5.17/5.53 ( ( ord_less_eq_nat @ A @ B )
% 5.17/5.53 => ( ( ord_less_eq_nat @ S2 @ T )
% 5.17/5.53 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % pair_leqI2
% 5.17/5.53 thf(fact_10209_filtermap__at__right__shift,axiom,
% 5.17/5.53 ! [D: real,A: real] :
% 5.17/5.53 ( ( filtermap_real_real
% 5.17/5.53 @ ^ [X3: real] : ( minus_minus_real @ X3 @ D )
% 5.17/5.53 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.17/5.53 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % filtermap_at_right_shift
% 5.17/5.53 thf(fact_10210_at__right__to__0,axiom,
% 5.17/5.53 ! [A: real] :
% 5.17/5.53 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.17/5.53 = ( filtermap_real_real
% 5.17/5.53 @ ^ [X3: real] : ( plus_plus_real @ X3 @ A )
% 5.17/5.53 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % at_right_to_0
% 5.17/5.53 thf(fact_10211_at__right__to__top,axiom,
% 5.17/5.53 ( ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) )
% 5.17/5.53 = ( filtermap_real_real @ inverse_inverse_real @ at_top_real ) ) ).
% 5.17/5.53
% 5.17/5.53 % at_right_to_top
% 5.17/5.53 thf(fact_10212_at__top__to__right,axiom,
% 5.17/5.53 ( at_top_real
% 5.17/5.53 = ( filtermap_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.17/5.53
% 5.17/5.53 % at_top_to_right
% 5.17/5.53 thf(fact_10213_filtermap__ln__at__right,axiom,
% 5.17/5.53 ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.17/5.53 = at_bot_real ) ).
% 5.17/5.53
% 5.17/5.53 % filtermap_ln_at_right
% 5.17/5.53 thf(fact_10214_gcd__nat_Oordering__top__axioms,axiom,
% 5.17/5.53 ( ordering_top_nat @ dvd_dvd_nat
% 5.17/5.53 @ ^ [M5: nat,N4: nat] :
% 5.17/5.53 ( ( dvd_dvd_nat @ M5 @ N4 )
% 5.17/5.53 & ( M5 != N4 ) )
% 5.17/5.53 @ zero_zero_nat ) ).
% 5.17/5.53
% 5.17/5.53 % gcd_nat.ordering_top_axioms
% 5.17/5.53 thf(fact_10215_bot__nat__0_Oordering__top__axioms,axiom,
% 5.17/5.53 ( ordering_top_nat
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] : ( ord_less_eq_nat @ Y6 @ X3 )
% 5.17/5.53 @ ^ [X3: nat,Y6: nat] : ( ord_less_nat @ Y6 @ X3 )
% 5.17/5.53 @ zero_zero_nat ) ).
% 5.17/5.53
% 5.17/5.53 % bot_nat_0.ordering_top_axioms
% 5.17/5.53
% 5.17/5.53 % Helper facts (40)
% 5.17/5.53 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.17/5.53 ! [X: int,Y4: int] :
% 5.17/5.53 ( ( if_int @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.17/5.53 ! [X: int,Y4: int] :
% 5.17/5.53 ( ( if_int @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.17/5.53 ! [X: nat,Y4: nat] :
% 5.17/5.53 ( ( if_nat @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.17/5.53 ! [X: nat,Y4: nat] :
% 5.17/5.53 ( ( if_nat @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.17/5.53 ! [X: num,Y4: num] :
% 5.17/5.53 ( ( if_num @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.17/5.53 ! [X: num,Y4: num] :
% 5.17/5.53 ( ( if_num @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.17/5.53 ! [X: rat,Y4: rat] :
% 5.17/5.53 ( ( if_rat @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.17/5.53 ! [X: rat,Y4: rat] :
% 5.17/5.53 ( ( if_rat @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.17/5.53 ! [X: real,Y4: real] :
% 5.17/5.53 ( ( if_real @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.17/5.53 ! [X: real,Y4: real] :
% 5.17/5.53 ( ( if_real @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.17/5.53 ! [P: real > $o] :
% 5.17/5.53 ( ( P @ ( fChoice_real @ P ) )
% 5.17/5.53 = ( ? [X8: real] : ( P @ X8 ) ) ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.17/5.53 ! [X: complex,Y4: complex] :
% 5.17/5.53 ( ( if_complex @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.17/5.53 ! [X: complex,Y4: complex] :
% 5.17/5.53 ( ( if_complex @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.17/5.53 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.53 ( ( if_Code_integer @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.17/5.53 ! [X: code_integer,Y4: code_integer] :
% 5.17/5.53 ( ( if_Code_integer @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.17/5.53 ! [X: list_int,Y4: list_int] :
% 5.17/5.53 ( ( if_list_int @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.17/5.53 ! [X: list_int,Y4: list_int] :
% 5.17/5.53 ( ( if_list_int @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.17/5.53 ! [X: list_nat,Y4: list_nat] :
% 5.17/5.53 ( ( if_list_nat @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.17/5.53 ! [X: list_nat,Y4: list_nat] :
% 5.17/5.53 ( ( if_list_nat @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.17/5.53 ! [X: int > int,Y4: int > int] :
% 5.17/5.53 ( ( if_int_int @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.17/5.53 ! [X: int > int,Y4: int > int] :
% 5.17/5.53 ( ( if_int_int @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.17/5.53 ! [X: nat > rat,Y4: nat > rat] :
% 5.17/5.53 ( ( if_nat_rat @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001_062_It__Nat__Onat_Mt__Rat__Orat_J_T,axiom,
% 5.17/5.53 ! [X: nat > rat,Y4: nat > rat] :
% 5.17/5.53 ( ( if_nat_rat @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.17/5.53 ! [X: option_num,Y4: option_num] :
% 5.17/5.53 ( ( if_option_num @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.17/5.53 ! [X: option_num,Y4: option_num] :
% 5.17/5.53 ( ( if_option_num @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.17/5.53 ! [X: product_prod_int_int,Y4: product_prod_int_int] :
% 5.17/5.53 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.17/5.53 ! [X: product_prod_int_int,Y4: product_prod_int_int] :
% 5.17/5.53 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.17/5.53 ! [X: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.17/5.53 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.17/5.53 ! [X: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.17/5.53 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.17/5.53 ! [X: nat > int > int,Y4: nat > int > int] :
% 5.17/5.53 ( ( if_nat_int_int @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 5.17/5.53 ! [X: nat > int > int,Y4: nat > int > int] :
% 5.17/5.53 ( ( if_nat_int_int @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.17/5.53 ! [X: nat > nat > nat,Y4: nat > nat > nat] :
% 5.17/5.53 ( ( if_nat_nat_nat @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.17/5.53 ! [X: nat > nat > nat,Y4: nat > nat > nat] :
% 5.17/5.53 ( ( if_nat_nat_nat @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.17/5.53 ! [X: produc6271795597528267376eger_o,Y4: produc6271795597528267376eger_o] :
% 5.17/5.53 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.17/5.53 ! [X: produc6271795597528267376eger_o,Y4: produc6271795597528267376eger_o] :
% 5.17/5.53 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.17/5.53 ! [X: produc8923325533196201883nteger,Y4: produc8923325533196201883nteger] :
% 5.17/5.53 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y4 )
% 5.17/5.53 = Y4 ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.17/5.53 ! [X: produc8923325533196201883nteger,Y4: produc8923325533196201883nteger] :
% 5.17/5.53 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y4 )
% 5.17/5.53 = X ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_3_1_If_001_062_It__Nat__Onat_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_T,axiom,
% 5.17/5.53 ! [P: $o] :
% 5.17/5.53 ( ( P = $true )
% 5.17/5.53 | ( P = $false ) ) ).
% 5.17/5.53
% 5.17/5.53 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_T,axiom,
% 6.39/6.69 ! [X: nat > code_integer > code_integer,Y4: nat > code_integer > code_integer] :
% 6.39/6.69 ( ( if_nat5617392847756311170nteger @ $false @ X @ Y4 )
% 6.39/6.69 = Y4 ) ).
% 6.39/6.69
% 6.39/6.69 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_T,axiom,
% 6.39/6.69 ! [X: nat > code_integer > code_integer,Y4: nat > code_integer > code_integer] :
% 6.39/6.69 ( ( if_nat5617392847756311170nteger @ $true @ X @ Y4 )
% 6.39/6.69 = X ) ).
% 6.39/6.69
% 6.39/6.69 % Conjectures (1)
% 6.39/6.69 thf(conj_0,conjecture,
% 6.39/6.69 ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ ( suc @ ( suc @ ( divide_divide_nat @ va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 6.39/6.69
% 6.39/6.69 %------------------------------------------------------------------------------
% 6.39/6.69 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.yNXPF6ppCv/cvc5---1.0.5_20774.p...
% 6.39/6.69 (declare-sort $$unsorted 0)
% 6.39/6.69 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 6.39/6.69 (declare-sort tptp.produc859450856879609959at_nat 0)
% 6.39/6.69 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.39/6.69 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.39/6.69 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.39/6.69 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.39/6.69 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.39/6.69 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.39/6.69 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.39/6.69 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.39/6.69 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.39/6.69 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.39/6.69 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.39/6.69 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.39/6.69 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.39/6.69 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.39/6.69 (declare-sort tptp.product_prod_num_num 0)
% 6.39/6.69 (declare-sort tptp.product_prod_nat_num 0)
% 6.39/6.69 (declare-sort tptp.product_prod_nat_nat 0)
% 6.39/6.69 (declare-sort tptp.product_prod_int_int 0)
% 6.39/6.69 (declare-sort tptp.list_list_real 0)
% 6.39/6.69 (declare-sort tptp.set_list_real 0)
% 6.39/6.69 (declare-sort tptp.list_list_nat 0)
% 6.39/6.69 (declare-sort tptp.list_list_int 0)
% 6.39/6.69 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.39/6.69 (declare-sort tptp.set_list_nat 0)
% 6.39/6.69 (declare-sort tptp.set_list_int 0)
% 6.39/6.69 (declare-sort tptp.list_set_nat 0)
% 6.39/6.69 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.39/6.69 (declare-sort tptp.set_set_nat 0)
% 6.39/6.69 (declare-sort tptp.set_Code_integer 0)
% 6.39/6.69 (declare-sort tptp.list_list_o 0)
% 6.39/6.69 (declare-sort tptp.list_complex 0)
% 6.39/6.69 (declare-sort tptp.set_list_o 0)
% 6.39/6.69 (declare-sort tptp.set_complex 0)
% 6.39/6.69 (declare-sort tptp.filter_real 0)
% 6.39/6.69 (declare-sort tptp.option_num 0)
% 6.39/6.69 (declare-sort tptp.filter_nat 0)
% 6.39/6.69 (declare-sort tptp.filter_int 0)
% 6.39/6.69 (declare-sort tptp.set_char 0)
% 6.39/6.69 (declare-sort tptp.list_real 0)
% 6.39/6.69 (declare-sort tptp.set_real 0)
% 6.39/6.69 (declare-sort tptp.list_nat 0)
% 6.39/6.69 (declare-sort tptp.list_int 0)
% 6.39/6.69 (declare-sort tptp.vEBT_VEBT 0)
% 6.39/6.69 (declare-sort tptp.set_rat 0)
% 6.39/6.69 (declare-sort tptp.set_nat 0)
% 6.39/6.69 (declare-sort tptp.set_int 0)
% 6.39/6.69 (declare-sort tptp.code_integer 0)
% 6.39/6.69 (declare-sort tptp.extended_enat 0)
% 6.39/6.69 (declare-sort tptp.list_o 0)
% 6.39/6.69 (declare-sort tptp.complex 0)
% 6.39/6.69 (declare-sort tptp.set_o 0)
% 6.39/6.69 (declare-sort tptp.char 0)
% 6.39/6.69 (declare-sort tptp.real 0)
% 6.39/6.69 (declare-sort tptp.rat 0)
% 6.39/6.69 (declare-sort tptp.num 0)
% 6.39/6.69 (declare-sort tptp.nat 0)
% 6.39/6.69 (declare-sort tptp.int 0)
% 6.39/6.69 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.39/6.69 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.39/6.69 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.39/6.69 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.39/6.69 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 6.39/6.69 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.39/6.69 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.39/6.69 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.39/6.69 (declare-fun tptp.bNF_re1962705104956426057at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re895249473297799549at_rat ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re728719798268516973at_o_o ((-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> (-> tptp.nat tptp.rat) Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re4695409256820837752l_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real tptp.real)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re4521903465945308077real_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool) Bool) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) Bool) (-> tptp.real tptp.real Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re3023117138289059399t_real ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) (-> tptp.real tptp.real)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re4297313714947099218al_o_o ((-> (-> tptp.nat tptp.rat) tptp.real Bool) (-> Bool Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) (-> tptp.real Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re3403563459893282935_int_o ((-> tptp.int tptp.int Bool) (-> (-> tptp.int Bool) (-> tptp.int Bool) Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re711492959462206631nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.int) (-> tptp.int tptp.int) Bool) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re157797125943740599nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.product_prod_int_int)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re3461391660133120880nt_rat ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.rat)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re4712519889275205905nt_int ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int) (-> tptp.int tptp.int)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re6250860962936578807nt_int ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re2214769303045360666nt_rat ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re4785983289428654063nt_int ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.int tptp.int) (-> tptp.int tptp.int) Bool) (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re578469030762574527_nat_o ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat Bool) (-> tptp.nat Bool) Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re1345281282404953727at_nat ((-> tptp.nat tptp.nat Bool) (-> (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) Bool) (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.39/6.69 (declare-fun tptp.bNF_re6650684261131312217nt_int ((-> tptp.nat tptp.nat Bool) (-> tptp.int tptp.int Bool) (-> tptp.nat tptp.int) (-> tptp.nat tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re5653821019739307937at_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re6830278522597306478at_int ((-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.product_prod_nat_nat) (-> tptp.nat tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re8402795839162346335um_int ((-> tptp.num tptp.num Bool) (-> (-> tptp.num tptp.int) (-> tptp.num tptp.int) Bool) (-> tptp.num tptp.num tptp.int) (-> tptp.num tptp.num tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re1822329894187522285nt_int ((-> tptp.num tptp.num Bool) (-> tptp.int tptp.int Bool) (-> tptp.num tptp.int) (-> tptp.num tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re5228765855967844073nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int) Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re8699439704749558557nt_o_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re7145576690424134365nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.product_prod_int_int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re7627151682743391978at_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat) Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat tptp.rat)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re1494630372529172596at_o_o ((-> tptp.product_prod_int_int tptp.rat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_int_int Bool) (-> tptp.rat Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re8279943556446156061nt_rat ((-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int) (-> tptp.rat tptp.rat)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re717283939379294677_int_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re7408651293131936558nt_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re6644619430987730960nt_o_o ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.int Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re4555766996558763186at_nat ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.int tptp.nat)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re7400052026677387805at_int ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.int tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re4202695980764964119_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re3099431351363272937at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool) (-> 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 tptp.product_prod_nat_nat)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re3666534408544137501at_o_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> Bool Bool Bool) (-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re8246922863344978751at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat)) Bool)
% 6.39/6.70 (declare-fun tptp.bNF_re2241393799969408733at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) Bool)
% 6.39/6.70 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.39/6.70 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.39/6.70 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se3928097537394005634nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.boolea2445317508997433345nteger ((-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer tptp.code_integer) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.code_integer (-> tptp.code_integer tptp.code_integer tptp.code_integer)) Bool)
% 6.39/6.70 (declare-fun tptp.boolea8527374999097803216ff_int ((-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int tptp.int (-> tptp.int tptp.int tptp.int)) Bool)
% 6.39/6.70 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.39/6.70 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.39/6.70 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.39/6.70 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.39/6.70 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.39/6.70 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.39/6.70 (declare-fun tptp.code_T6385005292777649522of_nat (tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.39/6.70 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.39/6.70 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.39/6.70 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.39/6.70 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.39/6.70 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.39/6.70 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.39/6.70 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.39/6.70 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.39/6.70 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.39/6.70 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.39/6.70 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.39/6.70 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.39/6.70 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.39/6.70 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.39/6.70 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.39/6.70 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.39/6.70 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.39/6.70 (declare-fun tptp.at_top_int () tptp.filter_int)
% 6.39/6.70 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.39/6.70 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.39/6.70 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.39/6.70 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.39/6.70 (declare-fun tptp.filterlim_nat_int ((-> tptp.nat tptp.int) tptp.filter_int tptp.filter_nat) Bool)
% 6.39/6.70 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.39/6.70 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.39/6.70 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.39/6.70 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.39/6.70 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.39/6.70 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.39/6.70 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.39/6.70 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.39/6.70 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.39/6.70 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.39/6.70 (declare-fun tptp.bij_betw_int_nat ((-> tptp.int tptp.nat) tptp.set_int tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.bij_be8532844293280997160at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.39/6.70 (declare-fun tptp.bij_betw_nat_int ((-> tptp.nat tptp.int) tptp.set_nat tptp.set_int) Bool)
% 6.39/6.70 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.bij_be5333170631980326235at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat tptp.set_nat) Bool)
% 6.39/6.70 (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)
% 6.39/6.70 (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)
% 6.39/6.70 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.39/6.70 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.39/6.70 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.id_o (Bool) Bool)
% 6.39/6.70 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.inj_on_int_nat ((-> tptp.int tptp.nat) tptp.set_int) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on2178005380612969504at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.39/6.70 (declare-fun tptp.inj_on_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.map_fu434086159418415080_int_o ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat Bool) tptp.int Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.int tptp.int) Bool)
% 6.39/6.70 (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)
% 6.39/6.70 (declare-fun tptp.map_fu4826362097070443709at_o_o ((-> tptp.int tptp.product_prod_nat_nat) (-> Bool Bool) (-> tptp.product_prod_nat_nat Bool) tptp.int) Bool)
% 6.39/6.70 (declare-fun tptp.map_fu2345160673673942751at_nat ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat) tptp.int) tptp.nat)
% 6.39/6.70 (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)
% 6.39/6.70 (declare-fun tptp.map_fu4333342158222067775at_rat ((-> tptp.rat tptp.product_prod_int_int) (-> (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.map_fu898904425404107465nt_o_o ((-> tptp.rat tptp.product_prod_int_int) (-> Bool Bool) (-> tptp.product_prod_int_int Bool) tptp.rat) Bool)
% 6.39/6.70 (declare-fun tptp.map_fu5673905371560938248nt_rat ((-> tptp.rat tptp.product_prod_int_int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.map_fu1532550112467129777l_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) (-> (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.map_fu7146612038024189824t_real ((-> tptp.real tptp.nat tptp.rat) (-> (-> tptp.nat tptp.rat) tptp.real) (-> (-> tptp.nat tptp.rat) tptp.nat tptp.rat) tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.map_fu1856342031159181835at_o_o ((-> tptp.real tptp.nat tptp.rat) (-> Bool Bool) (-> (-> tptp.nat tptp.rat) Bool) tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.fun_is_measure_int ((-> tptp.int tptp.nat)) Bool)
% 6.39/6.70 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 6.39/6.70 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 6.39/6.70 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.39/6.70 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.39/6.70 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.39/6.70 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.39/6.70 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.one_one_int () tptp.int)
% 6.39/6.70 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.39/6.70 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.39/6.70 (declare-fun tptp.one_one_real () tptp.real)
% 6.39/6.70 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.39/6.70 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.39/6.70 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.39/6.70 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.39/6.70 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.39/6.70 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.39/6.70 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.groups3417619833198082522nteger ((-> Bool tptp.code_integer) tptp.code_integer tptp.list_o) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.39/6.70 (declare-fun tptp.groups9119017779487936845_o_nat ((-> Bool tptp.nat) tptp.nat tptp.list_o) tptp.nat)
% 6.39/6.70 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.39/6.70 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.39/6.70 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.if_nat5617392847756311170nteger (Bool (-> tptp.nat tptp.code_integer tptp.code_integer) (-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (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)
% 6.39/6.70 (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)
% 6.39/6.70 (declare-fun tptp.if_nat_rat (Bool (-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.39/6.70 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.39/6.70 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.39/6.70 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.39/6.70 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.39/6.70 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.39/6.70 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.39/6.70 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 6.39/6.70 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 6.39/6.70 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 6.39/6.70 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.39/6.70 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.39/6.70 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.39/6.70 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.39/6.70 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.39/6.70 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.39/6.70 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 6.39/6.70 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.concat_o (tptp.list_list_o) tptp.list_o)
% 6.39/6.70 (declare-fun tptp.concat_int (tptp.list_list_int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.concat_nat (tptp.list_list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.concat_real (tptp.list_list_real) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.foldr_nat_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.list_nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.foldr_real_real ((-> tptp.real tptp.real tptp.real) tptp.list_real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.nil_int () tptp.list_int)
% 6.39/6.70 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.map_complex_real ((-> tptp.complex tptp.real) tptp.list_complex) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.map_int_real ((-> tptp.int tptp.real) tptp.list_int) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.map_nat_real ((-> tptp.nat tptp.real) tptp.list_nat) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.map_real_real ((-> tptp.real tptp.real) tptp.list_real) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.map_set_nat_real ((-> tptp.set_nat tptp.real) tptp.list_set_nat) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.map_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.map_VEBT_VEBT_real ((-> tptp.vEBT_VEBT tptp.real) tptp.list_VEBT_VEBT) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.39/6.70 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_list_o2 (tptp.list_list_o) tptp.set_list_o)
% 6.39/6.70 (declare-fun tptp.set_list_int2 (tptp.list_list_int) tptp.set_list_int)
% 6.39/6.70 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 6.39/6.70 (declare-fun tptp.set_list_real2 (tptp.list_list_real) tptp.set_list_real)
% 6.39/6.70 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.39/6.70 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.39/6.70 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.39/6.70 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.39/6.70 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.39/6.70 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.39/6.70 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.39/6.70 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.39/6.70 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.39/6.70 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.39/6.70 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.39/6.70 (declare-fun tptp.subseqs_o (tptp.list_o) tptp.list_list_o)
% 6.39/6.70 (declare-fun tptp.subseqs_int (tptp.list_int) tptp.list_list_int)
% 6.39/6.70 (declare-fun tptp.subseqs_nat (tptp.list_nat) tptp.list_list_nat)
% 6.39/6.70 (declare-fun tptp.subseqs_real (tptp.list_real) tptp.list_list_real)
% 6.39/6.70 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.39/6.70 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.39/6.70 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.39/6.70 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.semiri3842193898606819883omplex () tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.semiring_1_Nats_int () tptp.set_int)
% 6.39/6.70 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.39/6.70 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s2710708370519433104list_o (tptp.list_list_o) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s533118279054570080st_int (tptp.list_list_int) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s6660260683639930848t_real (tptp.list_list_real) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.39/6.70 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.39/6.70 (declare-fun tptp.nat_int_decode (tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.nat_int_encode (tptp.int) tptp.nat)
% 6.39/6.70 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.39/6.70 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.39/6.70 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.39/6.70 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.one () tptp.num)
% 6.39/6.70 (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)
% 6.39/6.70 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.39/6.70 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.39/6.70 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.39/6.70 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.39/6.70 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.39/6.70 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.39/6.70 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.39/6.70 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.39/6.70 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.none_num () tptp.option_num)
% 6.39/6.70 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.39/6.70 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.39/6.70 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.39/6.70 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.39/6.70 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.39/6.70 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.39/6.70 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 6.39/6.70 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.39/6.70 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.39/6.70 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.39/6.70 (declare-fun tptp.ord_Least_real ((-> tptp.real Bool)) tptp.real)
% 6.39/6.70 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.39/6.70 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.39/6.70 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.39/6.70 (declare-fun tptp.ord_min_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.39/6.70 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.39/6.70 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.order_mono_real_real ((-> tptp.real tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.39/6.70 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.39/6.70 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 6.39/6.70 (declare-fun tptp.top_top_set_list_nat () tptp.set_list_nat)
% 6.39/6.70 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.top_to4669805908274784177at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.39/6.70 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.39/6.70 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.39/6.70 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.39/6.70 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.39/6.70 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.39/6.70 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.39/6.70 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.39/6.70 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 6.39/6.70 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.39/6.70 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.39/6.70 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.39/6.70 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.39/6.70 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.39/6.70 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.39/6.70 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.39/6.70 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.39/6.70 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.39/6.70 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.39/6.70 (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)
% 6.39/6.70 (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)
% 6.39/6.70 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.39/6.70 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.39/6.70 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.39/6.70 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.39/6.70 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.39/6.70 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.39/6.70 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.39/6.70 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.39/6.70 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.39/6.70 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.39/6.70 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.39/6.70 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.39/6.70 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.39/6.70 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.39/6.70 (declare-fun tptp.real2 ((-> tptp.nat tptp.rat)) tptp.real)
% 6.39/6.70 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 6.39/6.70 (declare-fun tptp.cr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.pcr_real ((-> tptp.nat tptp.rat) tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.positive2 (tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.realrel ((-> tptp.nat tptp.rat) (-> tptp.nat tptp.rat)) Bool)
% 6.39/6.70 (declare-fun tptp.rep_real (tptp.real tptp.nat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 6.39/6.70 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.real_V470468836141973256s_real () tptp.set_real)
% 6.39/6.70 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.39/6.70 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.39/6.70 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.39/6.70 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.39/6.70 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.39/6.70 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.39/6.70 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.39/6.70 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.39/6.70 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.39/6.70 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.39/6.70 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.39/6.70 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.39/6.70 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.39/6.70 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.39/6.70 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.39/6.70 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.39/6.70 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.39/6.70 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.39/6.70 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.39/6.70 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.39/6.70 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.39/6.70 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.39/6.70 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.39/6.70 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.39/6.70 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.39/6.70 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.image_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.39/6.70 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.39/6.70 (declare-fun tptp.image_2486076414777270412at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.39/6.70 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.39/6.70 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 6.39/6.70 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.39/6.70 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.39/6.70 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.39/6.70 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.39/6.70 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 6.39/6.70 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.39/6.70 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.39/6.70 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.39/6.70 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.39/6.70 (declare-fun tptp.topolo7531315842566124627t_real ((-> tptp.nat tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.39/6.70 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 6.39/6.70 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.39/6.70 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.39/6.70 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.39/6.70 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.pi () tptp.real)
% 6.39/6.70 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.39/6.70 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.39/6.70 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.39/6.70 (declare-fun tptp.bi_tot896582865486249351at_int ((-> tptp.product_prod_nat_nat tptp.int Bool)) Bool)
% 6.39/6.70 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.39/6.70 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.39/6.70 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.39/6.70 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.39/6.70 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.39/6.70 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_V8646137997579335489_i_l_d (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_V8346862874174094_d_u_p (tptp.nat) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_V1247956027447740395_p_rel (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_V5144397997797733112_d_rel (tptp.nat tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_cnt (tptp.vEBT_VEBT) tptp.real)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_cnt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_space (tptp.vEBT_VEBT) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_space2 (tptp.vEBT_VEBT) tptp.nat)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_space_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.39/6.70 (declare-fun tptp.vEBT_VEBT_space_rel2 (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.39/6.70 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.39/6.70 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.39/6.70 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.39/6.70 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.39/6.70 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.39/6.70 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.39/6.70 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.39/6.70 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.39/6.70 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.39/6.70 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.39/6.70 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 6.39/6.70 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.39/6.70 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.39/6.70 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.39/6.70 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.39/6.70 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.39/6.70 (declare-fun tptp.member_list_real (tptp.list_real tptp.set_list_real) Bool)
% 6.39/6.70 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.39/6.70 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.39/6.70 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.39/6.70 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.39/6.70 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.39/6.70 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.39/6.70 (declare-fun tptp.va () tptp.nat)
% 6.39/6.70 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.va)))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.suc (@ tptp.suc tptp.va)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_2) _let_3)) (=> (= X (@ (@ tptp.divide_divide_nat _let_3) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_V8646137997579335489_i_l_d _let_1))) (@ (@ tptp.times_times_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one)))))))))))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc tptp.va)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) _let_2)) (=> (= X (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_V8646137997579335489_i_l_d X))) (@ (@ tptp.times_times_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup X))) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))))))))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc tptp.va)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) _let_2) (=> (= X (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_V8646137997579335489_i_l_d X))) (@ (@ tptp.times_times_real (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup X))) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))))))))))
% 6.39/6.70 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_space2 T))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_cnt T)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.39/6.70 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.39/6.70 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.39/6.70 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.39/6.70 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.39/6.70 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.39/6.70 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.39/6.70 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.39/6.70 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.39/6.70 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A2))) A2)))
% 6.39/6.70 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A2))) A2)))
% 6.39/6.70 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X3 tptp.list_nat)) (@ (@ tptp.member_list_nat X3) A2))) A2)))
% 6.39/6.70 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A2))) A2)))
% 6.39/6.70 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2))) A2)))
% 6.39/6.70 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A2))) A2)))
% 6.39/6.70 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) X4)))))))))
% 6.39/6.70 (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)))
% 6.39/6.70 (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)))
% 6.39/6.70 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y) (=> (@ (@ R Y) Z2) (@ _let_1 Z2))))) (=> (forall ((N2 tptp.nat)) (@ (@ R N2) (@ tptp.suc N2))) (@ (@ R M) N)))))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (forall ((N tptp.nat) (M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M3) (exists ((M4 tptp.nat)) (= M3 (@ tptp.suc M4))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y4)) (= X Y4))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F N))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F N))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F N))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F N))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F N))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F N))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N3))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N3))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N3))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N3))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N3))))))
% 6.39/6.70 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N3) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ F N3))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y4) (@ (@ tptp.times_times_complex Y4) _let_1)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ (@ tptp.times_times_real Y4) _let_1)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ (@ tptp.times_times_rat Y4) _let_1)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y4) (@ (@ tptp.times_times_nat Y4) _let_1)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ (@ tptp.times_times_int Y4) _let_1)))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.39/6.70 (assert (forall ((Y4 tptp.num)) (=> (not (= Y4 tptp.one)) (=> (forall ((X22 tptp.num)) (not (= Y4 (@ tptp.bit0 X22)))) (not (forall ((X32 tptp.num)) (not (= Y4 (@ tptp.bit1 X32)))))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 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 X) _let_1) (@ (@ tptp.divide_divide_nat Y4) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y4)) (= X Y4)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.39/6.70 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.39/6.70 (assert (forall ((S tptp.set_real)) (=> (exists ((X5 tptp.real)) (@ (@ tptp.member_real X5) S)) (=> (exists ((Z3 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z3)))) (exists ((Y tptp.real)) (and (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S) (@ (@ tptp.ord_less_eq_real X5) Y))) (forall ((Z3 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S) (@ (@ tptp.ord_less_eq_real X4) Z3))) (@ (@ tptp.ord_less_eq_real Y) Z3)))))))))
% 6.39/6.70 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 6.39/6.70 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))))
% 6.39/6.70 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K2))))))))
% 6.39/6.70 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 6.39/6.70 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K3))))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K3))))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K3 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K3))))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K3))))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K3))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.39/6.70 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3))))))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.code_integer) (Z4 tptp.code_integer)) (= Y5 Z4)) (lambda ((A3 tptp.code_integer) (B2 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 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A3 tptp.nat) (B2 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 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A3 tptp.int) (B2 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 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R2)) (@ (@ tptp.divide_divide_real A) R2)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y4) Z)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y4) Z)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y4) Z)))))
% 6.39/6.70 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y4) W)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y4) W)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y4) W)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.39/6.70 (assert (forall ((X33 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X33) (@ tptp.bit1 Y32)) (= X33 Y32))))
% 6.39/6.70 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X2) (@ tptp.bit0 Y2)) (= X2 Y2))))
% 6.39/6.70 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.39/6.70 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 6.39/6.70 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 6.39/6.70 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.39/6.70 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.39/6.70 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.39/6.70 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) X)))
% 6.39/6.70 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.vEBT_VEBT_cnt T))))
% 6.39/6.70 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.39/6.70 (assert (forall ((X33 tptp.num)) (not (= tptp.one (@ tptp.bit1 X33)))))
% 6.39/6.70 (assert (forall ((X2 tptp.num) (X33 tptp.num)) (not (= (@ tptp.bit0 X2) (@ tptp.bit1 X33)))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.39/6.70 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.39/6.70 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.39/6.70 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.39/6.70 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.39/6.70 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.39/6.70 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.39/6.70 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 6.39/6.70 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.70 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.39/6.70 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.70 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.39/6.70 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (@ tptp.suc N2))))))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va))))))))))
% 6.39/6.70 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 6.39/6.70 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.39/6.70 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y4 (@ tptp.suc Nat3))))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 6.39/6.70 (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 ((Y tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y))) (=> (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ P X4) Y) (@ (@ P (@ tptp.suc X4)) (@ tptp.suc Y)))) (@ (@ P M) N))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y4)))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y4) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y4)))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y4) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y4)))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y4) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W) Y4)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.39/6.70 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.39/6.70 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real B) A) (not (= B A))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (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)))))))))))))))))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (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)))))))))))))))))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (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)))))))))))))))))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (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)))))))))))))))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_real Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_real Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y4))) (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)))))))))))))))))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((X3 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y6) (@ (@ tptp.ord_less_eq_set_int Y6) X3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((X3 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y6) (@ (@ tptp.ord_less_eq_rat Y6) X3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((X3 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y6) (@ (@ tptp.ord_less_eq_num Y6) X3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((X3 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y6) (@ (@ tptp.ord_less_eq_int Y6) X3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((X3 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y6) (@ (@ tptp.ord_less_eq_real Y6) X3)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_eq_real A) C)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.39/6.70 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y4) (=> (@ (@ tptp.ord_less_eq_set_int Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (= X Y4)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 6.39/6.70 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_set_int Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.39/6.70 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.39/6.70 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.39/6.70 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (@ (@ tptp.ord_less_eq_set_int A3) B2)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (@ (@ tptp.ord_less_eq_rat A3) B2)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (@ (@ tptp.ord_less_eq_num A3) B2)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (@ (@ tptp.ord_less_eq_int A3) B2)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (@ (@ tptp.ord_less_eq_real A3) B2)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A B)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A B)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int B2) A3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ tptp.ord_less_eq_rat B2) A3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ tptp.ord_less_eq_num B2) A3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ tptp.ord_less_eq_int B2) A3)))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (@ (@ tptp.ord_less_eq_real B2) A3)))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.39/6.70 (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_eq_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.39/6.70 (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_eq_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 6.39/6.70 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_set_int X) Y4))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_num X) Y4))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_nat X) Y4))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_int X) Y4))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (= X Y4) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (or (= A B) (not (@ (@ tptp.ord_less_eq_real A) B)) (not (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y4) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y4) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real Y4) X))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.39/6.70 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.39/6.70 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.39/6.70 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.39/6.70 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))
% 6.39/6.70 (assert (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y4) X) (= (@ (@ tptp.ord_less_eq_set_int X) Y4) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (= (@ (@ tptp.ord_less_eq_rat X) Y4) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (= (@ (@ tptp.ord_less_eq_num X) Y4) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (= (@ (@ tptp.ord_less_eq_nat X) Y4) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (= (@ (@ tptp.ord_less_eq_int X) Y4) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (= (@ (@ tptp.ord_less_eq_real X) Y4) (= X Y4)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A3) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.39/6.70 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.39/6.70 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.39/6.70 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.39/6.70 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.39/6.70 (assert (= (@ tptp.vEBT_V8646137997579335489_i_l_d tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.39/6.70 (assert (= (@ tptp.vEBT_V8646137997579335489_i_l_d (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.39/6.70 (assert (forall ((X2 tptp.num)) (not (= tptp.one (@ tptp.bit0 X2)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (= (@ tptp.vEBT_V8346862874174094_d_u_p (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.complex) (Z4 tptp.complex)) (= Y5 Z4)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.rat) (Z4 tptp.rat)) (= Y5 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y4) Z)))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y4) Z)))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y4) Z)))))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y4) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y4) Z)))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.39/6.70 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.70 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 6.39/6.70 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.39/6.70 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.39/6.70 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.39/6.70 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.39/6.70 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.39/6.70 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 6.39/6.70 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 6.39/6.70 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 6.39/6.70 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y4) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y4)) Z)))))
% 6.39/6.70 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y4) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y4)) Z)))))
% 6.39/6.70 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y4) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y4)) Z)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y4))) (@ (@ tptp.times_times_complex Y4) Z)))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z)))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z)))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (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))))))))
% 6.39/6.70 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 6.39/6.70 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 6.39/6.70 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.39/6.70 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))))
% 6.39/6.70 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.39/6.70 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_set_nat) (B4 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (@ (@ tptp.ord_less_eq_set_int A2) B4))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (= A2 B4) (@ (@ tptp.ord_less_eq_set_int B4) A2))))
% 6.39/6.70 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A5 tptp.set_complex) (B5 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_set_real (lambda ((A5 tptp.set_real) (B5 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A5 tptp.set_set_nat) (B5 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A5) (@ _let_1 B5)))))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 6.39/6.70 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (=> (@ P X4) (@ Q X4))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C2) (@ _let_1 C2))))))
% 6.39/6.70 (assert (= (lambda ((Y5 tptp.set_int) (Z4 tptp.set_int)) (= Y5 Z4)) (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (@ (@ tptp.ord_less_eq_set_int B5) A5)))))
% 6.39/6.70 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X3 tptp.real)) (=> (@ P X3) (@ Q X3))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z))) tptp.zero_zero_rat))))))
% 6.39/6.70 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z))) tptp.zero_zero_real))))))
% 6.39/6.70 (assert (= (@ tptp.vEBT_V8346862874174094_d_u_p tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X4 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 D2))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X4)) (@ _let_2 Y)) D2) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X4)) (@ _let_1 Y)) D2)))))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_V8346862874174094_d_u_p N)) (@ tptp.vEBT_V8646137997579335489_i_l_d N))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.39/6.70 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.39/6.70 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.39/6.70 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.39/6.70 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.39/6.70 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.39/6.70 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.39/6.70 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.39/6.70 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.39/6.70 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.39/6.70 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.39/6.70 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (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))))
% 6.39/6.70 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.39/6.70 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.39/6.70 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.39/6.70 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (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)))))))))
% 6.39/6.70 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.39/6.70 (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)))))
% 6.39/6.70 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.39/6.70 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.39/6.70 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.39/6.70 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.39/6.70 (assert (forall ((X5 tptp.real)) (exists ((Y tptp.real)) (@ (@ tptp.ord_less_real Y) X5))))
% 6.39/6.70 (assert (forall ((X5 tptp.rat)) (exists ((Y tptp.rat)) (@ (@ tptp.ord_less_rat Y) X5))))
% 6.39/6.70 (assert (forall ((X5 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X5) X_1))))
% 6.39/6.70 (assert (forall ((X5 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X5) X_1))))
% 6.39/6.70 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.39/6.70 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.39/6.70 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.39/6.70 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.39/6.70 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.39/6.70 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 6.39/6.70 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.39/6.70 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.39/6.70 (assert (forall ((X tptp.real)) (exists ((Y tptp.real)) (@ (@ tptp.ord_less_real Y) X))))
% 6.39/6.70 (assert (forall ((X tptp.rat)) (exists ((Y tptp.rat)) (@ (@ tptp.ord_less_rat Y) X))))
% 6.39/6.70 (assert (forall ((X tptp.int)) (exists ((Y tptp.int)) (@ (@ tptp.ord_less_int Y) X))))
% 6.39/6.70 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.39/6.70 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.39/6.70 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.39/6.70 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z2) (@ (@ tptp.ord_less_real Z2) Y4))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z2) (@ (@ tptp.ord_less_rat Z2) Y4))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (= X Y4)))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y3) X4) (@ P Y3))) (@ P X4))) (@ P A))))
% 6.39/6.70 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y4) X)) (= (not (@ (@ tptp.ord_less_real X) Y4)) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y4) X)) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y4) X)) (= (not (@ (@ tptp.ord_less_num X) Y4)) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y4) X)) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (= X Y4)))))
% 6.39/6.70 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y4) X)) (= (not (@ (@ tptp.ord_less_int X) Y4)) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_num Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (=> (not (= X Y4)) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.70 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.39/6.70 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.39/6.70 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.39/6.70 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.39/6.70 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.39/6.70 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.39/6.70 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.39/6.70 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.39/6.70 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.39/6.70 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.39/6.70 (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 ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N4) (not (@ P3 M5)))))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ tptp.ord_less_real A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.real)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.real) (B3 tptp.real)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.rat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_num A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.num)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.39/6.70 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.int)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y4)) (or (@ (@ tptp.ord_less_real Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (or (@ (@ tptp.ord_less_rat Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y4)) (or (@ (@ tptp.ord_less_num Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (or (@ (@ tptp.ord_less_nat Y4) X) (= X Y4)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y4)) (or (@ (@ tptp.ord_less_int Y4) X) (= X Y4)))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (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))))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.39/6.70 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (@ (@ tptp.ord_less_num Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (= X Y4)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (@ (@ tptp.ord_less_num Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_rat X) Y4) (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_num X) Y4) (@ (@ tptp.ord_less_num Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_nat X) Y4) (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (= X Y4)) (or (@ (@ tptp.ord_less_int X) Y4) (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.70 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.39/6.70 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.39/6.70 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_real Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_rat Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_num Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_nat Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ _let_1 Z))))))
% 6.39/6.70 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.39/6.71 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.39/6.71 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.39/6.71 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.39/6.71 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (@ (@ tptp.ord_less_num Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) P))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y4) (=> (@ (@ tptp.ord_less_rat Y4) X) P))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y4) (=> (@ (@ tptp.ord_less_num Y4) X) P))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y4) (=> (@ (@ tptp.ord_less_nat Y4) X) P))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y4) (=> (@ (@ tptp.ord_less_int Y4) X) P))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y4) (= X Y4) (@ (@ tptp.ord_less_real Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y4) (= X Y4) (@ (@ tptp.ord_less_rat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X) Y4) (= X Y4) (@ (@ tptp.ord_less_num Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y4) (= X Y4) (@ (@ tptp.ord_less_nat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X) Y4) (= X Y4) (@ (@ tptp.ord_less_int Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (= Y4 X)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (= Y4 X)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (= Y4 X)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (= Y4 X)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (= Y4 X)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (not (@ (@ tptp.ord_less_real Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (not (@ (@ tptp.ord_less_rat Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (not (@ (@ tptp.ord_less_num Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (not (@ (@ tptp.ord_less_nat Y4) X)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (not (@ (@ tptp.ord_less_int Y4) X)))))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_real (@ F N)) (@ F N3))))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N3))))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_num (@ F N)) (@ F N3))))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N3))))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_int (@ F N)) (@ F N3))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X5)))))))
% 6.39/6.71 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (not (@ (@ tptp.ord_less_eq_num T) X5)))))))
% 6.39/6.71 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X5)))))))
% 6.39/6.71 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (not (@ (@ tptp.ord_less_eq_int T) X5)))))))
% 6.39/6.71 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (not (@ (@ tptp.ord_less_eq_real T) X5)))))))
% 6.39/6.71 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z2) (@ (@ tptp.ord_less_eq_rat X5) T))))))
% 6.39/6.71 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z2) (@ (@ tptp.ord_less_eq_num X5) T))))))
% 6.39/6.71 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z2) (@ (@ tptp.ord_less_eq_nat X5) T))))))
% 6.39/6.71 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z2) (@ (@ tptp.ord_less_eq_int X5) T))))))
% 6.39/6.71 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z2) (@ (@ tptp.ord_less_eq_real X5) T))))))
% 6.39/6.71 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (@ (@ tptp.ord_less_eq_rat T) X5))))))
% 6.39/6.71 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (@ (@ tptp.ord_less_eq_num T) X5))))))
% 6.39/6.71 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (@ (@ tptp.ord_less_eq_nat T) X5))))))
% 6.39/6.71 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (@ (@ tptp.ord_less_eq_int T) X5))))))
% 6.39/6.71 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (@ (@ tptp.ord_less_eq_real T) X5))))))
% 6.39/6.71 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X5) (not (@ (@ tptp.ord_less_eq_rat X5) T)))))))
% 6.39/6.71 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X5) (not (@ (@ tptp.ord_less_eq_num X5) T)))))))
% 6.39/6.71 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X5) (not (@ (@ tptp.ord_less_eq_nat X5) T)))))))
% 6.39/6.71 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X5) (not (@ (@ tptp.ord_less_eq_int X5) T)))))))
% 6.39/6.71 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X5) (not (@ (@ tptp.ord_less_eq_real X5) T)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((B6 tptp.rat) (A6 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B6) A6)) (@ (@ tptp.ord_less_rat A6) B6))))
% 6.39/6.71 (assert (forall ((B6 tptp.num) (A6 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B6) A6)) (@ (@ tptp.ord_less_num A6) B6))))
% 6.39/6.71 (assert (forall ((B6 tptp.nat) (A6 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B6) A6)) (@ (@ tptp.ord_less_nat A6) B6))))
% 6.39/6.71 (assert (forall ((B6 tptp.int) (A6 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B6) A6)) (@ (@ tptp.ord_less_int A6) B6))))
% 6.39/6.71 (assert (forall ((B6 tptp.real) (A6 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B6) A6)) (@ (@ tptp.ord_less_real A6) B6))))
% 6.39/6.71 (assert (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y4) X) (not (@ (@ tptp.ord_less_set_int X) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (not (@ (@ tptp.ord_less_rat X) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (not (@ (@ tptp.ord_less_num X) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (not (@ (@ tptp.ord_less_nat X) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (not (@ (@ tptp.ord_less_int X) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (not (@ (@ tptp.ord_less_real X) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y4)) (= (@ (@ tptp.ord_less_eq_set_int X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y4)) (= (@ (@ tptp.ord_less_eq_rat X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y4)) (= (@ (@ tptp.ord_less_eq_num X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y4)) (= (@ (@ tptp.ord_less_eq_nat X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y4)) (= (@ (@ tptp.ord_less_eq_int X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y4)) (= (@ (@ tptp.ord_less_eq_real X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y4) (= (not (@ (@ tptp.ord_less_set_int X) Y4)) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (= (not (@ (@ tptp.ord_less_num X) Y4)) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (= (not (@ (@ tptp.ord_less_int X) Y4)) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (= (not (@ (@ tptp.ord_less_real X) Y4)) (= X Y4)))))
% 6.39/6.71 (assert (forall ((Z tptp.rat) (Y4 tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (@ (@ tptp.ord_less_eq_rat Y4) X4))) (@ (@ tptp.ord_less_eq_rat Y4) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.real) (Y4 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (@ (@ tptp.ord_less_eq_real Y4) X4))) (@ (@ tptp.ord_less_eq_real Y4) Z))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (Z tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat X4) Z))) (@ (@ tptp.ord_less_eq_rat Y4) Z))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y4) Z))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y6) (not (@ (@ tptp.ord_less_eq_set_int Y6) X3))))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y6) (not (@ (@ tptp.ord_less_eq_rat Y6) X3))))))
% 6.39/6.71 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y6) (not (@ (@ tptp.ord_less_eq_num Y6) X3))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X3))))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y6) (not (@ (@ tptp.ord_less_eq_int Y6) X3))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y6) (not (@ (@ tptp.ord_less_eq_real Y6) X3))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y4) X)) (@ (@ tptp.ord_less_rat X) Y4))))
% 6.39/6.71 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y4) X)) (@ (@ tptp.ord_less_num X) Y4))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y4) X)) (@ (@ tptp.ord_less_nat X) Y4))))
% 6.39/6.71 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y4) X)) (@ (@ tptp.ord_less_int X) Y4))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y4) X)) (@ (@ tptp.ord_less_real X) Y4))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A3) B2) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B2) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B2) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B2) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B2) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (= A3 B2))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (@ (@ tptp.ord_less_eq_set_int B2) A3))))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (@ (@ tptp.ord_less_eq_rat B2) A3))))))
% 6.39/6.71 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (@ (@ tptp.ord_less_eq_num B2) A3))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (@ (@ tptp.ord_less_eq_nat B2) A3))))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (@ (@ tptp.ord_less_eq_int B2) A3))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (@ (@ tptp.ord_less_eq_real B2) A3))))))
% 6.39/6.71 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X) (@ (@ tptp.ord_less_eq_rat Y4) W2)))) (@ (@ tptp.ord_less_eq_rat Y4) Z)))))
% 6.39/6.71 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X) (@ (@ tptp.ord_less_eq_real Y4) W2)))) (@ (@ tptp.ord_less_eq_real Y4) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W2) (=> (@ (@ tptp.ord_less_rat W2) Y4) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y4) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y4) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y4) Z)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B2) A3) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B2) A3) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B2) A3) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B2) A3) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B2) A3) (= A3 B2)))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (= A3 B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (= A3 B2))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (@ (@ tptp.ord_less_eq_set_int A3) B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (@ (@ tptp.ord_less_eq_rat A3) B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (@ (@ tptp.ord_less_eq_num A3) B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (@ (@ tptp.ord_less_eq_int A3) B2))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (@ (@ tptp.ord_less_eq_real A3) B2))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.39/6.71 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.39/6.71 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.39/6.71 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.39/6.71 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_set_int (lambda ((X3 tptp.set_int) (Y6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_num (lambda ((X3 tptp.num) (Y6 tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Y6 tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y6) (not (= X3 Y6))))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y6) (not (= X3 Y6))))))
% 6.39/6.71 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y6) (not (= X3 Y6))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (not (= X3 Y6))))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y6) (not (= X3 Y6))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y6) (not (= X3 Y6))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y4)) (@ (@ tptp.ord_less_rat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y4)) (@ (@ tptp.ord_less_num Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y4)) (@ (@ tptp.ord_less_nat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y4)) (@ (@ tptp.ord_less_int Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y4)) (@ (@ tptp.ord_less_real Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y4) (@ (@ tptp.ord_less_eq_set_int X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y4) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y4) (@ (@ tptp.ord_less_eq_num X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y4) (@ (@ tptp.ord_less_eq_nat X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y4) (@ (@ tptp.ord_less_eq_int X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.39/6.71 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y4) (=> (@ (@ tptp.ord_less_set_int Y4) Z) (@ (@ tptp.ord_less_set_int X) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ (@ tptp.ord_less_rat Y4) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (=> (@ (@ tptp.ord_less_num Y4) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (=> (@ (@ tptp.ord_less_nat Y4) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_real Y4) Z) (@ (@ tptp.ord_less_real X) Z)))))
% 6.39/6.71 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_set_int Y4) Z) (@ _let_1 Z))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) Z) (@ _let_1 Z))))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) Z) (@ _let_1 Z))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) Z) (@ _let_1 Z))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z) (@ _let_1 Z))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) Z) (@ _let_1 Z))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.39/6.71 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 6.39/6.71 (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) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.39/6.71 (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_eq_num (@ F B)) C) (=> (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (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_eq_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_rat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y4) (@ (@ tptp.ord_less_num Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y4) (@ (@ tptp.ord_less_nat Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y4) (@ (@ tptp.ord_less_int Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_real Y4) X))))
% 6.39/6.71 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y4) (or (@ (@ tptp.ord_less_set_int X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (or (@ (@ tptp.ord_less_rat X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (or (@ (@ tptp.ord_less_num X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (or (@ (@ tptp.ord_less_nat X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (or (@ (@ tptp.ord_less_int X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (or (@ (@ tptp.ord_less_real X) Y4) (= X Y4)))))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.71 (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 ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.39/6.71 (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 ((E tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.39/6.71 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y4 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y4))) (and (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y4)))) (=> (@ (@ tptp.ord_less_nat X) Y4) (@ P tptp.zero_zero_int))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C2) (= (@ (@ tptp.minus_minus_set_nat B4) (@ (@ tptp.minus_minus_set_nat C2) A2)) A2)))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C2) (= (@ (@ tptp.minus_minus_set_int B4) (@ (@ tptp.minus_minus_set_int C2) A2)) A2)))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B4)) A2)))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B4)) A2)))
% 6.39/6.71 (assert (forall ((A2 tptp.set_nat) (C2 tptp.set_nat) (D3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C2) (=> (@ (@ tptp.ord_less_eq_set_nat D3) B4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B4)) (@ (@ tptp.minus_minus_set_nat C2) D3))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (C2 tptp.set_int) (D3 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C2) (=> (@ (@ tptp.ord_less_eq_set_int D3) B4) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B4)) (@ (@ tptp.minus_minus_set_int C2) D3))))))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.39/6.71 (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))))))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P N) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M6 tptp.nat)) (and (= M (@ tptp.suc M6)) (@ (@ tptp.ord_less_nat N) M6))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.39/6.71 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.39/6.71 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.39/6.71 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.39/6.71 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2))))))) (@ P N)))))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (or (@ (@ tptp.ord_less_nat M5) N4) (= M5 N4)))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N4) (not (= M5 N4))))))
% 6.39/6.71 (assert (forall ((Z tptp.int)) (not (forall ((M4 tptp.nat) (N2 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X)) Y4)))) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X)) Y4)))) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.39/6.71 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y4)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P tptp.zero_zero_nat) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P tptp.zero_zero_nat) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P (@ tptp.suc I2))))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.39/6.71 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 6.39/6.71 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.39/6.71 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.39/6.71 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.39/6.71 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.39/6.71 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.39/6.71 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.39/6.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K2) (not (@ P I4)))) (@ P K2)))))))
% 6.39/6.71 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.39/6.71 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.39/6.71 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.39/6.71 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ (@ 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 X) Z)) (@ (@ tptp.divide_divide_rat Y4) W))))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ 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 X) Z)) (@ (@ tptp.divide_divide_real Y4) W))))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y4) W))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y4) W))))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y4) W)))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y4) W)))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y4)))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) tptp.zero_zero_real)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y4)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y4)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y4)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y4) X)) X)))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y4) X)) X)))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y4) X)) X)))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y4)) X)))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y4)) X)))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y4)) X)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) K2) (not (@ P I4)))) (@ P (@ tptp.suc K2))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (X7 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X X7) (=> (=> _let_2 (= P P4)) (= (and (@ _let_1 X) P) (and _let_2 P4))))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (X7 tptp.int) (P Bool) (P4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X X7) (=> (=> _let_2 (= P P4)) (= (=> (@ _let_1 X) P) (=> _let_2 P4))))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat A) B))) (=> _let_1 (=> _let_2 (and _let_2 _let_1)))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (=> (and (@ (@ tptp.dvd_dvd_nat A) B) _let_1) _let_1))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (=> (and _let_1 (not (= A B))) _let_1))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat A) B) (not (= A B))))) (= _let_1 _let_1))))
% 6.39/6.71 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (= A3 B2))) (or (and (@ (@ tptp.dvd_dvd_nat A3) B2) (not _let_1)) _let_1)))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (= (and _let_1 (not (= A B))) (and _let_1 (not (@ (@ tptp.dvd_dvd_nat B) A)))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (and (@ _let_1 B) (not (= A B))) (=> (@ (@ tptp.dvd_dvd_nat B) C) (and (@ _let_1 C) (not (= A C))))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (= B C))) (and (@ _let_1 C) (not (= A C))))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (and (@ _let_1 B) (not (= A B))) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (= B C))) (and (@ _let_1 C) (not (= A C))))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= A B)))))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat A) A) (not (= A A))))))
% 6.39/6.71 (assert (= (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat A3) B2) (@ (@ tptp.dvd_dvd_nat B2) A3)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat A) B) (not (= A B))) (not (and (@ (@ tptp.dvd_dvd_nat B) A) (not (= B A)))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))))))))
% 6.39/6.71 (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)))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y4)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y4)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z))) tptp.zero_zero_real))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z))) tptp.zero_zero_rat))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.39/6.71 (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 ((B3 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B3 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B3) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B3) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B3)))))))))))))))
% 6.39/6.71 (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 ((B3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B3 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B3) tptp.one_one_nat) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_nat A) B3) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B3)))))))))))))))
% 6.39/6.71 (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 ((B3 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B3) tptp.one_one_int) (=> (= (@ _let_1 A) B3) (=> (= (@ _let_1 B3) A) (=> (= (@ (@ tptp.times_times_int A) B3) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B3)))))))))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.39/6.71 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.39/6.71 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.39/6.71 (assert (= tptp.divide_divide_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M5) N4) (= N4 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M5) N4)) N4))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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)))))))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X 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 X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X 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 X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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 ((Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q3))) (@ P Q3))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _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)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ P N))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D3))))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D3))))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D3))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.real Bool)) (D3 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D3))))) (=> (forall ((X4 tptp.real) (K2 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K2) D3))))) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D3))))) (=> (forall ((X4 tptp.rat) (K2 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K2) D3))))) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D3))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D3))))) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3)))) (= (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.39/6.71 (assert (forall ((P5 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P5) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= P5 (@ (@ tptp.times_times_nat X4) Y)) (=> (@ (@ tptp.dvd_dvd_nat X4) A) (not (@ (@ tptp.dvd_dvd_nat Y) B)))))))))
% 6.39/6.71 (assert (forall ((P5 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P5) (@ (@ tptp.times_times_int A) B)) (not (forall ((X4 tptp.int) (Y tptp.int)) (=> (= P5 (@ (@ tptp.times_times_int X4) Y)) (=> (@ (@ tptp.dvd_dvd_int X4) A) (not (@ (@ tptp.dvd_dvd_int Y) B)))))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B7 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C4)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B7 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C4)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT)) (@ (@ tptp.ord_less_nat (@ tptp.vEBT_VEBT_space T)) (@ tptp.vEBT_VEBT_space2 T))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X 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 X)) (@ _let_1 X)))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.39/6.71 (assert (forall ((X 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 X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.39/6.71 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.39/6.71 (assert (forall ((X 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 X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 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 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y4) _let_1)) (= X Y4))))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 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 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y4) _let_1)) (= X Y4))))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 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 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y4) _let_1)) (= X Y4))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y4) _let_1)) (= X Y4))))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.39/6.71 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.39/6.71 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.39/6.71 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.39/6.71 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.39/6.71 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.39/6.71 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.39/6.71 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.39/6.71 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((B tptp.rat) (X tptp.nat) (Y4 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 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (X tptp.nat) (Y4 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 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.39/6.71 (assert (forall ((B tptp.int) (X tptp.nat) (Y4 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 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.39/6.71 (assert (forall ((B tptp.real) (X tptp.nat) (Y4 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 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y4) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y4) _let_1) (= Y4 _let_1)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.semiri8010041392384452111omplex Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.semiri5074537144036343181t_real Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.semiri681578069525770553at_rat Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y4)) (= _let_1 Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) (@ tptp.semiri1314217659103216013at_int Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y4))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B4) (exists ((B3 tptp.complex)) (@ (@ tptp.member_complex B3) (@ (@ tptp.minus_811609699411566653omplex B4) A2))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B4) (exists ((B3 tptp.real)) (@ (@ tptp.member_real B3) (@ (@ tptp.minus_minus_set_real B4) A2))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B4) (exists ((B3 tptp.set_nat)) (@ (@ tptp.member_set_nat B3) (@ (@ tptp.minus_2163939370556025621et_nat B4) A2))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B4) (exists ((B3 tptp.int)) (@ (@ tptp.member_int B3) (@ (@ tptp.minus_minus_set_int B4) A2))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (exists ((B3 tptp.nat)) (@ (@ tptp.member_nat B3) (@ (@ tptp.minus_minus_set_nat B4) A2))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.power_power_real X) N2))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N2)) Y4))))))
% 6.39/6.71 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (= A5 B5))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_int B4) C2) (@ _let_1 C2))))))
% 6.39/6.71 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A5))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B4) (=> (@ (@ tptp.ord_less_set_int B4) C2) (@ (@ tptp.ord_less_set_int A2) C2)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B5) (= A5 B5)))))
% 6.39/6.71 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.71 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y6) (= X3 Y6)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.39/6.71 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.39/6.71 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N)) A))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (P4 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P4 X4) (@ P4 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (= (@ P X4) (@ P4 X4))))) (=> (exists ((X_12 tptp.int)) (@ P4 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.39/6.71 (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) (K2 tptp.int)) (= (@ P1 X4) (@ P1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (= (@ P X4) (@ P1 X4))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.39/6.71 (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 ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3) (= (@ (@ tptp.power_power_real Y3) N) A)) (= Y3 X4)))))))))
% 6.39/6.71 (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 ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N) A)))))))
% 6.39/6.71 (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))))))))))
% 6.39/6.71 (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 ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K) D))))))))))
% 6.39/6.71 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y3 tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y3) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X)))))))
% 6.39/6.71 (assert (forall ((A tptp.int) (A6 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A6) B))))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B6 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B6))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((A tptp.int) (A6 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A6) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A6) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B6 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) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B6)) (@ _let_1 B))))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 6.39/6.71 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= K (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X)))) tptp.one_one_real)))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N))) (let ((_let_2 (@ tptp.times_times_complex Y4))) (=> (= (@ (@ tptp.times_times_complex X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N))) (let ((_let_2 (@ tptp.times_times_real Y4))) (=> (= (@ (@ tptp.times_times_real X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N))) (let ((_let_2 (@ tptp.times_times_rat Y4))) (=> (= (@ (@ tptp.times_times_rat X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y4))) (=> (= (@ (@ tptp.times_times_nat X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y4))) (=> (= (@ (@ tptp.times_times_int X) Y4) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ _let_2 _let_1)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y4) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y4) N)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y4) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) N)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y4) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) N)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y4) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y4) N)))))
% 6.39/6.71 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y4) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) N)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y4) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) N)) tptp.one_one_complex))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y4) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) N)) tptp.one_one_real))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y4) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y4) N)) tptp.one_one_rat))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y4) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y4) N)) tptp.one_one_nat))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y4) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) N)) tptp.one_one_int))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y4) M))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y4) M))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y4) M))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y4) M))))))
% 6.39/6.71 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y4) M))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ 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 N5)) (@ _let_1 N))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.39/6.71 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))))
% 6.39/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))))
% 6.39/6.71 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X) X)) X)) X))))
% 6.39/6.71 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))))
% 6.39/6.71 (assert (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.39/6.71 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y4)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y4) X)) _let_1)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y4)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y4) X)) _let_1)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y4)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y4) X)) _let_1)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y4)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y4) X)) _let_1)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N)))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4) (@ (@ tptp.ord_less_eq_nat X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_eq_int X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 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 X) _let_2) (@ (@ tptp.power_power_rat Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 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 X) _let_2) (@ (@ tptp.power_power_nat Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 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 X) _let_2) (@ (@ tptp.power_power_int Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 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 X) _let_2) (@ (@ tptp.power_power_real Y4) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= X Y4))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (= tptp.power_power_complex (lambda ((P6 tptp.complex) (M5 tptp.nat)) (@ (@ (@ tptp.if_complex (= M5 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P6) (@ (@ tptp.power_power_complex P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.71 (assert (= tptp.power_power_real (lambda ((P6 tptp.real) (M5 tptp.nat)) (@ (@ (@ tptp.if_real (= M5 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P6) (@ (@ tptp.power_power_real P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.71 (assert (= tptp.power_power_rat (lambda ((P6 tptp.rat) (M5 tptp.nat)) (@ (@ (@ tptp.if_rat (= M5 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P6) (@ (@ tptp.power_power_rat P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.71 (assert (= tptp.power_power_nat (lambda ((P6 tptp.nat) (M5 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P6) (@ (@ tptp.power_power_nat P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.71 (assert (= tptp.power_power_int (lambda ((P6 tptp.int) (M5 tptp.nat)) (@ (@ (@ tptp.if_int (= M5 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P6) (@ (@ tptp.power_power_int P6) (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_rat X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4) (@ (@ tptp.ord_less_nat X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_int X) Y4))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_real X) Y4))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_space2 T))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real))))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt T)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_2) N)) (@ (@ 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))))))))))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_space T)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) U))))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_real (@ tptp.vEBT_VEBT_cnt T)) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_1) N)) tptp.one_one_real)))))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= U (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_space2 T)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) U))))))
% 6.39/6.71 (assert (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) E2)))))))
% 6.39/6.71 (assert (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) E2)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.nat)) (=> (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) N2)))) (not (forall ((N2 tptp.nat)) (not (= X (@ (@ tptp.plus_plus_nat N2) (@ tptp.suc N2)))))))))
% 6.39/6.71 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y4)) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))
% 6.39/6.71 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.39/6.71 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.39/6.71 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.39/6.71 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.39/6.71 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y4) _let_1)) X)) N) Y4)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.39/6.71 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.39/6.71 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.39/6.71 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.39/6.71 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.39/6.71 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_less_set_complex A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.71 (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_less_set_set_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.71 (assert (forall ((A2 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B4) (=> (@ _let_1 A2) (@ _let_1 B4))))))
% 6.39/6.71 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N2 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.39/6.71 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.39/6.71 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.39/6.71 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C5 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C5))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.39/6.71 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.39/6.71 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E2)) C))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E2)) C))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E2)) C))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E2)) C))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.39/6.71 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (= (@ (@ P A4) B3) (@ (@ P B3) A4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) tptp.zero_zero_nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (let ((_let_1 (@ P A4))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.plus_plus_nat A4) B3))))) (@ (@ P A) B))))))
% 6.39/6.71 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 6.39/6.71 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (= tptp.ord_less_eq_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ (@ tptp.plus_plus_nat M5) K3))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N2 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N2))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y4) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y4) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y4) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y4) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_rat X) Y4) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))))
% 6.39/6.71 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_nat X) Y4) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat))))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_int X) Y4) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_real X) Y4) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y4)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y4)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y4)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y4) tptp.zero_zero_int)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.39/6.71 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.39/6.71 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.39/6.71 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.39/6.71 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.39/6.71 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.39/6.71 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C) D))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C) D))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C) D))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_real X) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ (@ tptp.minus_minus_rat X) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y4)) (@ (@ tptp.minus_minus_int X) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y4) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y4)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y4) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y4)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y4) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.39/6.71 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2))))) (=> (@ (@ tptp.ord_less_real X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2))))) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2))))) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2))))) (=> (@ (@ tptp.ord_less_int X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2)))) (=> (@ (@ tptp.ord_less_real X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2)))) (=> (@ (@ tptp.ord_less_rat X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2)))) (=> (@ (@ tptp.ord_less_nat X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2)))) (=> (@ (@ tptp.ord_less_int X5) Z2) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2))))) (=> (@ (@ tptp.ord_less_real Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2))))) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2))))) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2))))) (=> (@ (@ tptp.ord_less_int Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X5) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X5) S2)))) (=> (@ (@ tptp.ord_less_real Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X5 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X5) S2)))) (=> (@ (@ tptp.ord_less_rat Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X5 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X5) S2)))) (=> (@ (@ tptp.ord_less_nat Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X5) S2)))) (=> (@ (@ tptp.ord_less_int Z2) X5) (= _let_1 _let_1)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M5) K3)))))))
% 6.39/6.71 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 6.39/6.71 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 6.39/6.71 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q4 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q4)))))))))
% 6.39/6.71 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I) K2) J))))))
% 6.39/6.71 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N2) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.39/6.71 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.39/6.71 (assert (= tptp.suc (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_nat N4) tptp.one_one_nat))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y4 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 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D))) (exists ((X4 tptp.nat) (Y 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 Y)) D)) (= (@ _let_3 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D)))))))))))))))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D2 tptp.nat) (X4 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 D2))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D2)) (= (@ _let_2 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D2))))))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y4) E)))) (@ (@ tptp.ord_less_eq_rat X) Y4))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y4) E)))) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4)))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))) tptp.zero_zero_real))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4))) tptp.zero_zero_rat))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4))) tptp.zero_zero_int))))
% 6.39/6.71 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))) (or (not (= X tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y4) Y4))) (or (not (= X tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y4) Y4))) (or (not (= X tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int))))))
% 6.39/6.71 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 6.39/6.71 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.39/6.71 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (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))))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y4))) (@ (@ tptp.times_times_complex Y4) Z)))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z)))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z)))))))
% 6.39/6.71 (assert (forall ((Y4 tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y4)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y4))) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y4)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y4))) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y4)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y4))) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y4))) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y4))) Y4)))))
% 6.39/6.71 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y4)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y4))) Y4)))))
% 6.39/6.71 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y4) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y4) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y4) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y4)) Z)))))
% 6.39/6.71 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 6.39/6.71 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 6.39/6.71 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 6.39/6.71 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.39/6.71 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X 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 X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M)))))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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)))))))
% 6.39/6.71 (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))))
% 6.39/6.71 (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))))
% 6.39/6.71 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 6.39/6.71 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.39/6.71 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 6.39/6.71 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (assert (forall ((D tptp.code_integer) (D3 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D3) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K4) D3))) T))))))))
% 6.39/6.71 (assert (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T))))))))
% 6.39/6.71 (assert (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T))))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T))))))))
% 6.39/6.71 (assert (forall ((D tptp.code_integer) (D3 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D3) (forall ((X5 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X5) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X5) (@ (@ tptp.times_3573771949741848930nteger K4) D3))) T)))))))))
% 6.39/6.71 (assert (forall ((D tptp.real) (D3 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D3) (forall ((X5 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K4) D3))) T)))))))))
% 6.39/6.71 (assert (forall ((D tptp.rat) (D3 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D3) (forall ((X5 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K4) D3))) T)))))))))
% 6.39/6.71 (assert (forall ((D tptp.int) (D3 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K4) D3))) T)))))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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 ((D4 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D4)) (not (@ P D4)))))))))
% 6.39/6.71 (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 ((D4 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D4)) (@ P D4)))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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))))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D2 tptp.nat) (X4 tptp.nat) (Y 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) Y)) D2))))))))
% 6.39/6.71 (assert (forall ((X tptp.rat) (A tptp.rat) (Y4 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 X) A) (=> (@ (@ tptp.ord_less_eq_rat Y4) 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) X)) (@ (@ tptp.times_times_rat V) Y4))) A)))))))))
% 6.39/6.71 (assert (forall ((X tptp.int) (A tptp.int) (Y4 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 X) A) (=> (@ (@ tptp.ord_less_eq_int Y4) 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) X)) (@ (@ tptp.times_times_int V) Y4))) A)))))))))
% 6.39/6.71 (assert (forall ((X tptp.real) (A tptp.real) (Y4 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 X) A) (=> (@ (@ tptp.ord_less_eq_real Y4) 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) X)) (@ (@ tptp.times_times_real V) Y4))) A)))))))))
% 6.39/6.71 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.39/6.71 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (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)))))
% 6.39/6.71 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 6.39/6.71 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (assert (= tptp.plus_plus_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N4) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)) N4))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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 ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J3)) (@ P I2))))))))))
% 6.39/6.72 (assert (= tptp.times_times_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N4) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)) N4))))))
% 6.39/6.72 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) 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)))))))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (A tptp.rat) (Y4 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y4) 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) X)) (@ (@ tptp.times_times_rat V) Y4))) A)))))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (A tptp.int) (Y4 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y4) 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) X)) (@ (@ tptp.times_times_int V) Y4))) A)))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (A tptp.real) (Y4 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y4) 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) X)) (@ (@ tptp.times_times_real V) Y4))) A)))))))))
% 6.39/6.72 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 6.39/6.72 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S2))) V))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) tptp.zero_zero_real)))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) tptp.zero_zero_rat)))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) tptp.zero_zero_int)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real)))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat)))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int)))))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_Code_integer))))))))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_nat))))))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3)) tptp.one_one_int))))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y4) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y4)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y4) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.39/6.72 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N2 tptp.nat)) (and (not (@ P N2)) (@ P (@ tptp.suc N2))))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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)) X)) Y4)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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)) X)) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y4) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 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 X) Y4)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y4) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y4)))))))
% 6.39/6.72 (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.39/6.72 (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))))))))))
% 6.39/6.72 (assert (forall ((U tptp.rat) (X tptp.rat) (Y4 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 X) Y4)) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y4)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.39/6.72 (assert (forall ((U tptp.real) (X tptp.real) (Y4 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 X) Y4)) (=> (@ _let_2 X) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat Y4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) X))))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y4) _let_1)) X)) N) X)))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A4 tptp.real) (B3 tptp.real) (C3 tptp.real)) (let ((_let_1 (@ P A4))) (=> (@ _let_1 B3) (=> (@ (@ P B3) C3) (=> (@ (@ tptp.ord_less_eq_real A4) B3) (=> (@ (@ tptp.ord_less_eq_real B3) 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 ((A4 tptp.real) (B3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A4) X4) (@ (@ tptp.ord_less_eq_real X4) B3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B3) A4)) D5)) (@ (@ P A4) B3)))))))) (@ (@ P A) B))))))
% 6.39/6.72 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y4) Z)) (@ (@ tptp.ord_less_eq_rat X) Y4)))))
% 6.39/6.72 (assert (forall ((Z tptp.int) (X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y4) Z)) (@ (@ tptp.ord_less_eq_int X) Y4)))))
% 6.39/6.72 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y4) Z)) (@ (@ tptp.ord_less_eq_real X) Y4)))))
% 6.39/6.72 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 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 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_rat X) Y4))))))
% 6.39/6.72 (assert (forall ((Z tptp.int) (X tptp.int) (Y4 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 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_int X) Y4))))))
% 6.39/6.72 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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))))))))))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.72 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.39/6.72 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.39/6.72 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.39/6.72 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.39/6.72 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (= tptp.neg_numeral_dbl_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real X3) X3))))
% 6.39/6.72 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat X3) X3))))
% 6.39/6.72 (assert (= tptp.neg_numeral_dbl_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) X3))))
% 6.39/6.72 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N4 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N4)))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (D tptp.int) (X tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((Z tptp.extended_enat) (Y4 tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y4) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y4) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y4)) Z))))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.39/6.72 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N4 tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N4))))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 6.39/6.72 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 6.39/6.72 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 6.39/6.72 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 6.39/6.72 (assert (= tptp.ord_less_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N4)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M5)))))
% 6.39/6.72 (assert (= tptp.ord_less_eq_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M5)) tptp.one_one_real)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 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)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 6.39/6.72 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.39/6.72 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B6 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B6) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.39/6.72 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B6 tptp.int) (Q5 tptp.int) (R4 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 B6) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B6) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (=> (@ (@ tptp.ord_less_eq_int B6) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.39/6.72 (assert (forall ((B6 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B6) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B6) (@ _let_1 Q5)))))))
% 6.39/6.72 (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 ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) (@ (@ tptp.times_times_int K) D))))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.39/6.72 (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 ((I2 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) I2)) J3))) (@ P I2)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 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) I2)) J3))) (@ P I2))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((X 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 X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((N tptp.nat) (X 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)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 6.39/6.72 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y4) Z)) (@ (@ tptp.ord_less_real X) Y4)))))
% 6.39/6.72 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y4) Z)) (@ (@ tptp.ord_less_rat X) Y4)))))
% 6.39/6.72 (assert (forall ((Z tptp.int) (X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y4) Z)) (@ (@ tptp.ord_less_int X) Y4)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5074537144036343181t_real N))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.39/6.72 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.39/6.72 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ 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 R2) S2))))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ 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 R2) S2))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4))) E2))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4))) E2))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y4) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y4) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y4)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y4)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y4))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y4) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y4) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y4))) E2))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y4))) E2))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (R2 tptp.real) (Y4 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (R2 tptp.real) (Y4 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y4))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y4))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (=> P Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.39/6.72 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.39/6.72 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.39/6.72 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.39/6.72 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.39/6.72 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.39/6.72 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.39/6.72 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.39/6.72 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.39/6.72 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.39/6.72 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.39/6.72 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.39/6.72 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.39/6.72 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P5))) P5)))
% 6.39/6.72 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P5))) P5)))
% 6.39/6.72 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P5))) P5)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (assert (forall ((P5 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P5) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P5 Q2))))
% 6.39/6.72 (assert (forall ((P5 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P5) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P5 Q2))))
% 6.39/6.72 (assert (forall ((P5 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P5) (@ tptp.zero_n356916108424825756nteger Q2)) (= P5 Q2))))
% 6.39/6.72 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.semiri8010041392384452111omplex X)) N) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.semiri5074537144036343181t_real X)) N) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.semiri681578069525770553at_rat X)) N) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat (@ tptp.semiri1316708129612266289at_nat X)) N) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.semiri1314217659103216013at_int X)) N) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A6) B6)) C))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A6) B6)) C))))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A6 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A6) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A6) B6)) C))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.nat) (C tptp.nat) (A6 tptp.nat) (B tptp.nat) (B6 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A6) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B6) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A6) B6)) C))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A6) B6)) C))))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A6 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A6) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A6) B6)) C))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.int) (C tptp.int) (A6 tptp.int) (B tptp.int) (B6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A6) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B6) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A6) B6)) C))))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A6 tptp.code_integer) (B tptp.code_integer) (B6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A6) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B6) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A6) B6)) C))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.39/6.72 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.39/6.72 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.39/6.72 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.39/6.72 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.39/6.72 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (not (or (and P5 (not (@ P tptp.one_one_complex))) (and (not P5) (not (@ P tptp.zero_zero_complex))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (not (or (and P5 (not (@ P tptp.one_one_real))) (and (not P5) (not (@ P tptp.zero_zero_real))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.rat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P5)) (not (or (and P5 (not (@ P tptp.one_one_rat))) (and (not P5) (not (@ P tptp.zero_zero_rat))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P tptp.one_one_nat))) (and (not P5) (not (@ P tptp.zero_zero_nat))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P tptp.one_one_int))) (and (not P5) (not (@ P tptp.zero_zero_int))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (not (or (and P5 (not (@ P tptp.one_one_Code_integer))) (and (not P5) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (and (=> P5 (@ P tptp.one_one_complex)) (=> (not P5) (@ P tptp.zero_zero_complex))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (and (=> P5 (@ P tptp.one_one_real)) (=> (not P5) (@ P tptp.zero_zero_real))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.rat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P5)) (and (=> P5 (@ P tptp.one_one_rat)) (=> (not P5) (@ P tptp.zero_zero_rat))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P tptp.one_one_nat)) (=> (not P5) (@ P tptp.zero_zero_nat))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P tptp.one_one_int)) (=> (not P5) (@ P tptp.zero_zero_int))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (and (=> P5 (@ P tptp.one_one_Code_integer)) (=> (not P5) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.39/6.72 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P6 Bool)) (@ (@ (@ tptp.if_complex P6) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.39/6.72 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P6 Bool)) (@ (@ (@ tptp.if_real P6) tptp.one_one_real) tptp.zero_zero_real))))
% 6.39/6.72 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_rat P6) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.39/6.72 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_nat P6) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.39/6.72 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P6 Bool)) (@ (@ (@ tptp.if_int P6) tptp.one_one_int) tptp.zero_zero_int))))
% 6.39/6.72 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P6 Bool)) (@ (@ (@ tptp.if_Code_integer P6) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.39/6.72 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P5 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P5) (=> (@ (@ tptp.ord_less_nat M) P5) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) P5) (=> (@ P N2) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) P5))))) (@ P M)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ P N2) (@ (@ tptp.modulo_modulo_nat M4) N2)) (@ (@ P M4) N2)))) (@ (@ P M) N)))))
% 6.39/6.72 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.39/6.72 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q4 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q4))))))
% 6.39/6.72 (assert (= tptp.modulo_modulo_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M5) N4)) M5) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M5) N4)) N4)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y4) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y4) (@ _let_1 Q22))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X) N))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N))))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y4) N)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (exists ((Q4 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y4) (@ (@ tptp.times_times_nat N) Q4))))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X) N)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (= tptp.modulo_modulo_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.minus_minus_nat M5) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M5) N4)) N4)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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 ((I2 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I2)) J3)) (@ P J3))))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N) R2))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A4 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.nat) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B3)) (@ (@ tptp.times_times_nat _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.39/6.72 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A4 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A4) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.int) (B3 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B3)) (@ (@ tptp.times_times_int _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.39/6.72 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A4 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (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) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.39/6.72 (assert (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (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) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.39/6.72 (assert (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (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) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.39/6.72 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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 ((I2 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) I2)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I2 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) I2)) J3))) (@ P J3))))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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 ((I2 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) I2)) J3))) (@ (@ P I2) J3)))))))
% 6.39/6.72 (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 ((I2 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) I2)) J3))) (@ (@ P I2) J3)))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (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)))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R2)) (@ (@ tptp.power_power_nat N) R2)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((L tptp.nat)) (let ((_let_1 (@ tptp.vEBT_VEBT_cnt (@ tptp.vEBT_vebt_buildup (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc tptp.va))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (= (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.replicate_real L) _let_1)) tptp.zero_zero_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real L)) _let_1)))))
% 6.39/6.72 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 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)))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 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)))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 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)))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 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)))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 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)))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y4)) (@ (@ tptp.ord_less_real X) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (= (@ tptp.ln_ln_real X) (@ tptp.ln_ln_real Y4)) (= X Y4)))))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1408675320244567234ct_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri2265585572941072030t_real N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri5044797733671781792omplex N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((M tptp.nat) (X tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (= (@ (@ tptp.replicate_real M) X) (@ (@ tptp.replicate_real N) Y4)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X Y4))))))
% 6.39/6.72 (assert (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y4 tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N) Y4)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 6.39/6.72 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.39/6.72 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.39/6.72 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.39/6.72 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.72 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.39/6.72 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.39/6.72 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.39/6.72 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.39/6.72 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N) tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N) tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N) tptp.zero_zero_nat))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N) tptp.zero_zero_complex))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y4))))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y4))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R2)))) (@ (@ tptp.power_power_nat N) R2)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y4))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y4)) Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_rat (= M5 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M5)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.72 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_int (= M5 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.72 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M5)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.72 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_real (= M5 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M5)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.72 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M5 tptp.nat)) (@ (@ (@ tptp.if_complex (= M5 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M5)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M5) tptp.one_one_nat)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.39/6.72 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.39/6.72 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((W tptp.real) (Y4 tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X) (= Y4 Z)))))))
% 6.39/6.72 (assert (forall ((W tptp.rat) (Y4 tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X) (= Y4 Z)))))))
% 6.39/6.72 (assert (forall ((W tptp.nat) (Y4 tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X) (= Y4 Z)))))))
% 6.39/6.72 (assert (forall ((W tptp.int) (Y4 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X) (= Y4 Z)))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y4) Z)) (= Y4 (@ (@ tptp.plus_plus_real X) Z)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 6.39/6.72 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.39/6.72 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N4) K3))) (let ((_let_2 (@ tptp.ord_less_nat N4))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ 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 K3)))))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.39/6.72 (assert (forall ((X 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) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _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 A3) _let_1))))))))))
% 6.39/6.72 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _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 A3) _let_1))))))))))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ (@ tptp.divide_divide_nat tptp.va) _let_2)))) (let ((_let_4 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_5 (@ tptp.suc _let_3))) (= (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) (@ (@ tptp.replicate_VEBT_VEBT (@ (@ tptp.power_power_nat _let_2) _let_5)) _let_4))) tptp.zero_zero_real) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)) _let_5)) (@ tptp.vEBT_VEBT_cnt _let_4)))))))))
% 6.39/6.72 (assert (forall ((X 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 X)) (@ (@ 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) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.39/6.72 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 6.39/6.72 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 6.39/6.72 (assert (forall ((B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B)) B)))
% 6.39/6.72 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 6.39/6.72 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.72 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y4) (@ (@ tptp.dvd_dvd_real X) Y4))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y4) (@ (@ tptp.dvd_dvd_int X) Y4))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y4) (@ (@ tptp.dvd_dvd_complex X) Y4))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X)) Y4) (@ (@ tptp.dvd_dvd_Code_integer X) Y4))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y4) (@ (@ tptp.dvd_dvd_rat X) Y4))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y4)) (@ _let_1 Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y4)) (@ _let_1 Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y4)) (@ _let_1 Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y4)) (@ _let_1 Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y4)) (@ _let_1 Y4)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.39/6.72 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.39/6.72 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.39/6.72 (assert (= (@ tptp.tanh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (= (@ tptp.tanh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.39/6.72 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.39/6.72 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.39/6.72 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.39/6.72 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.39/6.72 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.39/6.72 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.39/6.72 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.39/6.72 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.39/6.72 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.39/6.72 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.39/6.72 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.39/6.72 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.39/6.72 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y4)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y4)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y4)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 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))) Y4)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y4)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y4)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y4)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y4)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y4)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y4)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y4)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y4)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y4))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.39/6.72 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))
% 6.39/6.72 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.39/6.72 (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))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.39/6.72 (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))
% 6.39/6.72 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.39/6.72 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (= (@ tptp.abs_abs_real X) (@ tptp.abs_abs_real Y4)) (or (= X Y4) (= X (@ tptp.uminus_uminus_real Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (= (@ tptp.abs_abs_int X) (@ tptp.abs_abs_int Y4)) (or (= X Y4) (= X (@ tptp.uminus_uminus_int Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X) (@ tptp.abs_abs_Code_integer Y4)) (or (= X Y4) (= X (@ tptp.uminus1351360451143612070nteger Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (= (@ tptp.abs_abs_rat X) (@ tptp.abs_abs_rat Y4)) (or (= X Y4) (= X (@ tptp.uminus_uminus_rat Y4))))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.39/6.72 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.39/6.72 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.39/6.72 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.72 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 6.39/6.72 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.39/6.72 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.72 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.39/6.72 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int) (A6 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A6) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A6)) B)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A6 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A6) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A6)) B)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.72 (assert (forall ((Z tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)))))))))
% 6.39/6.72 (assert (= tptp.dvd_dvd_int (lambda ((D4 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int D4)) __flatten_var_0))))
% 6.39/6.72 (assert (= tptp.dvd_dvd_int (lambda ((D4 tptp.int) (T2 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) (@ tptp.uminus_uminus_int T2)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.39/6.72 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.39/6.72 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.39/6.72 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.39/6.72 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.39/6.72 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.39/6.72 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.39/6.72 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.39/6.72 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.72 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.39/6.72 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.39/6.72 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.39/6.72 (assert (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.39/6.72 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.39/6.72 (assert (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.39/6.72 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.39/6.72 (assert (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.39/6.72 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.39/6.72 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.39/6.72 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.39/6.72 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 6.39/6.72 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N2))) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))) (@ P Z)))))
% 6.39/6.72 (assert (forall ((Z tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (= tptp.minus_minus_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real Y6)))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E))) (= X tptp.zero_zero_rat))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E))) (= X tptp.zero_zero_real))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y4)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y4) X))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y4)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y4) X))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y4)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y4) X))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y4)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y4) X))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y4) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y4))))))
% 6.39/6.72 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y4) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.39/6.72 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.39/6.72 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.39/6.72 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.39/6.72 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.39/6.72 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.39/6.72 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.39/6.72 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.39/6.72 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.39/6.72 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ (@ tptp.power_power_rat X) _let_1)))))
% 6.39/6.72 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D2) (and (@ (@ tptp.ord_less_real A) Y3) (@ (@ tptp.ord_less_real Y3) B))))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y4)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y4)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y4)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y4) (=> (@ (@ 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 X) U)) Y4))) V)))))
% 6.39/6.72 (assert (forall ((M tptp.int)) (=> (forall ((N2 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N2)))) (not (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y4))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y4) (@ tptp.uminus_uminus_real X)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.uminus_uminus_real X)))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y4))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)))))))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 6.39/6.72 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 6.39/6.72 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((Z tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 6.39/6.72 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 6.39/6.72 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D2) (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y3))) D2) (and (@ (@ tptp.ord_less_eq_real A) Y3) (@ (@ tptp.ord_less_eq_real Y3) B))))))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus_uminus_real Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus_uminus_int Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus1482373934393186551omplex Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus1351360451143612070nteger Y4)))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y4) _let_1)) (or (= X Y4) (= X (@ tptp.uminus_uminus_rat Y4)))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))))))
% 6.39/6.72 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.39/6.72 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.39/6.72 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N2 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.39/6.72 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) (@ tptp.abs_abs_Code_integer Y4)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) (@ tptp.abs_abs_rat Y4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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))))))))))))
% 6.39/6.72 (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))))))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (assert (forall ((U tptp.real) (X 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 X) _let_1)))))
% 6.39/6.72 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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))))
% 6.39/6.72 (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)))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))))))))
% 6.39/6.72 (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))))))))))
% 6.39/6.72 (assert (forall ((Y4 tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y4) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y4))))))
% 6.39/6.72 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y4))))))
% 6.39/6.72 (assert (forall ((Y4 tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y4))))))
% 6.39/6.72 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y4))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))))))
% 6.39/6.72 (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))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (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)))))))))))))
% 6.39/6.72 (assert (forall ((X 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))) X) (=> (@ (@ tptp.ord_less_eq_real X) 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) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.39/6.72 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.39/6.72 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.39/6.72 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.39/6.72 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (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))))))))
% 6.39/6.72 (assert (forall ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R2) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R2) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.39/6.72 (assert (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.39/6.72 (assert (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.39/6.72 (assert (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.39/6.72 (assert (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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)))))
% 6.39/6.72 (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))))))
% 6.39/6.72 (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))))))
% 6.39/6.73 (assert (forall ((X 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)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) 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) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.73 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4) tptp.one_one_nat)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X 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 X)) (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X 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 X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X 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 X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X 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 X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y4)) (@ (@ tptp.ord_less_eq_set_int Y4) X))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_complex) (F (-> tptp.complex tptp.real)) (Y4 tptp.real)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_complex_real F) Xs)) Y4)))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_set_nat) (F (-> tptp.set_nat tptp.real)) (Y4 tptp.real)) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_set_nat_real F) Xs)) Y4)))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.real)) (Y4 tptp.real)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real F) Xs)) Y4)))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_nat) (F (-> tptp.nat tptp.real)) (Y4 tptp.real)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_nat_real F) Xs)) Y4)))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_real) (F (-> tptp.real tptp.real)) (Y4 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_real_real F) Xs)) Y4)))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_int) (F (-> tptp.int tptp.real)) (Y4 tptp.real)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_int_real F) Xs)) Y4)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.39/6.73 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((C tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus8566677241136511917omplex A2))))))
% 6.39/6.73 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus612125837232591019t_real A2))))))
% 6.39/6.73 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2))))))
% 6.39/6.73 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2))))))
% 6.39/6.73 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A2)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2))))))
% 6.39/6.73 (assert (forall ((C tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ tptp.uminus8566677241136511917omplex A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.39/6.73 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.39/6.73 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.73 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (assert (forall ((X tptp.set_nat) (N tptp.nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (assert (forall ((X tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y4 tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y4))) (and (= X Y4) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (A tptp.real) (P (-> tptp.real Bool))) (= (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (A tptp.real) (P (-> tptp.real Bool))) (= (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.39/6.73 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.39/6.73 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.39/6.73 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.39/6.73 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.39/6.73 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.39/6.73 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((C tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ tptp.uminus8566677241136511917omplex A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ tptp.uminus612125837232591019t_real A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (assert (forall ((C tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A2)) (not (@ _let_1 A2))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y4) X) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X) Y4)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y4))))))
% 6.39/6.73 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.abs_abs_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I2)) I2))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 6.39/6.73 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 6.39/6.73 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 6.39/6.73 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((D tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))))
% 6.39/6.73 (assert (forall ((D tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.39/6.73 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y4) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y4)) (@ tptp.uminus1532241313380277803et_int X)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y4) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y4)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y4))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X 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 X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))))))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.39/6.73 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.arctan X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.73 (assert (= (@ tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.39/6.73 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.39/6.73 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.39/6.73 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.39/6.73 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.39/6.73 (assert (forall ((L tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.39/6.73 (assert (forall ((X tptp.list_real) (Y4 tptp.list_real)) (=> (not (= (@ tptp.size_size_list_real X) (@ tptp.size_size_list_real Y4))) (not (= X Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.list_o) (Y4 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y4))) (not (= X Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y4))) (not (= X Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.list_int) (Y4 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y4))) (not (= X Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y4))) (not (= X Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (= (= (@ tptp.sgn_sgn_complex X) tptp.zero_zero_complex) (= X tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sgn_sgn_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex X)) (@ tptp.sgn_sgn_complex Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.sgn_sgn_real Y4)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L)) R2)))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 6.39/6.73 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))))
% 6.39/6.73 (assert (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))))
% 6.39/6.73 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 6.39/6.73 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 6.39/6.73 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X)) (@ tptp.abs_abs_Code_integer X)) X)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) (@ tptp.abs_abs_real X)) X)))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X)) (@ tptp.abs_abs_rat X)) X)))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 6.39/6.73 (assert (forall ((K tptp.int)) (not (forall ((N2 tptp.nat) (L2 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L2)) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 6.39/6.73 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 6.39/6.73 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 6.39/6.73 (assert (forall ((X Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 6.39/6.73 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (= tptp.sgn_sgn_int (lambda ((I2 tptp.int)) (@ (@ (@ tptp.if_int (= I2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I2)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X)))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X)))) (let ((_let_2 (= X tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y4)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y4)))))))))
% 6.39/6.73 (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)))))))))))))))))))
% 6.39/6.73 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L3))))) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L3))) (@ 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 L3) K3))))))))))))
% 6.39/6.73 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N4 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.39/6.73 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.39/6.73 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 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 (= K3 tptp.zero_zero_int) (= L3 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L3) (@ (@ (@ tptp.if_int (= L3 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 6.39/6.73 (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)))))))))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y4)) (= X Y4))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X)) (@ _let_1 X)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.73 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)) (@ (@ tptp.ord_less_real X) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.39/6.73 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.semiri1314217659103216013at_int N)) N)))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.39/6.73 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.39/6.73 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.39/6.73 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.39/6.73 (assert (forall ((P Bool)) (= (@ tptp.nat2 (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) tptp.one_one_nat)))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.39/6.73 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((V tptp.num) (V2 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V2)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V2))))))
% 6.39/6.73 (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)))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X))))
% 6.39/6.73 (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)))
% 6.39/6.73 (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)))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_nat Y4)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N4)))))
% 6.39/6.73 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N4)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))))
% 6.39/6.73 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (not (= (@ tptp.exp_complex X) tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (not (= (@ tptp.exp_real X) tptp.zero_zero_real))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int) (R2 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 R2) S2)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L S2)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (exists ((X4 tptp.real)) (= (@ tptp.exp_real X4) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.39/6.73 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) Z)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y4) Ya)) Z)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) X))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y4))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.numeral_numeral_nat (lambda ((I2 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I2)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= tptp.sgn_sgn_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real X3) (@ tptp.abs_abs_real X3)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y4)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y4) (@ (@ tptp.times_times_complex Y4) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y4) (@ (@ tptp.times_times_real Y4) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y4)))))
% 6.39/6.73 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se1745604003318907178nteger N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se8260200283734997820nteger 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)))))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se1745604003318907178nteger N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2793503036327961859nteger 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)))))))))))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se1745604003318907178nteger N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se1345352211410354436nteger 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)))))))))))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M5) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y4))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y4) Y4))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y4) Ya)) Z)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) Z)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.39/6.73 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y4) (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 Y4) tptp.one_one_real)) (= (@ tptp.exp_real X4) Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y4)) X)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y4)) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y4)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y4)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y4))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.73 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.73 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y4) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.39/6.73 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.73 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X) (=> (= X (@ (@ 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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X)))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X)))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ tptp.sqrt X) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y4)))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) Y4) (= X tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) X) (= Y4 tptp.zero_zero_real)))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))) (@ (@ tptp.plus_plus_real X) Y4))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 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 K3)) (not (@ _let_2 L3))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X 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) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y4))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 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 K3) _let_1))) _let_1)))))
% 6.39/6.73 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X2)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (U tptp.real) (Y4 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 X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y4)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))) U))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ 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 X) _let_1))) N)) (@ tptp.exp_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X) _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 X) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L3 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L3))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L3))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K3) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) _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 L3) K3))))) _let_2)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (U tptp.real) (Y4 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 X) _let_4) (=> (@ (@ tptp.ord_less_real Y4) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y4) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))) U)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((Xs tptp.list_nat) (Y4 tptp.nat)) (=> (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 Xs))) (=> (@ (@ tptp.member_nat X4) _let_1) (=> (@ (@ tptp.member_nat Y) _let_1) (= X4 Y))))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (= X4 Y4))) (= (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) Xs) tptp.zero_zero_nat) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) Y4))))))
% 6.39/6.73 (assert (forall ((X 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) X) (= (@ (@ tptp.log _let_1) X) (@ (@ 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 X)))))))
% 6.39/6.73 (assert (forall ((X 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) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))))
% 6.39/6.73 (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))))))))))))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_real X) Y4)))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X 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 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X) Y4)))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.39/6.73 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) tptp.zero_zero_nat)))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) tptp.one_one_nat)))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (not (= tptp.pi tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X4 tptp.num)) (=> (@ P X4) (@ P (@ tptp.inc X4)))) (@ P X)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y4)) (@ tptp.inc (@ _let_1 Y4))))))
% 6.39/6.73 (assert (= tptp.log (lambda ((A3 tptp.real) (X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) (@ tptp.ln_ln_real A3)))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.39/6.73 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.39/6.73 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.39/6.73 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y4)) (@ (@ tptp.plus_plus_num (@ _let_1 Y4)) X)))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real) (X 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) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X)) tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y4)))))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y4)))))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X)))))))
% 6.39/6.73 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.39/6.73 (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)))
% 6.39/6.73 (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)))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real) (X 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 X) (= (@ (@ tptp.log A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X)))))))))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.39/6.73 (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))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))
% 6.39/6.73 (assert (forall ((Y4 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 Y4))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y4))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.39/6.73 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M5 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 M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M5 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 M5)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (assert (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.73 (assert (= (@ tptp.archim6058952711729229775r_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.39/6.73 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.39/6.73 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.39/6.73 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.39/6.73 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.39/6.73 (assert (= (@ tptp.archim7802044766580827645g_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.39/6.73 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.39/6.73 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.39/6.73 (assert (= (@ tptp.sin_real tptp.pi) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.sin_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X))) (let ((_let_2 (@ tptp.cos_complex X))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (let ((_let_2 (@ tptp.cos_real X))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) tptp.one_one_int) (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.39/6.73 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.39/6.73 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) tptp.one_one_complex))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1)) tptp.one_one_complex))))
% 6.39/6.73 (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)))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.39/6.73 (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))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim7802044766580827645g_real X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim2889992004027027881ng_rat X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (exists ((R3 tptp.real) (A4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X (@ _let_1 (@ tptp.cos_real A4))) (= Y4 (@ _let_1 (@ tptp.sin_real A4))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.sin_real Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.cos_complex X) tptp.one_one_complex) (= (@ tptp.sin_complex X) tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (= (@ tptp.cos_real X) tptp.one_one_real) (= (@ tptp.sin_real X) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (=> (= (@ tptp.sin_complex X) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X))) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X))) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X))) (@ tptp.cos_complex X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X))) (@ tptp.cos_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (exists ((Y tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ tptp.sin_real Y) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y) (@ tptp.cos_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y4)) (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y4)) (@ tptp.archim7802044766580827645g_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (not (= (@ tptp.cos_real (@ tptp.arctan X)) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4))))) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim6058952711729229775r_real Y4))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y4))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y4)))))
% 6.39/6.73 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R2) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R2))))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R2))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) Y4))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim7802044766580827645g_real Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y4))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y4) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4)) (@ _let_1 X))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y4)) (= X Y4)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X 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)) X)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X)) _let_2)))))))
% 6.39/6.73 (assert (forall ((X 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)) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X)) _let_2)))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R2)))) R2))))
% 6.39/6.73 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R2)))) R2))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 6.39/6.73 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 6.39/6.73 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y4)) (@ (@ tptp.ord_less_real Y4) X)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.pi) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y4)) (@ tptp.cos_real X)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _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) (= X (@ tptp.cos_real T3)) (= Y4 (@ tptp.sin_real T3)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ 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 X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ 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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ 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)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.39/6.73 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.39/6.73 (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 ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real Y3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y3) tptp.zero_zero_real)) (= Y3 X4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y4)) (@ tptp.cos_real X)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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) Y4) (forall ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.cos_real Y3) Y4)) (= Y3 X4)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) (=> (@ _let_2 Y4) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _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)))) (= X (@ tptp.cos_real T3)) (= Y4 (@ tptp.sin_real T3)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _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)) (= X (@ tptp.cos_real T3)) (= Y4 (@ tptp.sin_real T3))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _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)) (=> (= X (@ tptp.cos_real T3)) (not (= Y4 (@ tptp.sin_real T3))))))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X 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)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y4)) (@ tptp.sin_real X))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (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 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4)) (@ _let_1 Y4)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y4)) (= X Y4))))))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X)) (@ (@ 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))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.cos_real X))) (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 X)) (@ (@ 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))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X 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)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y4)) (@ tptp.sin_real X))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y4)) (@ (@ tptp.ord_less_real X) Y4))))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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) Y4) (forall ((Y3 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)) Y3) (@ (@ tptp.ord_less_eq_real Y3) _let_1) (= (@ tptp.sin_real Y3) Y4)) (= Y3 X4)))))))))))
% 6.39/6.73 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.39/6.73 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X3 tptp.nat)) (= X (@ (@ 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)) (= X (@ 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))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) 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) (= X (@ (@ 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) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) 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)) (= X (@ (@ 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)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_complex X) 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)))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X))) (=> (not (= (@ tptp.cos_real X) 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)))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ 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)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ 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 X)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.39/6.73 (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)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.39/6.73 (assert (forall ((W tptp.real) (Z tptp.real)) (= (= (@ (@ tptp.powr_real W) Z) tptp.zero_zero_real) (= W tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.powr_real tptp.zero_zero_real) Z) tptp.zero_zero_real)))
% 6.39/6.73 (assert (= (@ tptp.tan_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.arcsin tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X) tptp.zero_zero_real))) (let ((_let_2 (= X tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) A)) (not (= X tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.73 (assert (= (@ tptp.tan_real tptp.pi) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y4)) Y4)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y4)) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N))))))
% 6.39/6.73 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.zero_zero_complex (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y4) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y4))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) A))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) A)))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y4) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ _let_1 (@ (@ tptp.powr_real X) Y4)))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real) (Y4 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 X) (@ _let_1 Y4)) (= X Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 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) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) B))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y4)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) A))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y4)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y4) A))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y4)) (@ (@ tptp.times_times_real Y4) (@ tptp.ln_ln_real X))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) B)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (B tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y4)) (@ (@ tptp.times_times_real Y4) (@ _let_1 X)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y4)) (= X Y4))))))
% 6.39/6.73 (assert (= tptp.tan_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X3)) (@ tptp.cos_complex X3)))))
% 6.39/6.73 (assert (= tptp.tan_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X3)) (@ tptp.cos_real X3)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) N)))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y4)) X) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.log B) X)))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y4)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y4))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y4) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y4)))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y4)) X))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y4)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y4)) (@ (@ tptp.ord_less_real X) Y4))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y4)) X))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y4) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y4)))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y4))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y4)) X) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.log B) X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 6.39/6.73 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 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 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y4)))))))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 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 X) (= (@ (@ tptp.plus_plus_real Y4) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y4)) X))))))))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 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 X) (= (@ (@ tptp.minus_minus_real Y4) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y4)) X))))))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 6.39/6.73 (assert (= tptp.powr_real (lambda ((X3 tptp.real) (A3 tptp.real)) (@ (@ (@ tptp.if_real (= X3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A3) (@ tptp.ln_ln_real X3)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (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 Y4) (@ tptp.tan_real X4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.39/6.73 (assert (forall ((Y4 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) Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (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 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4)) (@ _let_1 Y4)))))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y4))) (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 Y4) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y4)) (@ tptp.tan_real X))))))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X 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)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y4)) (@ tptp.tan_real X))))))))
% 6.39/6.73 (assert (forall ((Y4 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) Y4) (forall ((Y3 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)) Y3) (@ (@ tptp.ord_less_real Y3) _let_1) (= (@ tptp.tan_real Y3) Y4)) (= Y3 X4)))))))))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y4)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y4)))))
% 6.39/6.73 (assert (forall ((B tptp.real) (X tptp.real) (Y4 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 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y4))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y4))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X)) (@ tptp.tan_complex Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y4))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (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) Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ 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 X))) tptp.one_one_real))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y4) (= (@ tptp.arctan Y4) X)))))))
% 6.39/6.73 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arctan Y4))) (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) Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y4))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (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 X)) (@ tptp.tan_complex Y4))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) Y4))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y4))) (let ((_let_2 (@ tptp.cos_real X))) (=> (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 X)) (@ tptp.tan_real Y4))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) Y4))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y4))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X) Y4))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y4) 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))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y4))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_real X) Y4))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y4) 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))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y4))) (let ((_let_2 (@ tptp.tan_complex X))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X) Y4))) (=> (not (= (@ tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y4) 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))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y4))) (let ((_let_2 (@ tptp.tan_real X))) (let ((_let_3 (@ (@ tptp.plus_plus_real X) Y4))) (=> (not (= (@ tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y4) 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))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z2 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)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_real Y4) 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))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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 Y4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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))))))))
% 6.39/6.73 (assert (forall ((X 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y4))) (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)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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) Y4))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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) Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y4) (@ _let_1 (@ tptp.sin_real Y4)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y4))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y4) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y4)) X))))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((W tptp.int) (Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real W) (@ tptp.ring_1_of_int_real Z)) (= W Z))))
% 6.39/6.73 (assert (forall ((W tptp.int) (Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex W) (@ tptp.ring_17405671764205052669omplex Z)) (= W Z))))
% 6.39/6.73 (assert (forall ((W tptp.int) (Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat W) (@ tptp.ring_1_of_int_rat Z)) (= W Z))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_real N4))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N4))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_rat N4))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)) X) (exists ((N4 tptp.int)) (= X (@ tptp.ring_1_of_int_real N4))))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z)) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 6.39/6.73 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.39/6.73 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 6.39/6.73 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.zero_zero_real) tptp.zero_zero_complex))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X) tptp.zero_zero_complex) (= X tptp.zero_zero_real))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.39/6.73 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.39/6.73 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.39/6.73 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger Z)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y4)))))
% 6.39/6.73 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y4)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri8010041392384452111omplex N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri5074537144036343181t_real N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri681578069525770553at_rat N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y4)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri8010041392384452111omplex N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int X)))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger X)))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real X)))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat X)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_real (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.39/6.73 (assert (forall ((P Bool)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.39/6.73 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_rat (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.39/6.73 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((P Bool)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.39/6.73 (assert (= (@ tptp.sin_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.sin_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.zero_zero_complex))
% 6.39/6.73 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X)) Z))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X)) Z))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) Z))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X)) Z))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X 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 X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X 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 X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X 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 X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.ring_17405671764205052669omplex Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.ring_1_of_int_real Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.ring_1_of_int_rat Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y4) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= (@ tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.39/6.73 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 Z)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y4)) Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X 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 X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X 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 X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y4) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= (@ tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y4) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N) (@ tptp.ring_1_of_int_real Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N) (@ tptp.ring_17405671764205052669omplex Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N) (@ tptp.ring_18347121197199848620nteger Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N) (@ tptp.ring_1_of_int_rat Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y4))))
% 6.39/6.73 (assert (forall ((X 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 X)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X) (@ tptp.numeral_numeral_real B))))))
% 6.39/6.73 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.39/6.73 (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))
% 6.39/6.73 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.39/6.73 (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))
% 6.39/6.73 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.39/6.73 (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)))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.39/6.73 (assert (forall ((X 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 X))) 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 X))) N)) A))))
% 6.39/6.73 (assert (forall ((X 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 X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.39/6.73 (assert (forall ((X 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 X))) 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 X))) N)) A))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((A tptp.int) (X 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 X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.39/6.73 (assert (forall ((X 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 X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.39/6.73 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z2)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y4) (@ (@ tptp.times_times_complex Y4) _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ (@ tptp.times_times_real Y4) _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ (@ tptp.times_times_rat Y4) _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ (@ tptp.times_times_int Y4) _let_1)))))
% 6.39/6.73 (assert (forall ((M tptp.int) (X 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 X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X)))))))
% 6.39/6.73 (assert (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))))
% 6.39/6.73 (assert (forall ((M tptp.int) (X 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 X))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X)))))))
% 6.39/6.73 (assert (forall ((M tptp.int) (X tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X))) X)))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))) X)))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))))
% 6.39/6.73 (assert (= tptp.real_V4546457046886955230omplex (lambda ((R5 tptp.real)) (@ (@ tptp.complex2 R5) tptp.zero_zero_real))))
% 6.39/6.73 (assert (= tptp.real_V4546457046886955230omplex (lambda ((X3 tptp.real)) (@ (@ tptp.complex2 X3) tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real) (Xa tptp.real)) (= (= (@ (@ tptp.complex2 X) Y4) (@ tptp.real_V4546457046886955230omplex Xa)) (and (= X Xa) (= Y4 tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((R2 tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X) Y4)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y4)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R2)) (@ (@ tptp.times_times_real Y4) R2)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X)) (@ tptp.real_V1803761363581548252l_real Y4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X)) (@ tptp.real_V4546457046886955230omplex Y4))))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) A))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X)) A))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (=> (= X (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (=> (= X (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) (@ tptp.arccos X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y4)) (= X Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y4)) (@ (@ tptp.ord_less_eq_real Y4) X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y3) tptp.one_one_int)))) (= Y3 X4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y3)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y3) tptp.one_one_int)))) (= Y3 X4)))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.39/6.73 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R2))) (@ (@ tptp.plus_plus_rat R2) tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) (@ (@ tptp.plus_plus_real R2) tptp.one_one_real))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.39/6.73 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R2))) tptp.one_one_rat)) R2)))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R2))) tptp.one_one_real)) R2)))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 6.39/6.73 (assert (= tptp.ord_less_eq_int (lambda ((N4 tptp.int) (M5 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N4)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M5)) tptp.one_one_real)))))
% 6.39/6.73 (assert (= tptp.ord_less_int (lambda ((N4 tptp.int) (M5 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 M5)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) tptp.pi))))))
% 6.39/6.73 (assert (forall ((Theta tptp.real)) (not (forall ((K2 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 K2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.39/6.73 (assert (forall ((X 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 X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y4)) (@ tptp.arccos X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y4)) (@ (@ tptp.ord_less_real Y4) X))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) tptp.pi)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 6.39/6.73 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (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 I2)))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (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 I2)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) Z))))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X) Z))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y4)) Y4))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I2))) (=> (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 I2)))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I2 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I2))) (=> (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 I2)))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1))))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X 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)) X) (=> (@ (@ tptp.ord_less_eq_rat X) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X) Z))))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X 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)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.archim7802044766580827645g_real X) Z))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real X) _let_1)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) Z) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X)) Z) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 6.39/6.73 (assert (forall ((Z tptp.int) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X 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 X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X 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 X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X)))) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.real) (P5 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 P5) Q2)))) Q2)) P5))))
% 6.39/6.73 (assert (forall ((Q2 tptp.rat) (P5 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 P5) Q2)))) Q2)) P5))))
% 6.39/6.73 (assert (forall ((Q2 tptp.rat) (P5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_eq_rat P5) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P5) Q2)))) Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_eq_real P5) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P5) Q2)))) Q2)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 6.39/6.73 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))
% 6.39/6.73 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))
% 6.39/6.73 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K3))))))
% 6.39/6.73 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))
% 6.39/6.73 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))
% 6.39/6.73 (assert (forall ((Q2 tptp.real) (P5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q2) (@ (@ tptp.ord_less_real P5) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P5) Q2)))) tptp.one_one_real)) Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.rat) (P5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q2) (@ (@ tptp.ord_less_rat P5) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P5) Q2)))) tptp.one_one_rat)) Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.real) (P5 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 P5) Q2)))) tptp.one_one_real)) Q2)) P5))))
% 6.39/6.73 (assert (forall ((Q2 tptp.rat) (P5 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 P5) Q2)))) tptp.one_one_rat)) Q2)) P5))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.39/6.73 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X3 tptp.int)) (= X (@ (@ 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))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) 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) Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I2) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ 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) X) (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)))))))))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 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 Y4))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 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 Y4))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ 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 X) N))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ 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 X) N))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) X))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ 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 X)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) (@ (@ 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 X)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X) (@ (@ 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 X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ 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 X)))))
% 6.39/6.73 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.39/6.73 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.39/6.73 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.39/6.73 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X)) (@ tptp.archim8280529875227126926d_real Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X)) (@ tptp.archim8280529875227126926d_real X))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim7778729529865785530nd_rat X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X)) (@ tptp.archim7802044766580827645g_real X))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))
% 6.39/6.73 (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))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X)) tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X))))
% 6.39/6.73 (assert (= (@ tptp.cot_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.cot_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (@ tptp.archim2898591450579166408c_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (= (@ tptp.archimedean_frac_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat)))
% 6.39/6.73 (assert (= (@ tptp.cot_real tptp.pi) tptp.zero_zero_real))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.39/6.73 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (not (= tptp.imaginary_unit tptp.zero_zero_complex)))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X))))
% 6.39/6.73 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (= (@ (@ tptp.complex2 X) Y4) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y4 tptp.one_one_real)))))
% 6.39/6.73 (assert (= tptp.archim2898591450579166408c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real X3) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X3))))))
% 6.39/6.73 (assert (= tptp.archimedean_frac_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat X3) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X3))))))
% 6.39/6.73 (assert (= tptp.cot_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X3)) (@ tptp.sin_complex X3)))))
% 6.39/6.73 (assert (= tptp.cot_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X3)) (@ tptp.sin_real X3)))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.39/6.73 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) X) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) X) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X)) (@ tptp.archim2898591450579166408c_real Y4)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X) Y4)))) (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)))))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y4)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) Y4)))) (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)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.cot_real X))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.39/6.73 (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)))
% 6.39/6.73 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N4))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ 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 K3) N4))))))))
% 6.39/6.73 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 6.39/6.73 (assert (= (@ tptp.csqrt tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.39/6.73 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.39/6.73 (assert (forall ((Z tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ tptp.cis (@ tptp.arg Z)) (@ tptp.sgn_sgn_complex Z)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.39/6.73 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N) (@ (@ tptp.bit_se1148574629649215175it_nat M) N))))
% 6.39/6.73 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N))))))
% 6.39/6.73 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((M tptp.nat) (A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.bit_se8260200283734997820nteger M) A)) N) (and (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (= M N))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (not (= (@ tptp.cis A) tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N)))))
% 6.39/6.73 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.39/6.73 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.39/6.73 (assert (forall ((B Bool) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N) (and B (= N tptp.zero_zero_nat)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((Z tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z) X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A3) N4)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N4) A3))))
% 6.39/6.73 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A3) N4)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N4) A3))))
% 6.39/6.73 (assert (= tptp.bit_se1345352211410354436nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (@ (@ (@ (@ (@ tptp.if_nat5617392847756311170nteger (@ (@ tptp.bit_se9216721137139052372nteger A3) N4)) tptp.bit_se8260200283734997820nteger) tptp.bit_se2793503036327961859nteger) N4) A3))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= (@ tptp.arg tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N4) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4)))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (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))))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (=> (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (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))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((K tptp.int)) (not (forall ((N2 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 N2) M2) (= (@ _let_1 M2) (@ _let_1 N2))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (not (@ _let_1 N2)))))))))))
% 6.39/6.73 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 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 A3) (@ (@ tptp.power_8256067586552552935nteger _let_1) N4))))))))
% 6.39/6.73 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 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 A3) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 6.39/6.73 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 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 A3) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 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 K3) (@ (@ tptp.power_power_int _let_1) N4))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (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))))))))))
% 6.39/6.73 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 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) A3))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A3) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 6.39/6.73 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 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) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A3) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 6.39/6.73 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 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) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A3) _let_1)) (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)))))))))
% 6.39/6.73 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N4)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 6.39/6.73 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N4))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ 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) X) (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)))))))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A)))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.39/6.73 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.39/6.73 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X))) (= (@ _let_1 (@ _let_1 Y4)) Y4))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.73 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.39/6.73 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.inverse_inverse_real X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X) tptp.one_one_complex) (= X tptp.one_one_complex))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X) tptp.one_one_rat) (= X tptp.one_one_rat))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.39/6.73 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.39/6.73 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) X) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.inverse_inverse_real _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.sgn_sgn_real A)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.sgn_sgn_complex A)))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.sgn_sgn_rat A)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.39/6.73 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.39/6.73 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.39/6.73 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.39/6.73 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.39/6.73 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.39/6.73 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) tptp.zero_zero_rat) (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X)) (not (@ (@ tptp.member_real X) tptp.ring_1_Ints_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X)) (not (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y4))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 6.39/6.73 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.39/6.73 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_nat Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_nat Y4)))))))
% 6.39/6.73 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y4)))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.real_V1803761363581548252l_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.inverse_inverse_real X)) (@ tptp.invers8013647133539491842omplex (@ tptp.real_V4546457046886955230omplex X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (@ (@ tptp.member_complex tptp.zero_zero_complex) tptp.ring_1_Ints_complex))
% 6.39/6.73 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.ring_1_Ints_real))
% 6.39/6.73 (assert (@ (@ tptp.member_rat tptp.zero_zero_rat) tptp.ring_1_Ints_rat))
% 6.39/6.73 (assert (@ (@ tptp.member_int tptp.zero_zero_int) tptp.ring_1_Ints_int))
% 6.39/6.73 (assert (forall ((N tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex N)) tptp.ring_1_Ints_complex)))
% 6.39/6.73 (assert (forall ((N tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real N)) tptp.ring_1_Ints_real)))
% 6.39/6.73 (assert (forall ((N tptp.num)) (@ (@ tptp.member_rat (@ tptp.numeral_numeral_rat N)) tptp.ring_1_Ints_rat)))
% 6.39/6.73 (assert (forall ((N tptp.num)) (@ (@ tptp.member_int (@ tptp.numeral_numeral_int N)) tptp.ring_1_Ints_int)))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat))
% 6.39/6.73 (assert (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int))
% 6.39/6.73 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 6.39/6.73 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.ring_1_Ints_complex))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer (@ tptp.uminus1351360451143612070nteger A)) tptp.ring_11222124179247155820nteger))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.uminus_uminus_real X)) tptp.ring_1_Ints_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (= (@ (@ tptp.member_int (@ tptp.uminus_uminus_int X)) tptp.ring_1_Ints_int) (@ (@ tptp.member_int X) tptp.ring_1_Ints_int))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.member_complex (@ tptp.uminus1482373934393186551omplex X)) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex X) tptp.ring_1_Ints_complex))))
% 6.39/6.73 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.member_Code_integer (@ tptp.uminus1351360451143612070nteger X)) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.member_rat (@ tptp.uminus_uminus_rat X)) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)) K))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)) K))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.gbinomial_nat N) K)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)) K))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat B2) A3))))
% 6.39/6.73 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int B2) A3))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.39/6.73 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.39/6.73 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.39/6.73 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y4))) (let ((_let_2 (@ tptp.times_times_real X))) (=> (= (@ (@ tptp.times_times_real Y4) X) (@ _let_2 Y4)) (= (@ (@ tptp.times_times_real _let_1) X) (@ _let_2 _let_1)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.complex) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y4))) (let ((_let_2 (@ tptp.times_times_complex X))) (=> (= (@ (@ tptp.times_times_complex Y4) X) (@ _let_2 Y4)) (= (@ (@ tptp.times_times_complex _let_1) X) (@ _let_2 _let_1)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y4))) (let ((_let_2 (@ tptp.times_times_rat X))) (=> (= (@ (@ tptp.times_times_rat Y4) X) (@ _let_2 Y4)) (= (@ (@ tptp.times_times_rat _let_1) X) (@ _let_2 _let_1)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.ring_1_Ints_complex)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_real (@ tptp.semiri5074537144036343181t_real N)) tptp.ring_1_Ints_real)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.ring_1_Ints_rat)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N)) tptp.ring_1_Ints_int)))
% 6.39/6.73 (assert (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se6526347334894502574or_int Y4) Z)) X) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.bit_se725231765392027082nd_int Y4) X)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X)))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int Y4) Z)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ tptp.abs_abs_int A)) tptp.ring_1_Ints_int))))
% 6.39/6.73 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer (@ tptp.abs_abs_Code_integer A)) tptp.ring_11222124179247155820nteger))))
% 6.39/6.73 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ tptp.abs_abs_rat A)) tptp.ring_1_Ints_rat))))
% 6.39/6.73 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ tptp.abs_abs_real A)) tptp.ring_1_Ints_real))))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (@ (@ tptp.member_int (@ tptp.ring_1_of_int_int Z)) tptp.ring_1_Ints_int)))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (@ (@ tptp.member_real (@ tptp.ring_1_of_int_real Z)) tptp.ring_1_Ints_real)))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (@ (@ tptp.member_complex (@ tptp.ring_17405671764205052669omplex Z)) tptp.ring_1_Ints_complex)))
% 6.39/6.73 (assert (forall ((Z tptp.int)) (@ (@ tptp.member_rat (@ tptp.ring_1_of_int_rat Z)) tptp.ring_1_Ints_rat)))
% 6.39/6.73 (assert (forall ((Q2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int Q2) tptp.ring_1_Ints_int) (=> (forall ((Z2 tptp.int)) (@ P (@ tptp.ring_1_of_int_int Z2))) (@ P Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.real) (P (-> tptp.real Bool))) (=> (@ (@ tptp.member_real Q2) tptp.ring_1_Ints_real) (=> (forall ((Z2 tptp.int)) (@ P (@ tptp.ring_1_of_int_real Z2))) (@ P Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.complex) (P (-> tptp.complex Bool))) (=> (@ (@ tptp.member_complex Q2) tptp.ring_1_Ints_complex) (=> (forall ((Z2 tptp.int)) (@ P (@ tptp.ring_17405671764205052669omplex Z2))) (@ P Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.rat) (P (-> tptp.rat Bool))) (=> (@ (@ tptp.member_rat Q2) tptp.ring_1_Ints_rat) (=> (forall ((Z2 tptp.int)) (@ P (@ tptp.ring_1_of_int_rat Z2))) (@ P Q2)))))
% 6.39/6.73 (assert (forall ((Q2 tptp.int)) (=> (@ (@ tptp.member_int Q2) tptp.ring_1_Ints_int) (not (forall ((Z2 tptp.int)) (not (= Q2 (@ tptp.ring_1_of_int_int Z2))))))))
% 6.39/6.73 (assert (forall ((Q2 tptp.real)) (=> (@ (@ tptp.member_real Q2) tptp.ring_1_Ints_real) (not (forall ((Z2 tptp.int)) (not (= Q2 (@ tptp.ring_1_of_int_real Z2))))))))
% 6.39/6.73 (assert (forall ((Q2 tptp.complex)) (=> (@ (@ tptp.member_complex Q2) tptp.ring_1_Ints_complex) (not (forall ((Z2 tptp.int)) (not (= Q2 (@ tptp.ring_17405671764205052669omplex Z2))))))))
% 6.39/6.73 (assert (forall ((Q2 tptp.rat)) (=> (@ (@ tptp.member_rat Q2) tptp.ring_1_Ints_rat) (not (forall ((Z2 tptp.int)) (not (= Q2 (@ tptp.ring_1_of_int_rat Z2))))))))
% 6.39/6.73 (assert (forall ((R2 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V7735802525324610683m_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X))) (@ tptp.inverse_inverse_real R2))))))
% 6.39/6.73 (assert (forall ((R2 tptp.real) (X tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R2) (@ tptp.real_V1022390504157884413omplex X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X))) (@ tptp.inverse_inverse_real R2))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.39/6.73 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 6.39/6.73 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.39/6.73 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.39/6.73 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 6.39/6.73 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) A3))))
% 6.39/6.73 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) A3))))
% 6.39/6.73 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B2)) A3))))
% 6.39/6.73 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.39/6.73 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.39/6.73 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))))
% 6.39/6.73 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.39/6.73 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.39/6.73 (assert (= tptp.divide_divide_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat A3) (@ tptp.inverse_inverse_rat B2)))))
% 6.39/6.73 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.39/6.73 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.39/6.73 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.39/6.73 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.39/6.73 (assert (forall ((Xa tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.39/6.73 (assert (forall ((Xa tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.39/6.73 (assert (forall ((Xa tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X) (@ (@ tptp.times_times_rat X) _let_1)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((Xa tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X) (@ (@ tptp.times_times_real X) _let_1)))))
% 6.39/6.73 (assert (forall ((Xa tptp.int) (X tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X) (@ (@ tptp.times_times_complex X) _let_1)))))
% 6.39/6.73 (assert (forall ((Xa tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa)))) (= (@ (@ tptp.times_times_rat _let_1) X) (@ (@ tptp.times_times_rat X) _let_1)))))
% 6.39/6.73 (assert (= tptp.divide_divide_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (@ (@ tptp.times_times_real X3) (@ tptp.inverse_inverse_real Y6)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex N)) K))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N)) K))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N) K)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)) K))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.39/6.73 (assert (forall ((Y4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y4)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y4) A))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) X)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)))) X)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (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)))))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D2) E) (=> (@ P D2) (@ P E)))) (=> (forall ((N2 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 6.39/6.73 (assert (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (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) E2)))))))
% 6.39/6.73 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D2 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D2) E) (=> (@ P D2) (@ P E)))) (=> (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (not (= X tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X))))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (not (= X tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer) (= X tptp.zero_z3403309356797280102nteger)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat) (= X tptp.zero_zero_rat)))))
% 6.39/6.73 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int) (= X tptp.zero_zero_int)))))
% 6.39/6.73 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y4) tptp.ring_11222124179247155820nteger) (= (= X Y4) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Y4))) tptp.one_one_Code_integer))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.member_real X) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y4) tptp.ring_1_Ints_real) (= (= X Y4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y4))) tptp.one_one_real))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y4) tptp.ring_1_Ints_rat) (= (= X Y4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) Y4))) tptp.one_one_rat))))))
% 6.39/6.73 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y4) tptp.ring_1_Ints_int) (= (= X Y4) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Y4))) tptp.one_one_int))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2))) X))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N2))) X))))))
% 6.39/6.73 (assert (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (not (= X 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 X)) M))))))))
% 6.39/6.73 (assert (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (not (= X 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 X)) M))))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X 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 X)) M))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((A tptp.real) (X 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 X) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ (@ tptp.member_real X) 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 X)))))))))
% 6.39/6.73 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X)))) (let ((_let_2 (@ (@ tptp.member_rat X) 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 X)))))))))
% 6.39/6.73 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M5 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 M5) (@ (@ tptp.power_power_nat _let_1) N4))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K3)) A3)) tptp.one_one_complex)) K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K3)) A3)) tptp.one_one_real)) K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K3)) A3)) tptp.one_one_rat)) K3)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ 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))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (assert (forall ((X tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X) 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)))))
% 6.39/6.73 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X) 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)))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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))))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X)))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A3)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A3)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A3)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.39/6.73 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M5) _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 M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.39/6.73 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 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 M5)) (not (@ _let_2 N4)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (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)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ 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))))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.cosh_real X) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.39/6.73 (assert (forall ((X tptp.complex)) (= (= (@ tptp.cosh_complex X) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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)))))
% 6.39/6.73 (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))))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.73 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.73 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se545348938243370406it_int N) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se547839408752420682it_nat N) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.39/6.73 (assert (= (@ tptp.sinh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.73 (assert (= (@ tptp.sinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (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))))))
% 6.39/6.73 (assert (forall ((N tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N) L))))
% 6.39/6.73 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.39/6.73 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))
% 6.39/6.73 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.39/6.73 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X)) (@ tptp.cosh_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X)) (@ tptp.sinh_real Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (not (= (@ tptp.cosh_real X) tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.tanh_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X3)) (@ tptp.cosh_complex X3)))))
% 6.39/6.74 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X3)) (@ tptp.cosh_real X3)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)) (@ tptp.uminus_uminus_real (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)) (@ tptp.uminus1482373934393186551omplex (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.cosh_real X)) (@ tptp.sinh_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.cosh_complex X)) (@ tptp.sinh_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y4))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4)) (@ _let_1 X)))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4)) (@ (@ tptp.ord_less_eq_real X) Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X))) (@ tptp.cosh_complex X))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X))) (@ tptp.cosh_real X))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M5) tptp.one_one_nat)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4)) (@ (@ tptp.ord_less_real Y4) X))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4)) (@ (@ tptp.ord_less_real X) Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y4))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) tptp.one_one_complex)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) tptp.one_one_real)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_1)) tptp.one_one_complex))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_1)) tptp.one_one_real))))
% 6.39/6.74 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.39/6.74 (assert (= tptp.bit_concat_bit (lambda ((N4 tptp.nat) (K3 tptp.int) (L3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N4) K3)) (@ (@ tptp.bit_se545348938243370406it_int N4) L3)))))
% 6.39/6.74 (assert (= tptp.bit_se1345352211410354436nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.bit_se3222712562003087583nteger A3) (@ (@ tptp.bit_se7788150548672797655nteger N4) tptp.one_one_Code_integer)))))
% 6.39/6.74 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.39/6.74 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)))))
% 6.39/6.74 (assert (forall ((X 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)) X)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X)) _let_2)))))))
% 6.39/6.74 (assert (forall ((X 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)) X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X)) _let_2)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (not (= (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.39/6.74 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (not (= (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)) tptp.zero_zero_nat)))))
% 6.39/6.74 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.times_times_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.times_times_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.times_times_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (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 ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.bit_se7788150548672797655nteger N) B3))))))))
% 6.39/6.74 (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 ((B3 tptp.int)) (not (= A (@ (@ tptp.bit_se545348938243370406it_int N) B3))))))))
% 6.39/6.74 (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 ((B3 tptp.nat)) (not (= A (@ (@ tptp.bit_se547839408752420682it_nat N) B3))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y4))) (let ((_let_2 (@ tptp.tanh_complex X))) (=> (not (= (@ tptp.cosh_complex X) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y4) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X) Y4)) (@ (@ 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))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y4))) (let ((_let_2 (@ tptp.tanh_real X))) (=> (not (= (@ tptp.cosh_real X) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y4) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X) Y4)) (@ (@ 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))))))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 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) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y4) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y4)) _let_1)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L3 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 K3)) (not (@ _let_2 L3)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L3 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 (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L3)) (@ (@ (@ tptp.if_int (= L3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L3) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.39/6.74 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.39/6.74 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.39/6.74 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I))))))
% 6.39/6.74 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I))))))
% 6.39/6.74 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.real Bool)) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_real (@ (@ tptp.replicate_real N) X)) I))))))
% 6.39/6.74 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (= (@ tptp.bit_ri7919022796975470100ot_int X) (@ tptp.bit_ri7919022796975470100ot_int Y4)) (= X Y4))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_ri7919022796975470100ot_int X)) X)))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int Y4)) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X)) Y4) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) tptp.zero_zero_int)))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) tptp.zero_zero_int)))
% 6.39/6.74 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.39/6.74 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.39/6.74 (assert (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.39/6.74 (assert (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (@ tptp.bit_ri7632146776885996613nteger X))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (@ tptp.bit_ri7919022796975470100ot_int X))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X)) X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X) (@ tptp.bit_ri7632146776885996613nteger X)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ tptp.inc N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.39/6.74 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A3)) tptp.one_one_Code_integer))))
% 6.39/6.74 (assert (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A3)) tptp.one_one_int))))
% 6.39/6.74 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A3)) tptp.one_one_Code_integer))))
% 6.39/6.74 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((A3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A3)) tptp.one_one_int))))
% 6.39/6.74 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A3) tptp.one_one_Code_integer)))))
% 6.39/6.74 (assert (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A3) tptp.one_one_int)))))
% 6.39/6.74 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.39/6.74 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int B) N2) (@ (@ tptp.bit_se1146084159140164899it_int A) N2))) (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.bit_ri7919022796975470100ot_int B))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int))))))
% 6.39/6.74 (assert (= tptp.bit_se8260200283734997820nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.bit_se3949692690581998587nteger A3) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.bit_se7788150548672797655nteger N4) tptp.one_one_Code_integer))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 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) K3))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K3) _let_1))))))))
% 6.39/6.74 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X8 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) N4) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X8 M5)) (@ X8 N4)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.39/6.74 (assert (forall ((Xs tptp.list_real)) (= (@ tptp.size_s6660260683639930848t_real (@ tptp.subseqs_real Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_real Xs)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.sinh_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X3)))))))
% 6.39/6.74 (assert (= tptp.sinh_real (lambda ((X3 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_real (@ tptp.exp_real X3)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X3)))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex) (B tptp.real)) (= (= (@ (@ tptp.real_V2046097035970521341omplex A) X) (@ (@ tptp.real_V2046097035970521341omplex B) X)) (or (= A B) (= X tptp.zero_zero_complex)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (= (= (@ (@ tptp.real_V1485227260804924795R_real A) X) (@ (@ tptp.real_V1485227260804924795R_real B) X)) (or (= A B) (= X tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((A tptp.real)) (= (@ (@ tptp.real_V2046097035970521341omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.39/6.74 (assert (forall ((A tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((X tptp.complex) (A tptp.real) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X))) (let ((_let_2 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ _let_2 Y4)) (@ _let_2 (@ _let_1 Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (A tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ _let_2 Y4)) (@ _let_2 (@ _let_1 Y4)))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_complex X) Y4))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 X)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X) Y4))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (or (= X Y4) (= A tptp.zero_zero_real))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (= (@ _let_1 X) (@ _let_1 Y4)) (or (= X Y4) (= A tptp.zero_zero_real))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex A) (@ (@ tptp.real_V2046097035970521341omplex B) X)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real A) B)) X))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real A) (@ (@ tptp.real_V1485227260804924795R_real B) X)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real A) B)) X))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.re (@ tptp.semiri8010041392384452111omplex N)) (@ tptp.semiri5074537144036343181t_real N))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex tptp.zero_zero_real) X) tptp.zero_zero_complex)))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real tptp.zero_zero_real) X) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex)) (= (= (@ (@ tptp.real_V2046097035970521341omplex A) X) tptp.zero_zero_complex) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_complex)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (= (= (@ (@ tptp.real_V1485227260804924795R_real A) X) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.39/6.74 (assert (forall ((U tptp.real) (A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.minus_minus_real tptp.one_one_real) U)) A)) (@ (@ tptp.real_V2046097035970521341omplex U) A)) A)))
% 6.39/6.74 (assert (forall ((U tptp.real) (A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real tptp.one_one_real) U)) A)) (@ (@ tptp.real_V1485227260804924795R_real U) A)) A)))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex A) X)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V1022390504157884413omplex X)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.real_V7735802525324610683m_real X)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((Z tptp.complex) (R2 tptp.real)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R2))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) R2))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.39/6.74 (assert (forall ((U tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V2046097035970521341omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.times_times_real _let_1) (@ tptp.numeral_numeral_real W))) A)))))
% 6.39/6.74 (assert (forall ((U tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V1485227260804924795R_real _let_2) (@ (@ tptp.times_times_real _let_1) A)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.times_times_real _let_2) _let_1)) A))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((Y4 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (= (@ tptp.re Y4) tptp.zero_zero_real) (= (@ tptp.cos_real (@ tptp.arg Y4)) tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real W)) _let_1)) A)))))
% 6.39/6.74 (assert (forall ((V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.times_times_real _let_2) A)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real _let_2) _let_1)) A))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real _let_2) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real _let_2) (@ tptp.numeral_numeral_real W))) _let_1)) A))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (let ((_let_2 (@ tptp.numeral_numeral_real W))) (let ((_let_3 (@ tptp.numeral_numeral_real U))) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real _let_3) _let_1)) (@ (@ tptp.times_times_real _let_2) A)) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real _let_3) _let_2)) _let_1)) A)))))))
% 6.39/6.74 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex A) A)) A)))
% 6.39/6.74 (assert (forall ((A tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real A) A)) A)))
% 6.39/6.74 (assert (forall ((X tptp.complex) (A tptp.real) (B tptp.real)) (=> (not (= X tptp.zero_zero_complex)) (=> (= (@ (@ tptp.real_V2046097035970521341omplex A) X) (@ (@ tptp.real_V2046097035970521341omplex B) X)) (= A B)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= X tptp.zero_zero_real)) (=> (= (@ (@ tptp.real_V1485227260804924795R_real A) X) (@ (@ tptp.real_V1485227260804924795R_real B) X)) (= A B)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.minus_minus_complex (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real X) Y4)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.re X)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex A))) (=> (not (= A tptp.zero_zero_real)) (=> (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4))))))
% 6.39/6.74 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.39/6.74 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) __flatten_var_0))))
% 6.39/6.74 (assert (= tptp.real_V1485227260804924795R_real (lambda ((R5 tptp.real) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real R5)) __flatten_var_0))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.minus_minus_real A) B)) X) (@ (@ tptp.minus_minus_complex (@ (@ tptp.real_V2046097035970521341omplex A) X)) (@ (@ tptp.real_V2046097035970521341omplex B) X)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B)) X) (@ (@ tptp.minus_minus_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) X)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real) (Xa tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.minus_minus_real X) Y4)) Xa) (@ (@ tptp.minus_minus_complex (@ (@ tptp.real_V2046097035970521341omplex X) Xa)) (@ (@ tptp.real_V2046097035970521341omplex Y4) Xa)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real) (Xa tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real X) Y4)) Xa) (@ (@ tptp.minus_minus_real (@ (@ tptp.real_V1485227260804924795R_real X) Xa)) (@ (@ tptp.real_V1485227260804924795R_real Y4) Xa)))))
% 6.39/6.74 (assert (= (@ tptp.re tptp.imaginary_unit) tptp.zero_zero_real))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.39/6.74 (assert (= (@ tptp.re tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y4)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) X))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B) C))))))
% 6.39/6.74 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_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))))))
% 6.39/6.74 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_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))))))
% 6.39/6.74 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_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)))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)))))))
% 6.39/6.74 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_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)))))))
% 6.39/6.74 (assert (forall ((U tptp.real) (V tptp.real) (A tptp.complex) (X tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex U) A) (@ (@ tptp.real_V2046097035970521341omplex V) X))))))))
% 6.39/6.74 (assert (forall ((U tptp.real) (V tptp.real) (A tptp.real) (X tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A) X) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real U) A) (@ (@ tptp.real_V1485227260804924795R_real V) X))))))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (U tptp.real) (V tptp.real) (A tptp.complex)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_complex)) (=> (not _let_1) (= (@ (@ tptp.real_V2046097035970521341omplex V) X) (@ (@ tptp.real_V2046097035970521341omplex U) A))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (U tptp.real) (V tptp.real) (A tptp.real)) (let ((_let_1 (= V tptp.zero_zero_real))) (= (= X (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real U) V)) A)) (and (=> _let_1 (= X tptp.zero_zero_real)) (=> (not _let_1) (= (@ (@ tptp.real_V1485227260804924795R_real V) X) (@ (@ tptp.real_V1485227260804924795R_real U) A))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.39/6.74 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (= A tptp.zero_zero_real))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) B)) tptp.zero_zero_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B)) (= A tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 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 X) Y4) (=> (@ _let_1 B) (=> (@ _let_1 X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real B) Y4)))))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real A) C)) (@ (@ tptp.real_V1485227260804924795R_real B) D)))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 6.39/6.74 (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.real_V1485227260804924795R_real A) B))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X)))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) tptp.zero_zero_real)))))
% 6.39/6.74 (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.real_V1485227260804924795R_real A) B))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) X)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_complex X) X))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.plus_plus_real X) X))))
% 6.39/6.74 (assert (forall ((M tptp.real) (Y4 tptp.complex) (X tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y4 (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex M) X)) C)) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y4)) (@ _let_1 C)) X))))))
% 6.39/6.74 (assert (forall ((M tptp.real) (Y4 tptp.real) (X tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y4 (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X)) C)) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ _let_1 C)) X))))))
% 6.39/6.74 (assert (forall ((M tptp.real) (X tptp.complex) (C tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.real_V2046097035970521341omplex M) X)) C) Y4) (= X (@ (@ tptp.minus_minus_complex (@ _let_1 Y4)) (@ _let_1 C))))))))
% 6.39/6.74 (assert (forall ((M tptp.real) (X tptp.real) (C tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X)) C) Y4) (= X (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ _let_1 C))))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.complex)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= X tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.real_V2046097035970521341omplex A) X)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real A)) (@ tptp.invers8013647133539491842omplex X)))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.real_V1485227260804924795R_real A) X)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real X)))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.39/6.74 (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.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X9) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M8 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X9 M2)) (@ X9 N6)))) E2))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X9) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M8 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X9 M2)) (@ X9 N6)))) E2))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.complex))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X9 M4)) (@ X9 N2)))) E)))))))) (@ tptp.topolo6517432010174082258omplex X9))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M9 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X9 M4)) (@ X9 N2)))) E)))))))) (@ tptp.topolo4055970368930404560y_real X9))))
% 6.39/6.74 (assert (= tptp.topolo6517432010174082258omplex (lambda ((X8 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M5)) (@ X8 N4)))) E3)))))))))))
% 6.39/6.74 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X8 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M7 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M7) N4) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M5)) (@ X8 N4)))) E3)))))))))))
% 6.39/6.74 (assert (= tptp.cosh_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex X3)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X3)))))))
% 6.39/6.74 (assert (= tptp.cosh_real (lambda ((X3 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real (@ tptp.exp_real X3)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X3)))))))
% 6.39/6.74 (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)))))))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.39/6.74 (assert (= tptp.divide1717551699836669952omplex (lambda ((X3 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y6))) (let ((_let_3 (@ tptp.re Y6))) (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)))))))))))
% 6.39/6.74 (assert (forall ((Z tptp.int)) (= (@ tptp.im (@ tptp.ring_17405671764205052669omplex Z)) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri5044797733671781792omplex N)) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((Z tptp.real)) (= (@ tptp.im (@ tptp.real_V4546457046886955230omplex Z)) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X) N)) tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri8010041392384452111omplex N)) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((Z tptp.complex) (R2 tptp.real)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.real_V4546457046886955230omplex R2))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) R2))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.re X)) N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (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 X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X)) (@ (@ tptp.times_times_real R2) (@ tptp.im X)))))
% 6.39/6.74 (assert (= (@ tptp.im tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.39/6.74 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y4)))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.ring_1_Ints_complex) (and (= (@ tptp.im Z) tptp.zero_zero_real) (exists ((I2 tptp.int)) (= (@ tptp.re Z) (@ tptp.ring_1_of_int_real I2)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y4))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y4))))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.im Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.re Z))))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.re Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.abs_abs_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y4)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y4)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y4)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y4))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y4))))))
% 6.39/6.74 (assert (= tptp.minus_minus_complex (lambda ((X3 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X3)) (@ tptp.re Y6))) (@ (@ tptp.minus_minus_real (@ tptp.im X3)) (@ tptp.im Y6))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.times_times_complex (lambda ((X3 tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.re Y6))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X3)))) (let ((_let_3 (@ tptp.im Y6))) (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))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X))) (@ tptp.im X))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (assert (forall ((Xs tptp.list_list_real) (N tptp.nat)) (=> (forall ((X4 tptp.list_real)) (=> (@ (@ tptp.member_list_real X4) (@ tptp.set_list_real2 Xs)) (= (@ tptp.size_size_list_real X4) N))) (= (@ tptp.size_size_list_real (@ tptp.concat_real Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s6660260683639930848t_real Xs)) N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 6.39/6.74 (assert (= (@ tptp.cnj tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.39/6.74 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X) Y4)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X)) (@ tptp.cnj Y4)))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) R2)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.re R2))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y4) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y4) X) (and (= X tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y4) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y4)) (and (= X tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))))
% 6.39/6.74 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) R2)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.re R2))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.real_V2521375963428798218omplex)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ (@ tptp.member_real (@ tptp.semiri5074537144036343181t_real N)) tptp.real_V470468836141973256s_real)))
% 6.39/6.74 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.real_V2521375963428798218omplex)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real A) B)) tptp.real_V470468836141973256s_real)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real A) B)) tptp.real_V470468836141973256s_real)))))
% 6.39/6.74 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.minus_minus_complex A) B)) tptp.real_V2521375963428798218omplex)))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.times_times_real A) B)) tptp.real_V470468836141973256s_real)))))
% 6.39/6.74 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.times_times_complex A) B)) tptp.real_V2521375963428798218omplex)))))
% 6.39/6.74 (assert (forall ((W tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex W)) tptp.real_V2521375963428798218omplex)))
% 6.39/6.74 (assert (forall ((W tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real W)) tptp.real_V470468836141973256s_real)))
% 6.39/6.74 (assert (@ (@ tptp.member_real tptp.zero_zero_real) tptp.real_V470468836141973256s_real))
% 6.39/6.74 (assert (@ (@ tptp.member_complex tptp.zero_zero_complex) tptp.real_V2521375963428798218omplex))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.real_V2521375963428798218omplex) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (=> (not (= B tptp.zero_zero_complex)) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.real_V2521375963428798218omplex))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (=> (not (= B tptp.zero_zero_real)) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real A) B)) tptp.real_V470468836141973256s_real))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ tptp.member_complex (@ (@ tptp.complex2 X) tptp.zero_zero_real)) tptp.real_V2521375963428798218omplex)))
% 6.39/6.74 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (not (= A tptp.zero_zero_real)) (@ (@ tptp.member_real (@ tptp.inverse_inverse_real A)) tptp.real_V470468836141973256s_real)))))
% 6.39/6.74 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (not (= A tptp.zero_zero_complex)) (@ (@ tptp.member_complex (@ tptp.invers8013647133539491842omplex A)) tptp.real_V2521375963428798218omplex)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L3 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 K3)) (not (@ _let_2 L3))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1)))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) B) _let_1))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) B) _let_1))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) A) A)))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) A) A)))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) A) A)))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) A)))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.zero_zero_int) A)))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8568078237143864401it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se8568078237143864401it_int N) A)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.plus_plus_nat M) N)) A))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat M) (@ (@ tptp.bit_se8570568707652914677it_nat N) A)) (@ (@ tptp.bit_se8570568707652914677it_nat (@ (@ tptp.plus_plus_nat M) N)) A))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se8568078237143864401it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se8568078237143864401it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se8568078237143864401it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X) _let_1))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (B Bool)) (= (@ (@ tptp.bit_se3928097537394005634nteger N) (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.zero_n356916108424825756nteger (and (= N tptp.zero_zero_nat) B)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (B Bool)) (= (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.zero_n2684676970156552555ol_int (and (= N tptp.zero_zero_nat) B)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (B Bool)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.zero_n2687167440665602831ol_nat (and (= N tptp.zero_zero_nat) B)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y4)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.bit_ri7919022796975470100ot_int Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.bit_ri7919022796975470100ot_int Y4)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.numeral_numeral_int K)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.numeral_numeral_nat K)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.numeral_numeral_int K)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.numeral_numeral_nat K)))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger (@ tptp.bit_ri7632146776885996613nteger X)) X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int X)) X) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger X) (@ tptp.bit_ri7632146776885996613nteger X)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X) (@ tptp.bit_ri7919022796975470100ot_int X)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se3928097537394005634nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8568078237143864401it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4)))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X)))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.39/6.74 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K)))))
% 6.39/6.74 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K)))))
% 6.39/6.74 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K)))))
% 6.39/6.74 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ 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 X)) (@ tptp.numeral_numeral_int Y4)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y4)))))))
% 6.39/6.74 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int B))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat B))) (let ((_let_2 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.39/6.74 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int B2) A3))))
% 6.39/6.74 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat B2) A3))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int B) C))))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat B) C))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int Y4) Z)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int X))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int Y4) Z)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y4) Z)) X) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y4) X)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X)))))
% 6.39/6.74 (assert (forall ((Y4 tptp.int) (Z tptp.int) (X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y4) Z)) X) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y4) X)) (@ (@ tptp.bit_se1409905431419307370or_int Z) X)))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X) tptp.zero_zero_int) X)))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.bit_se1409905431419307370or_int A) B) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.bit_se1412395901928357646or_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int A) B)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N) (@ (@ tptp.bit_se1146084159140164899it_int B) N)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) N) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))))
% 6.39/6.74 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M5)) (@ tptp.semiri1314217659103216013at_int N4))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se8570568707652914677it_nat M) N)) (@ (@ tptp.bit_se8568078237143864401it_int M) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat M))) (= (@ tptp.semiri1316708129612266289at_nat (@ _let_1 N)) (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se8570568707652914677it_nat N) M)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se1412395901928357646or_nat M) N)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se1412395901928357646or_nat M) N)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y4)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (=> (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))) (= (@ (@ tptp.plus_plus_int A) B) (@ (@ tptp.bit_se1409905431419307370or_int A) B)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (forall ((N2 tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))) (= (@ (@ tptp.plus_plus_nat A) B) (@ (@ tptp.bit_se1412395901928357646or_nat A) B)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y4)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y4)) (@ (@ tptp.plus_plus_int X) Y4))))
% 6.39/6.74 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int A3)) (@ tptp.bit_ri7919022796975470100ot_int B2))))))
% 6.39/6.74 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int A3)) (@ tptp.bit_ri7919022796975470100ot_int B2))))))
% 6.39/6.74 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L3 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L3))))))
% 6.39/6.74 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N4) (@ (@ tptp.bit_se547839408752420682it_nat M5) tptp.one_one_nat)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) A) (= (@ (@ tptp.bit_se8568078237143864401it_int N) A) tptp.zero_zero_int))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) A) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) A) tptp.zero_zero_nat))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se8568078237143864401it_int N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.plus_plus_nat M) N)) A))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.plus_plus_nat M) N)) A))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se8568078237143864401it_int M))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N) M)) (@ _let_1 A))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se8570568707652914677it_nat M))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N) M)) (@ _let_1 A))))))
% 6.39/6.74 (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)))
% 6.39/6.74 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((X3 tptp.int) (Y6 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int X3) Y6)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int X3)) (@ tptp.bit_ri7919022796975470100ot_int Y6))))))
% 6.39/6.74 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((X3 tptp.int) (Y6 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int X3) (@ tptp.bit_ri7919022796975470100ot_int Y6))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X3)) Y6)))))
% 6.39/6.74 (assert (= tptp.bit_se2793503036327961859nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.bit_se1080825931792720795nteger A3) (@ (@ tptp.bit_se7788150548672797655nteger N4) tptp.one_one_Code_integer)))))
% 6.39/6.74 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int A3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.39/6.74 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N4) tptp.one_one_nat)))))
% 6.39/6.74 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L3))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L3)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)) (@ (@ tptp.bit_se8568078237143864401it_int N) A))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) (@ (@ tptp.bit_se8570568707652914677it_nat N) A))))
% 6.39/6.74 (assert (= tptp.bit_concat_bit (lambda ((N4 tptp.nat) (K3 tptp.int) (L3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N4) K3)) (@ (@ tptp.bit_se545348938243370406it_int N4) L3)))))
% 6.39/6.74 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se8568078237143864401it_int N4) A3)) tptp.one_one_int) tptp.one_one_int))))
% 6.39/6.74 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.bit_se8570568707652914677it_nat N4) A3)) tptp.one_one_nat) tptp.one_one_nat))))
% 6.39/6.74 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N4) tptp.one_one_int)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se545348938243370406it_int N) (@ (@ tptp.bit_se8568078237143864401it_int N) A))) (@ (@ tptp.bit_se2923211474154528505it_int N) A)) A)))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.bit_se547839408752420682it_nat N) (@ (@ tptp.bit_se8570568707652914677it_nat N) A))) (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) A)))
% 6.39/6.74 (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_se1080825931792720795nteger A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.39/6.74 (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_se1409905431419307370or_int A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.39/6.74 (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_se1412395901928357646or_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.39/6.74 (assert (forall ((A tptp.code_integer) (X tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (@ tptp.bit_se3949692690581998587nteger A))) (=> (= (@ _let_3 X) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y4) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y4) _let_1) (= X Y4))))))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (X tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (@ tptp.bit_se725231765392027082nd_int A))) (=> (= (@ _let_3 X) tptp.zero_zero_int) (=> (= (@ _let_2 X) _let_1) (=> (= (@ _let_3 Y4) tptp.zero_zero_int) (=> (= (@ _let_2 Y4) _let_1) (= X Y4))))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se8568078237143864401it_int N) A) A))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) A) A))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se8568078237143864401it_int N))) (= (@ _let_2 (@ (@ tptp.divide_divide_int A) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_2 A)) _let_1))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se8570568707652914677it_nat N))) (= (@ _let_2 (@ (@ tptp.divide_divide_nat A) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_2 A)) _let_1))))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (= (@ (@ tptp.bit_se3949692690581998587nteger X) Y4) tptp.zero_z3403309356797280102nteger) (=> (= (@ (@ tptp.bit_se1080825931792720795nteger X) Y4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= (@ tptp.bit_ri7632146776885996613nteger X) Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Y4) tptp.zero_zero_int) (=> (= (@ (@ tptp.bit_se1409905431419307370or_int X) Y4) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= (@ tptp.bit_ri7919022796975470100ot_int X) Y4)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N4 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int A) N) (= (@ (@ tptp.bit_ri631733984087533419it_int N) A) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) A) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat (@ tptp.suc N)) A) (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.39/6.74 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.divide_divide_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.divide_divide_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3928097537394005634nteger N) A)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) N)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se8568078237143864401it_int N) A)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se8570568707652914677it_nat N) A)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)))))
% 6.39/6.74 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N4 tptp.nat)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3928097537394005634nteger N4) A3))))))
% 6.39/6.74 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N4 tptp.nat)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se8568078237143864401it_int N4) A3))))))
% 6.39/6.74 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N4 tptp.nat)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se8570568707652914677it_nat N4) A3))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 6.39/6.74 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N)) (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N)) (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (N tptp.nat) (Y4 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) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y4) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y4)) _let_1)))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ tptp.bit_se8568078237143864401it_int N) A))) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.plus_plus_nat M) N))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N)))))))
% 6.39/6.74 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N4 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.bit_se1080825931792720795nteger (@ (@ tptp.bit_se1745604003318907178nteger N4) A3)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.bit_se9216721137139052372nteger A3) N4))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N4)))))))
% 6.39/6.74 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N4) A3)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int A3) N4))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N4)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N4 tptp.nat) (A3 tptp.int)) (@ (@ (@ tptp.if_int (= N4 tptp.zero_zero_nat)) A3) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N4 tptp.nat) (A3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) A3) (@ (@ tptp.bit_se8570568707652914677it_nat (@ (@ tptp.minus_minus_nat N4) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 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 M5)) (not (@ _let_2 N4))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1)))))))))
% 6.39/6.74 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L3 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 (= K3 _let_2) (= L3 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L3) (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L3) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 6.39/6.74 (assert (@ (@ (@ (@ (@ (@ tptp.boolea2445317508997433345nteger tptp.bit_se3949692690581998587nteger) tptp.bit_se1080825931792720795nteger) tptp.bit_ri7632146776885996613nteger) tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.bit_se3222712562003087583nteger))
% 6.39/6.74 (assert (@ (@ (@ (@ (@ (@ tptp.boolea8527374999097803216ff_int tptp.bit_se725231765392027082nd_int) tptp.bit_se1409905431419307370or_int) tptp.bit_ri7919022796975470100ot_int) tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bit_se6526347334894502574or_int))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 6.39/6.74 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (and (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))
% 6.39/6.74 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.39/6.74 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.39/6.74 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B) C)) A) (and (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real C) A)))))
% 6.39/6.74 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.39/6.74 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.39/6.74 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.39/6.74 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.39/6.74 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.39/6.74 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.39/6.74 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y4)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.ord_max_nat X) Y4)) (@ (@ tptp.ord_max_Code_integer (@ tptp.semiri4939895301339042750nteger X)) (@ tptp.semiri4939895301339042750nteger Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y4)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X) Y4)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X)) (@ tptp.semiri681578069525770553at_rat Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y4)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y4)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.ord_max_Code_integer X) Y4)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Z)) (@ (@ tptp.minus_8373710615458151222nteger Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y4)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y4)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y4)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y4) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y4) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y4) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y4) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y4) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y4)) (@ _let_1 Z))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y4)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y4)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y4)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y4)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y4)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y4) Z)))))
% 6.39/6.74 (assert (forall ((X tptp.extended_enat) (Y4 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y4) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y4) (= (@ (@ tptp.ord_max_Code_integer X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.set_int) (Y4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y4) (= (@ (@ tptp.ord_max_set_int X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y4) (= (@ (@ tptp.ord_max_rat X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y4) (= (@ (@ tptp.ord_max_num X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y4) (= (@ (@ tptp.ord_max_nat X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y4) (= (@ (@ tptp.ord_max_int X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (= (@ (@ tptp.ord_max_real X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((Y4 tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y4) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y4) X) (= (@ (@ tptp.ord_max_Code_integer X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y4) X) (= (@ (@ tptp.ord_max_set_int X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X) (= (@ (@ tptp.ord_max_rat X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X) (= (@ (@ tptp.ord_max_num X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X) (= (@ (@ tptp.ord_max_nat X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X) (= (@ (@ tptp.ord_max_int X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X) (= (@ (@ tptp.ord_max_real X) Y4) X))))
% 6.39/6.74 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.39/6.74 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.39/6.74 (assert (= tptp.ord_max_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B2)) B2) A3))))
% 6.39/6.74 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.39/6.74 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.39/6.74 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ (@ tptp.divide_divide_nat M5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M5 tptp.zero_zero_nat)) N4) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) M5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M5) _let_1)) (@ (@ tptp.modulo_modulo_nat N4) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M5) _let_1)) (@ (@ tptp.divide_divide_nat N4) _let_1))))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.39/6.74 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y4 tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa) Y4) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (not (= Y4 _let_1)))))) (=> (=> (exists ((N2 tptp.num)) (= X (@ tptp.bit0 N2))) (=> _let_1 (not (= Y4 (@ tptp.bit0 tptp.one))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit1 M4)) (not (= Y4 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))) (=> (=> (exists ((N2 tptp.num)) (= X (@ tptp.bit1 N2))) _let_2) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))) (not (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (=> (= Xa (@ tptp.bit1 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4)))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y4)) (= X Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_real X) Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X) Y4))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 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) Y4)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 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) Y4)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 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) Y4)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 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) Y4)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X) (@ (@ tptp.root M) (@ (@ tptp.root N) X)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y4)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y4)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y4) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y4)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y4) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y4)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X 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 X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X)) (@ tptp.sgn_sgn_real X)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N) X)))))))
% 6.39/6.74 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y4) N))) (@ tptp.abs_abs_real Y4)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N5) X))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X)) (@ (@ tptp.root N) X)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (= (@ (@ tptp.power_power_real Y4) N) X) (= (@ (@ tptp.root N) X) Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y4) N) X) (= (@ (@ tptp.root N) X) Y4)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N5) X))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N))) Y4))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X))) (=> (@ (@ 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)) X)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (B tptp.real) (X 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)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X)))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y6 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)) X) (@ P Y6))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))))
% 6.39/6.74 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X 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 X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X3 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X3) (@ (@ tptp.vEBT_VEBT_membermima T2) X3)))))
% 6.39/6.74 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A4 Bool) (B3 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A4) B3)))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y4 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y4 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.39/6.74 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.39/6.74 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.39/6.74 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.39/6.74 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_cnt (@ (@ tptp.vEBT_Leaf A) B)) tptp.one_one_real)))
% 6.39/6.74 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.39/6.74 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.39/6.74 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_space (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X) Y4) (=> (=> (exists ((A4 Bool) (B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A4) B3))) (not (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList2)) tptp.zero_zero_nat)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X) Y4) (=> (=> (exists ((A4 Bool) (B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A4) B3))) (not (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y4 (@ (@ 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 Summary2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList2)) tptp.zero_zero_nat)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X) Y4) (=> (=> (exists ((A4 Bool) (B3 Bool)) (= X (@ (@ tptp.vEBT_Leaf A4) B3))) (not (= Y4 tptp.one_one_real))) (not (forall ((Info2 tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2)) (not (= Y4 (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary2))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList2)) tptp.zero_zero_real)))))))))))
% 6.39/6.74 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N4 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X3) N4))) (@ (@ tptp.vEBT_VEBT_low X3) N4)))))
% 6.39/6.74 (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_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space X) Y4) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) X) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_1) (=> (= Y4 (@ 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) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y4 (@ (@ 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 Summary2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space) TreeList2)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel2) _let_1))))))))))))
% 6.39/6.74 (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_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.39/6.74 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_space2 X) Y4) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) X) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_1) (=> (= Y4 (@ 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) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 tptp.one)))) (@ tptp.vEBT_VEBT_space2 Summary2))) (@ (@ (@ tptp.foldr_nat_nat tptp.plus_plus_nat) (@ (@ tptp.map_VEBT_VEBT_nat tptp.vEBT_VEBT_space2) TreeList2)) tptp.zero_zero_nat))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_space_rel) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Y4 tptp.real)) (=> (= (@ tptp.vEBT_VEBT_cnt X) Y4) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) X) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_1) (=> (= Y4 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) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) Deg2) TreeList2) Summary2))) (=> (= X _let_1) (=> (= Y4 (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.vEBT_VEBT_cnt Summary2))) (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) (@ (@ tptp.map_VEBT_VEBT_real tptp.vEBT_VEBT_cnt) TreeList2)) tptp.zero_zero_real))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_cnt_rel) _let_1))))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X 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)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 6.39/6.74 (assert (forall ((X 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 X) _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 X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X))))))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M4 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M4)))))))
% 6.39/6.74 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X) (or (= X Mi) (= X Ma)))))
% 6.39/6.74 (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 ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X8)) (@ (@ 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_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ 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)))))))))))))))
% 6.39/6.74 (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 ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X8)) (@ (@ 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_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_1)))))) (=> (@ (@ 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)))))))))))))))
% 6.39/6.74 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A4 Bool) (B3 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A4) B3))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (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))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 N2) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (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))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N2)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N2) M4)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma2) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi2) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma2)))))))))))))))))))))))))))))))
% 6.39/6.74 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= A23 (@ (@ tptp.plus_plus_nat N4) N4)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N4))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N4) _let_1)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (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))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) N4) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N4)) (= A23 (@ (@ tptp.plus_plus_nat N4) N4)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N4 tptp.nat) (Summary3 tptp.vEBT_VEBT) (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))))) (let ((_let_3 (@ tptp.suc N4))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList3) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X3) N4))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N4) _let_3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I2)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N4))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma3) N4))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N4) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N4))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D2)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N2))))) (=> (forall ((N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N2))))) (=> (forall ((M4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N2))))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N2))))) (=> (forall ((M4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N2))))) (not (forall ((M4 tptp.num) (N2 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N2))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B3 Bool) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B3)) X4)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S3)) X4)))))))))
% 6.39/6.74 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList2) Vc)) X4)))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd)) X4)))))))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 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 R2)) (@ (@ (@ 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 R2)) tptp.one_one_int)))))))))
% 6.39/6.74 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R2)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R2 R4))))))
% 6.39/6.74 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.39/6.74 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.divide_divide_int K) L) Q2))))
% 6.39/6.74 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.modulo_modulo_int K) L) R2))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.unique5052692396658037445od_int (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N4))) (let ((_let_2 (@ tptp.numeral_numeral_int M5))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.39/6.74 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M5 tptp.num) (N4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N4))) (let ((_let_2 (@ tptp.numeral_numeral_nat M5))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (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) R2))))))))))
% 6.39/6.74 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 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) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q2)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.39/6.74 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)))))))
% 6.39/6.74 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L3 tptp.int) (K3 tptp.int) (Q3 tptp.int)) (and (= A12 K3) (= A23 L3) (= A32 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (not (= L3 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q3) L3)))) (exists ((R5 tptp.int) (L3 tptp.int) (K3 tptp.int) (Q3 tptp.int)) (and (= A12 K3) (= A23 L3) (= A32 (@ (@ tptp.product_Pair_int_int Q3) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L3)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L3)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) L3)) R5))))))))
% 6.39/6.74 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q4 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q4) A22)))))) (not (forall ((R3 tptp.int) (Q4 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q4) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) A22)) R3)))))))))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 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 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa Mi2) (= Xa Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList2) Vc))) (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa) Y4) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y4) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y4) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y4 (not (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList2) Vc))) (= Y4 (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd))) (= Y4 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))))
% 6.39/6.74 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M5 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M5) K3)) (@ (@ tptp.product_Pair_nat_nat M5) (@ (@ tptp.minus_minus_nat K3) M5))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M5) _let_1)))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa) Y4) (and (=> _let_2 (= Y4 (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X) Xa)))) (=> (not _let_2) (= Y4 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))))
% 6.39/6.74 (assert (forall ((Xs tptp.list_real) (Y4 tptp.real)) (=> (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_real2 Xs))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (= X4 Y))))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (= X4 Y4))) (= (@ (@ (@ tptp.foldr_real_real tptp.plus_plus_real) Xs) tptp.zero_zero_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.size_size_list_real Xs))) Y4))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.39/6.74 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.39/6.74 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.39/6.74 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.39/6.74 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.39/6.74 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.39/6.74 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.39/6.74 (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)))))))))))
% 6.39/6.74 (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))))))))))
% 6.39/6.74 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (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))))))))))))))))
% 6.39/6.74 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.power_power_nat _let_2))) (let ((_let_8 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_3))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (and (=> _let_9 (= _let_8 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_7 _let_4)) _let_5))))) (=> (not _let_9) (= _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (@ (@ tptp.times_times_nat (@ _let_7 _let_6)) _let_5))))))))))))))))
% 6.39/6.74 (assert (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.power_power_nat _let_2))) (let ((_let_9 (@ tptp.vEBT_V8346862874174094_d_u_p _let_3))) (let ((_let_10 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (and (=> _let_10 (= _let_9 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_8 _let_4)) _let_6))))) (=> (not _let_10) (= _let_9 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 _let_1)))) (@ tptp.vEBT_V8346862874174094_d_u_p _let_7))) (@ (@ tptp.times_times_nat (@ _let_8 _let_7)) _let_6)))))))))))))))))
% 6.39/6.74 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X 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 X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S2)) X) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (not (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))) (=> (= (@ tptp.vEBT_V8646137997579335489_i_l_d X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.power_power_nat _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (=> (= X _let_3) (not (and (=> _let_8 (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_7 _let_4)) _let_5))))) (=> (not _let_8) (= Y4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (@ (@ tptp.times_times_nat (@ _let_7 _let_6)) _let_5)))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (not (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)))))) (=> (= (@ tptp.vEBT_V8346862874174094_d_u_p X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.power_power_nat _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_2) _let_3))) (=> (= X _let_3) (not (and (=> _let_9 (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_8 _let_4)) _let_6))))) (=> (not _let_9) (= Y4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 _let_1)))) (@ tptp.vEBT_V8346862874174094_d_u_p _let_7))) (@ (@ tptp.times_times_nat (@ _let_8 _let_7)) _let_6))))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X 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 X) _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)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y4 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y4) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ 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))) (=> (= X _let_2) (not (and (=> _let_8 (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X 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 X) _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)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) Y4) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (= Y4 (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y4) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S3))) (= Y4 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A4) B3)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V3)) TreeList2) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa Mi2) (= Xa Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V3)) TreeList2) Vc))) (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V3)) (@ 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 TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V3)) TreeList2) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) 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 X) _let_1))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X) (@ 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 X) tptp.one_one_real)) (@ tptp.suc N4))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 6.39/6.74 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arctan X) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ 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)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ 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)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N2))) (@ G N2))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N4 tptp.nat)) (@ tptp.abs_abs_real (@ F N4))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ F I2)) (@ (@ tptp.power_power_real Z) I2))))))))))
% 6.39/6.74 (assert (forall ((X 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 X) _let_1))))) (@ tptp.sin_real X))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi2) (= Xa Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd))) (=> (= X _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 TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (= Y4 (or (= Xa Mi2) (= Xa Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) 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 TreeList2)))) (=> (= X _let_2) (=> (= Y4 (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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 ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) 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 TreeList2)))) (=> (= X _let_2) (=> (= Y4 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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))))))))))))))))))))
% 6.39/6.74 (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))
% 6.39/6.74 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ 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)))))) X))))
% 6.39/6.74 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y4 tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y4) (@ (@ 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 X) Y4))))))
% 6.39/6.74 (assert (forall ((X 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 X) _let_1))))) (@ tptp.cos_real X))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi2) (= Xa Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi2) (= Xa Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd))) (=> (= X _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 TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (=> (= X _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 TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (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 TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S3))) (=> (= X _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 TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y4 (and (=> _let_3 A4) (=> (not _let_3) (and (=> _let_2 B3) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V3 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V3))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) 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 TreeList2)))) (=> (= X _let_2) (=> (= Y4 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _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))))))))))))))))))
% 6.39/6.74 (assert (= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= Z5 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z5) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 6.39/6.74 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.39/6.74 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N))) N))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R2))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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 ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K3))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X 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 ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ (@ tptp.power_power_nat X) I2)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K3)) (@ 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))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_nat I2) (@ (@ tptp.binomial N) I2)))) (@ 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))))))
% 6.39/6.74 (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 ((Q3 tptp.nat)) (@ (@ tptp.ord_less_nat Q3) N))))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M10 tptp.nat)) (=> (@ P X) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M10))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M4)))))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ 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) X) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N)))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M5)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.39/6.74 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.39/6.74 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M5)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ 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)))))))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) (@ F I2)) (@ G I2)))) (@ 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 ((I2 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I2)) tptp.one_one_nat)))) _let_1))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M5)) (@ tptp.semiri2265585572941072030t_real M5)))) (@ 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 X) N))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X)) N)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X 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 X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M5)) (@ tptp.semiri2265585572941072030t_real M5)))) (@ 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 X) N)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N)))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M5)) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 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 K3))) (@ 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)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M5) N) (@ P M5))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N) (@ P M5))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.39/6.74 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I2) 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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((D3 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) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D3))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.39/6.74 (assert (forall ((D3 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) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D3))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.39/6.74 (assert (forall ((D3 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) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D3))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.plus_plus_int X4) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X5) (@ Q X5)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.39/6.74 (assert (forall ((D3 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) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D3))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ Q X4) (@ Q (@ (@ tptp.plus_plus_int X4) D3))))) (forall ((X5 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X5) D3))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X5) (@ Q X5)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.39/6.74 (assert (forall ((D tptp.int) (D3 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 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) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X5) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D3)) T)))))))))
% 6.39/6.74 (assert (forall ((D tptp.int) (D3 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 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) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X5) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X5) D3)) T))))))))))
% 6.39/6.74 (assert (forall ((D tptp.int) (D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X5))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D3)) T))))))))))
% 6.39/6.74 (assert (forall ((D tptp.int) (D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D3) (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X5))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D3)) T)))))))))))
% 6.39/6.74 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X8 tptp.int)) (@ P X8)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X3))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.minus_minus_int X5) D3) T))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) B4) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.minus_minus_int X5) D3) T)))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X5) D3)) T)))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) B4) (forall ((X5 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) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D3))))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X5 T) (= (@ (@ tptp.plus_plus_int X5) D3) T))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X5 T)) (not (= (@ (@ tptp.plus_plus_int X5) D3) T)))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X5) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X5) D3)) T))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 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) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D3)))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X5) D3)) T)))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B4) (forall ((X5 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) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.minus_minus_int X5) D3))))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X5) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X5) D3)) T))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X5 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) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X5) (@ _let_1 (@ (@ tptp.plus_plus_int X5) D3)))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X4) (= (@ P X4) (@ P4 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D3))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P4 X4) (@ P4 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D3))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P4 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A2) (@ P (@ (@ tptp.minus_minus_int Y6) X3))))))))))))))
% 6.39/6.74 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P4 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (exists ((Z3 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z3) (= (@ P X4) (@ P4 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb) Xa2))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D3))))) (=> (forall ((X4 tptp.int) (K2 tptp.int)) (= (@ P4 X4) (@ P4 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K2) D3))))) (= (exists ((X8 tptp.int)) (@ P X8)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (@ P4 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) B4) (@ P (@ (@ tptp.plus_plus_int Y6) X3))))))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q3 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat L3))) (@ (@ (@ 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))))
% 6.39/6.74 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L3 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q3 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int L3))) (@ (@ (@ 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))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.divmod_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N4 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M5) N4))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M5)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q3)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M5) N4)) N4))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 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 (= Y4 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y4) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _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))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y4 (@ (@ _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)))))))))))))))))))))))
% 6.39/6.74 (assert (= tptp.arctan (lambda ((Y6 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) Y6))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X3 tptp.real)) false))))))
% 6.39/6.74 (assert (= tptp.arccos (lambda ((Y6 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) Y6)))))))
% 6.39/6.74 (assert (= tptp.divmod_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M5) N4)) (@ (@ tptp.modulo_modulo_nat M5) N4)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.arcsin (lambda ((Y6 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) Y6))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V1247956027447740395_p_rel))) (let ((_let_3 (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))) (=> (= (@ tptp.vEBT_V8346862874174094_d_u_p X) Y4) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _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.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.vEBT_V8346862874174094_d_u_p _let_4))) (let ((_let_6 (@ (@ tptp.plus_plus_nat _let_5) tptp.one_one_nat))) (let ((_let_7 (@ tptp.suc _let_4))) (let ((_let_8 (@ tptp.power_power_nat _let_3))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_3) _let_1))) (=> (= X _let_1) (=> (and (=> _let_9 (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_2)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_8 _let_4)) _let_6))))) (=> (not _let_9) (= Y4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 _let_2)))) (@ tptp.vEBT_V8346862874174094_d_u_p _let_7))) (@ (@ tptp.times_times_nat (@ _let_8 _let_7)) _let_6))))) (not (@ (@ tptp.accp_nat tptp.vEBT_V1247956027447740395_p_rel) _let_1))))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_V5144397997797733112_d_rel))) (let ((_let_3 (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (=> (= (@ tptp.vEBT_V8646137997579335489_i_l_d X) Y4) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _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.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_2))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.vEBT_V8646137997579335489_i_l_d _let_4))) (let ((_let_6 (@ tptp.suc _let_4))) (let ((_let_7 (@ tptp.power_power_nat _let_3))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_3) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit1 _let_2)))) _let_5)) (@ (@ tptp.times_times_nat (@ _let_7 _let_4)) _let_5))))) (=> (not _let_8) (= Y4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ tptp.vEBT_V8646137997579335489_i_l_d _let_6))) (@ (@ tptp.times_times_nat (@ _let_7 _let_6)) _let_5))))) (not (@ (@ tptp.accp_nat tptp.vEBT_V5144397997797733112_d_rel) _let_1)))))))))))))))))))))))
% 6.39/6.74 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_set_encode (@ tptp.nat_set_decode N)) N)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N) (@ P M5))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N) (@ P M5))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.39/6.74 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.39/6.74 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I2)) (@ B I2)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.39/6.74 (assert (= tptp.code_T6385005292777649522of_nat tptp.semiri1314217659103216013at_int))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_3 (= Y4 (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X) Xa)))) (=> (not _let_3) (= Y4 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 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) (=> (= Y4 (@ 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) (=> (= Y4 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N2)) _let_1))))))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit0 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N2)) _let_1))))))))) (=> (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N2)) _let_1))))))))) (not (forall ((N2 tptp.num)) (=> (= X (@ tptp.bit1 N2)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N2)) _let_1))))))))))))))))))))))))
% 6.39/6.74 (assert (= tptp.int_ge_less_than (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.39/6.74 (assert (= tptp.int_ge_less_than2 (lambda ((D4 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D4) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.39/6.74 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (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) A1)))))
% 6.39/6.74 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.39/6.74 (assert (= tptp.unique4921790084139445826nteger (lambda ((L3 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q3 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L3))) (@ (@ (@ 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))))
% 6.39/6.74 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.39/6.74 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.39/6.74 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)))
% 6.39/6.74 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.74 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.74 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L) (@ tptp.uminus1351360451143612070nteger L))))
% 6.39/6.74 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.39/6.74 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.39/6.74 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.39/6.74 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.39/6.74 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 6.39/6.74 (assert (= tptp.zero_zero_int tptp.zero_zero_int))
% 6.39/6.74 (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))))
% 6.39/6.74 (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 ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M6) N)))) M)))))
% 6.39/6.74 (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 ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M6)))) M)))))
% 6.39/6.74 (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 ((K3 tptp.nat)) K3)) (@ _let_1 N))))))
% 6.39/6.74 (assert (= tptp.code_integer_of_int (lambda ((K3 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 K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.39/6.74 (assert (forall ((Xa tptp.nat) (X tptp.int)) (= (@ (@ tptp.bit_se1345352211410354436nteger Xa) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.bit_se2159334234014336723it_int Xa) X)))))
% 6.39/6.74 (assert (= tptp.zero_z3403309356797280102nteger (@ tptp.code_integer_of_int tptp.zero_zero_int)))
% 6.39/6.74 (assert (forall ((Xa tptp.nat) (X tptp.int)) (= (@ (@ tptp.bit_se8260200283734997820nteger Xa) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.bit_se4203085406695923979it_int Xa) X)))))
% 6.39/6.74 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa) X)))))
% 6.39/6.74 (assert (forall ((Xa tptp.nat) (X tptp.int)) (= (@ (@ tptp.bit_se2793503036327961859nteger Xa) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.bit_se7879613467334960850it_int Xa) X)))))
% 6.39/6.74 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.39/6.74 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.39/6.74 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 6.39/6.74 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa) X)))))
% 6.39/6.74 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_eq_int Xa) X))))
% 6.39/6.74 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa) X)))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y6) (= X3 Y6)))))
% 6.39/6.74 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (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 (= R2 (@ (@ tptp.plus_plus_rat S3) T3)))))))))))
% 6.39/6.74 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.39/6.74 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.39/6.74 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.39/6.74 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X23 tptp.nat)) X23))))
% 6.39/6.74 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 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 A3)) B2)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P5)))))
% 6.39/6.74 (assert (forall ((Q2 tptp.int) (P5 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P5)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.39/6.74 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((P5 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.39/6.74 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (= tptp.minus_minus_rat (lambda ((Q3 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q3) (@ tptp.uminus_uminus_rat R5)))))
% 6.39/6.74 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B2)) (@ (@ tptp.times_times_int C5) D4))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.39/6.74 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int C5) B2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.39/6.74 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int B2) C5))) (@ (@ tptp.times_times_int C5) D4))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.39/6.74 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D4 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int B2) C5))) (@ (@ tptp.times_times_int C5) D4))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.39/6.74 (assert (forall ((R2 tptp.rat) (P5 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.39/6.74 (assert (forall ((R2 tptp.product_prod_int_int) (P5 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.39/6.74 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P5 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P5) S2) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.39/6.74 (assert (= tptp.ord_less_rat (lambda ((P6 tptp.rat) (Q3 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D4 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int C5) B2)))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P6)))))
% 6.39/6.74 (assert (= tptp.ord_less_eq_rat (lambda ((P6 tptp.rat) (Q3 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C5 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D4 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A3) D4)) (@ (@ tptp.times_times_int C5) B2)))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P6)))))
% 6.39/6.74 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 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) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.bezw X) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ tptp.nat_set_decode (@ tptp.nat_set_encode A2)) A2))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.nat_set_decode N))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N8) (@ (@ tptp.ord_less_eq_nat X3) M5)))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N4)) U)))))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 6.39/6.74 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M)))))))
% 6.39/6.74 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 6.39/6.74 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N5))))
% 6.39/6.74 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N4) K))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I2) (@ (@ tptp.ord_less_eq_int I2) B)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_int I2) B)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I2) (@ (@ tptp.ord_less_int I2) B)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I2 tptp.int)) (and (@ (@ tptp.ord_less_int A) I2) (@ (@ tptp.ord_less_eq_int I2) B)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.39/6.74 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) I)))))))
% 6.39/6.74 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_atMost_nat K3))))))
% 6.39/6.74 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.set_ord_lessThan_nat K2))))))
% 6.39/6.74 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_lessThan_nat K3))))))
% 6.39/6.74 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M5 tptp.int)) (exists ((N4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M5) (@ tptp.abs_abs_int N4)) (@ (@ tptp.member_int N4) S)))))))
% 6.39/6.74 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M5 tptp.nat)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M5) N4) (@ (@ tptp.member_nat N4) S)))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L3))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L3)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _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 L3) S4)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) 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 L3)) S4)))))) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.39/6.74 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I2) N)))) (@ tptp.suc N))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M) (= (@ tptp.groups4561878855575611511st_nat L3) N5))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L3) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L3)) tptp.one_one_nat) N5))))))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L3) M) (= (@ tptp.groups4561878855575611511st_nat L3) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M)) tptp.one_one_nat)) N5))))
% 6.39/6.74 (assert (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M10)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M10) (@ (@ tptp.ord_less_nat K3) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M10) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 6.39/6.74 (assert (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M10) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M10) (@ (@ tptp.ord_less_nat K3) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M10) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I))))))))))
% 6.39/6.74 (assert (forall ((M10 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M10) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M10) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.39/6.74 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L3 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 K3)) (not (@ _let_2 L3)))))) (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 K3) _let_4) (@ (@ tptp.member_int L3) _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 K3) _let_1)) (@ (@ tptp.divide_divide_int L3) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Xa tptp.int) (Y4 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 X)) (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 X) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y4) (and (=> _let_5 (= Y4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 6.39/6.74 (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))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Xa tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) 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 X)) (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 X) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_6 (= Y4 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y4 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 6.39/6.74 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K2 tptp.int) (L2 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 K2) L2)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L2) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))) (@ (@ P K2) L2)))))) (@ (@ P A0) A1)))))
% 6.39/6.74 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.39/6.74 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.39/6.74 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.39/6.74 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.39/6.74 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.39/6.74 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.39/6.74 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.39/6.74 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.plus_plus_nat I2) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N4) (@ tptp.suc M5))))))
% 6.39/6.74 (assert (= tptp.set_ord_lessThan_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N4)))))
% 6.39/6.74 (assert (= tptp.set_ord_atMost_nat (lambda ((N4 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N4))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.binomial (lambda ((N4 tptp.nat) (K3 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) K3))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 6.39/6.74 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R2)))))
% 6.39/6.74 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y4) (@ (@ tptp.modulo_modulo_nat X) Y4)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y4) (= (@ (@ tptp.bezw X) Y4) (@ (@ 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 X) Y4)))))))))))
% 6.39/6.74 (assert (= tptp.bezw (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y6) (@ (@ tptp.modulo_modulo_nat X3) Y6)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y6 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) Y6)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y4) (and (=> _let_3 (= Y4 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y4 (@ (@ 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 X) Xa))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_4 (= Y4 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y4 (@ (@ 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 X) Xa)))))))) (not _let_1)))))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (= tptp.adjust_mod (lambda ((L3 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L3) R5)))))
% 6.39/6.74 (assert (= tptp.normalize (lambda ((P6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P6))) (let ((_let_2 (@ tptp.product_fst_int_int P6))) (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)))))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X) (@ (@ tptp.gcd_gcd_int _let_1) X)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.gcd_gcd_int X) tptp.zero_zero_int) (@ tptp.abs_abs_int X))))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ (@ tptp.gcd_gcd_int tptp.zero_zero_int) X) (@ tptp.abs_abs_int X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y4) X) (= (@ (@ tptp.gcd_gcd_int X) Y4) (@ tptp.abs_abs_int Y4)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int X) Y4) (= (@ (@ tptp.gcd_gcd_int X) Y4) (@ tptp.abs_abs_int X)))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (exists ((U2 tptp.int) (V3 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U2) X)) (@ (@ tptp.times_times_int V3) Y4)) (@ (@ tptp.gcd_gcd_int X) Y4)))))
% 6.39/6.74 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y4)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y4))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y4) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y4))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y4)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y4) (= (@ (@ tptp.gcd_gcd_int X) Y4) (@ (@ tptp.gcd_gcd_int Y4) (@ (@ tptp.modulo_modulo_int X) Y4))))))
% 6.39/6.74 (assert (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L3 tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L3 tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L3) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L3))))))))
% 6.39/6.74 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)))
% 6.39/6.74 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.gcd_gcd_nat A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.gcd_gcd_nat A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y4) (= (@ (@ tptp.gcd_gcd_nat X) Y4) X))))
% 6.39/6.74 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat Y4) X) (= (@ (@ tptp.gcd_gcd_nat X) Y4) Y4))))
% 6.39/6.74 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) C) (=> (@ (@ tptp.dvd_dvd_nat B) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.gcd_gcd_nat A) B)) (@ (@ tptp.gcd_gcd_nat C) D))))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= A (@ (@ tptp.gcd_gcd_nat A) B)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.gcd_gcd_nat A) B)) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat A) B) (not (= A B))) (= (@ (@ tptp.gcd_gcd_nat A) B) A))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat B) A) (not (= B A))) (= (@ (@ tptp.gcd_gcd_nat A) B) B))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 (@ (@ tptp.gcd_gcd_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.39/6.74 (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.gcd_gcd_nat B) C)))))))
% 6.39/6.74 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= A3 (@ (@ tptp.gcd_gcd_nat A3) B2)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.gcd_gcd_nat A) B)) A)))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.gcd_gcd_nat A) B)) B)))
% 6.39/6.74 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A3) B2) A3))))
% 6.39/6.74 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A3) B2) B2))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) C) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.gcd_gcd_nat A) B)) C))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.gcd_gcd_nat A) B)) C))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (let ((_let_2 (@ (@ tptp.gcd_gcd_nat B) C))) (=> (and (@ _let_1 _let_2) (not (= A _let_2))) (not (=> (and (@ _let_1 B) (not (= A B))) (not (and (@ _let_1 C) (not (= A C)))))))))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (not (= A B)))) (= (and (@ (@ tptp.dvd_dvd_nat A) B) _let_1) (and (= A (@ (@ tptp.gcd_gcd_nat A) B)) _let_1)))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (=> (and (@ (@ tptp.dvd_dvd_nat A) C) (not (= A C))) (and (@ (@ tptp.dvd_dvd_nat _let_1) C) (not (= _let_1 C)))))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (= B C))) (and (@ (@ tptp.dvd_dvd_nat _let_1) C) (not (= _let_1 C)))))))
% 6.39/6.74 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (= (and (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_nat A) B))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y4) (and (=> _let_1 (= Y4 X)) (=> (not _let_1) (= Y4 (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))))))))
% 6.39/6.74 (assert (= tptp.gcd_gcd_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y6 tptp.zero_zero_nat)) X3) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X3) Y6))))))
% 6.39/6.74 (assert (forall ((Y4 tptp.nat) (X tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X) Y4) (@ (@ tptp.gcd_gcd_nat Y4) (@ (@ tptp.modulo_modulo_nat X) Y4))))))
% 6.39/6.74 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K3 tptp.code_integer) (L3 tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L3 tptp.zero_z3403309356797280102nteger)) K3) (@ (@ tptp.gcd_gcd_Code_integer L3) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K3)) (@ tptp.abs_abs_Code_integer L3))))))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.39/6.74 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X4))) (let ((_let_6 (@ _let_4 Y))) (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)))))))))))))
% 6.39/6.74 (assert (= tptp.gcd_gcd_int (lambda ((X3 tptp.int) (Y6 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat (@ tptp.nat2 (@ tptp.abs_abs_int X3))) (@ tptp.nat2 (@ tptp.abs_abs_int Y6)))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y4))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y4)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y4)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I4) (@ P I4))) (@ P K2)))) (@ P M)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 X)) (=> (not _let_2) (= Y4 (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))))
% 6.39/6.74 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.39/6.74 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L3))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L3) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K3) (@ tptp.sgn_sgn_Code_integer L3))) _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 L3)) S4)))))) _let_1))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.39/6.74 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.39/6.74 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) M5)))))
% 6.39/6.74 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X3))) (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X3))))
% 6.39/6.74 (assert (forall ((K tptp.code_integer)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.code_nat_of_integer K)) (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) K))))
% 6.39/6.74 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 6.39/6.74 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M5 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M5) N4) (not (= M5 N4))))))
% 6.39/6.74 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L3 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L3))) (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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L3 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 L3)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6))) (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) X)))))
% 6.39/6.74 (assert (= (@ tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int))
% 6.39/6.74 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X) Xa)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X) Xa)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 6.39/6.74 (assert (forall ((X tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X) Xa)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.code_int_of_integer (@ tptp.semiri4939895301339042750nteger N)) (@ tptp.semiri1314217659103216013at_int N))))
% 6.39/6.74 (assert (forall ((Z tptp.int)) (not (forall ((X4 tptp.nat) (Y tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X4) Y))))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.int Bool)) (X tptp.int)) (=> (forall ((Y tptp.product_prod_nat_nat)) (@ P (@ tptp.abs_Integ Y))) (@ P X))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L3 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L3)))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.bit_se8260200283734997820nteger X) Xa)) (@ (@ tptp.bit_se4203085406695923979it_int X) (@ tptp.code_int_of_integer Xa)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.bit_se2793503036327961859nteger X) Xa)) (@ (@ tptp.bit_se7879613467334960850it_int X) (@ tptp.code_int_of_integer Xa)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.bit_se1345352211410354436nteger X) Xa)) (@ (@ tptp.bit_se2159334234014336723it_int X) (@ tptp.code_int_of_integer Xa)))))
% 6.39/6.74 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.39/6.74 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N4 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat)))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X3))) X)))))
% 6.39/6.74 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))) Xa) X))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))) Xa) X))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) V4)))) __flatten_var_0))) Xa) X)))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) U3)))) __flatten_var_0))) Xa) X)))))
% 6.39/6.74 (assert (forall ((M10 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M10) (= (@ tptp.gcd_Gcd_nat M10) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M10) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat A) A2) (@ (@ tptp.dvd_dvd_nat (@ tptp.gcd_Gcd_nat A2)) A))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (forall ((B3 tptp.nat)) (=> (@ (@ tptp.member_nat B3) A2) (@ (@ tptp.dvd_dvd_nat A) B3))) (@ (@ tptp.dvd_dvd_nat A) (@ tptp.gcd_Gcd_nat A2)))))
% 6.39/6.74 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.39/6.74 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N4 tptp.nat) (M5 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N4)) (@ tptp.suc M5))))))
% 6.39/6.74 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U3) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 6.39/6.74 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y6 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 Y6) V4)) (@ (@ tptp.plus_plus_nat U3) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int A) A2) (@ (@ tptp.dvd_dvd_int (@ tptp.gcd_Gcd_int A2)) A))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (forall ((B3 tptp.int)) (=> (@ (@ tptp.member_int B3) A2) (@ (@ tptp.dvd_dvd_int A) B3))) (@ (@ tptp.dvd_dvd_int A) (@ tptp.gcd_Gcd_int A2)))))
% 6.39/6.74 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.39/6.74 (assert (= tptp.nat2 (lambda ((X3 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X3)))))
% 6.39/6.74 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X3))))))
% 6.39/6.74 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M5) N4))) M5)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (= (@ tptp.nat_prod_encode X) (@ tptp.nat_prod_encode Y4)) (= X Y4))))
% 6.39/6.74 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.39/6.74 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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) (Y6 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 Y6))) (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))))))
% 6.39/6.74 (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) (Y6 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 Y6) U3)))) __flatten_var_0))))))
% 6.39/6.74 (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) (Y6 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 Y6) V4)))) __flatten_var_0))))))
% 6.39/6.74 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M5 tptp.nat) (N4 tptp.nat)) (= N4 (@ tptp.suc M5)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y4)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y4))) X)))))
% 6.39/6.74 (assert (forall ((C tptp.nat) (Y4 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y4))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y4))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y4))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y4) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I2 tptp.nat)) (@ (@ tptp.minus_minus_nat I2) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.39/6.74 (assert (forall ((M10 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M10) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M10) N5))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.39/6.74 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.39/6.74 (assert (= tptp.sqr (lambda ((X3 tptp.num)) (@ (@ tptp.times_times_num X3) X3))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y4)) (@ tptp.sqr (@ _let_1 Y4))))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.39/6.74 (assert (forall ((N5 tptp.set_nat)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N5)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat N5)))))
% 6.39/6.74 (assert (= tptp.comple4887499456419720421f_real (lambda ((X8 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X8))))))
% 6.39/6.74 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_lessThan_int K3))))))
% 6.39/6.74 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K3))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M5) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X9) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X9 I3))) (= (@ tptp.suminf_real X9) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X9) (@ tptp.set_ord_lessThan_nat I2)))) tptp.top_top_set_nat)))))))
% 6.39/6.74 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.39/6.74 (assert (@ tptp.fun_is_measure_int (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)))
% 6.39/6.74 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (not (@ tptp.finite_finite_int tptp.top_top_set_int)))
% 6.39/6.74 (assert (@ (@ (@ tptp.bij_be5333170631980326235at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 6.39/6.74 (assert (= (@ (@ tptp.image_2486076414777270412at_nat tptp.nat_prod_encode) tptp.top_to4669805908274784177at_nat) tptp.top_top_set_nat))
% 6.39/6.74 (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))))
% 6.39/6.74 (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 ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N4)))) X3)))))
% 6.39/6.74 (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)))))))))))
% 6.39/6.74 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o false) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 6.39/6.74 (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)))))))))))))
% 6.39/6.74 (assert (forall ((X1 Bool) (X2 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X2) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.39/6.74 (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))))))))))))
% 6.39/6.74 (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))))))))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((X1 Bool) (X2 Bool) (X33 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X2) X33) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real) (D3 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 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D3 _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 (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D3 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D3) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (S tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.member_real _let_1) S) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y3)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.39/6.74 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y3) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.39/6.74 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.39/6.74 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (Y4 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 X) (@ F Y4)))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H2))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H2))) (@ F X)))))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H2))) (@ F X)))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) 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 ((H2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_real H2) D2) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.minus_minus_real X) H2))))))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y4 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 X) _let_1) (=> (@ (@ tptp.member_real Y4) _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 X) (@ F Y4)))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F2 Z2)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y))) D) (= (@ F X) (@ F Y)))) (= L tptp.zero_zero_real))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y)))) (= L tptp.zero_zero_real))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y))) D) (@ (@ tptp.ord_less_eq_real (@ F Y)) (@ F X)))) (= L tptp.zero_zero_real))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X 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 X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S2))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) 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 X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 6.39/6.74 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F2 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L4 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F2 X0))) (=> (forall ((N2 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ F X3) N2))) (@ (@ F2 X0) N2)) (@ (@ 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 ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X4) N2)) (@ (@ F Y) N2)))) (@ (@ tptp.times_times_real (@ L4 N2)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y)))))))) (@ (@ (@ 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)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (=> (@ (@ (@ 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)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (let ((_let_3 (@ F X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _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 R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))
% 6.39/6.74 (assert (forall ((X 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2))))
% 6.39/6.74 (assert (forall ((X tptp.real) (D3 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D3 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D3 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D3) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.39/6.74 (assert (forall ((R 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 R)) R)) (@ 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 R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ 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)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X 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) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) 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 X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.39/6.74 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N)))))))))
% 6.39/6.74 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X 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 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.39/6.74 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ 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))))))))))))
% 6.39/6.74 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ 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)))))))))))
% 6.39/6.74 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real H) M5)))) (@ 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))))))))))))
% 6.39/6.74 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N)))))))))))))
% 6.39/6.74 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X 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 X))) (@ (@ (@ 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 X)) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real X) M5)))) (@ 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 X) N))))))))))
% 6.39/6.74 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M5)))) (@ 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)))))))))))))
% 6.39/6.74 (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 ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M5)))) (@ 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)))))))))))))
% 6.39/6.74 (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) (X 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 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X))) (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 X))) (= (@ F X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M5) C)) (@ tptp.semiri2265585572941072030t_real M5))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M5)))) (@ 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 X) C)) N))))))))))))))))))))
% 6.39/6.74 (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 ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real U3) P6)))) (@ 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 ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P6)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P6))) (@ (@ tptp.power_power_real T4) P6)))) (@ 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))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X10 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ 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)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X10) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (X 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 X) 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 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 6.39/6.74 (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) (M8 tptp.real)) (and (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (and (@ (@ tptp.ord_less_eq_real L5) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M8))))) (forall ((Y3 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L5) Y3) (@ (@ tptp.ord_less_eq_real Y3) M8)) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B) (= (@ F X4) Y3)))))))))))
% 6.39/6.74 (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 ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real (@ F X5)) tptp.zero_zero_real)))))))))
% 6.39/6.74 (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 ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (not (= (@ F X5) tptp.zero_zero_real))))))))))
% 6.39/6.74 (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 ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X5 tptp.real)) (=> (and (not (= X5 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X5))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X5))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.39/6.74 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.ln_ln_real))))
% 6.39/6.74 (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)))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (D3 tptp.real) (G (-> tptp.real tptp.real)) (X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D3) (@ (@ tptp.topolo2177554685111907308n_real (@ G X)) tptp.top_top_set_real)) (=> (not (= D3 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y) (=> (@ (@ tptp.ord_less_real Y) B) (= (@ F (@ G Y)) Y)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D3)) _let_1))))))))))
% 6.39/6.74 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 6.39/6.74 (assert (forall ((D tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) 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))) (@ F2 C3))))))))))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.39/6.74 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X9) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X9 I3))) B4)) (not (forall ((L5 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X9) (@ tptp.topolo2815343760600316023s_real L5)) tptp.at_top_nat))))))))
% 6.39/6.74 (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))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N2))) (@ G N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ G N2))) (=> (@ (@ (@ 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 ((L2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L2))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L2)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ G N6))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N2) (@ (@ tptp.ord_less_real R3) (@ X9 N2)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ X9 N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.39/6.74 (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))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))
% 6.39/6.74 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N2)) L)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N6)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N4)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.39/6.74 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N4))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.39/6.74 (assert (forall ((X 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 X) (@ tptp.semiri5074537144036343181t_real N4)))) N4))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.39/6.74 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ 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 R2)) tptp.at_top_nat)))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ 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)))))))))
% 6.39/6.74 (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 ((K2 (-> 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 (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.39/6.74 (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 ((K2 (-> 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 (@ K2 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)))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) 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 X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.39/6.74 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))))))))
% 6.39/6.74 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 6.39/6.74 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L2))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6)))) L2)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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 L2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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)))))))))
% 6.39/6.74 (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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat)))))
% 6.39/6.74 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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 ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))))) tptp.at_top_nat))))))
% 6.39/6.74 (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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N2))) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N2))) (@ A N2))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I2)) (@ A I2)))) (@ 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)))))))))
% 6.39/6.74 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C5 tptp.real)) (= F3 (lambda ((X3 tptp.real)) (@ (@ tptp.times_times_real X3) C5)))))))
% 6.39/6.74 (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))
% 6.39/6.74 (assert (= tptp.real_V975177566351809787t_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y6)))))
% 6.39/6.74 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X3 tptp.complex) (Y6 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y6)))))
% 6.39/6.74 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_bot_real))
% 6.39/6.74 (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))))
% 6.39/6.74 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F4) (=> (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) F4))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y6))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y6)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.39/6.74 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.39/6.74 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F4) (=> (@ (@ 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) F4))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.39/6.74 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_top_real) tptp.at_top_nat))
% 6.39/6.74 (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))
% 6.39/6.74 (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))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))
% 6.39/6.74 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y6))) Y6))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.39/6.74 (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 ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.39/6.74 (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))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ (@ (@ 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) (@ F2 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 (@ F2 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))))))))))
% 6.39/6.74 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 6.39/6.74 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 6.39/6.74 (assert (@ (@ (@ tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real) tptp.at_infinity_real) tptp.at_top_nat))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) 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) (@ F2 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 (@ F2 X3)) (@ G2 X3)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F4) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ (@ (@ 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) (@ F2 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 (@ F2 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))))))))))
% 6.39/6.74 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (F4 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) (@ F2 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 (@ F2 X3)) (@ G2 X3)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X3)) (@ G0 X3)))) F4) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (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) (@ F2 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 (@ F2 X3)) (@ G2 X3)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F4) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (F4 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (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) (@ F2 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 (@ F2 X3)) (@ G2 X3)))) F4) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F4) _let_1))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F2 (-> 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) (@ F2 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 (@ F2 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)))))))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ (@ (@ 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) (@ F2 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 (@ F2 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))))))))))
% 6.39/6.74 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real)) (X 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 X))) (=> (@ (@ (@ 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) (@ F2 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 (@ F2 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))))))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I2 tptp.nat)) (@ P (@ tptp.suc I2)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.39/6.74 (assert (forall ((F4 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F4) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F4)))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (@ (@ (@ tptp.filterlim_nat_int tptp.semiri1314217659103216013at_int) tptp.at_top_int) tptp.at_top_nat))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y tptp.nat)) (=> (@ P Y) (@ (@ tptp.ord_less_eq_nat Y) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_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))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (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)) G))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((L2 tptp.real) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L2)))))))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.arcosh_real (@ F X3)))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C3 tptp.real) (D2 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C3) D2)) (@ (@ tptp.ord_less_eq_real C3) D2)))))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F2 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ F2 Z2) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F2 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F2 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.39/6.74 (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_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (exists ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y3)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.39/6.74 (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_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (exists ((Y3 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y3) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y3) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 6.39/6.74 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))))))))
% 6.39/6.74 (assert (= (@ (@ tptp.image_int_nat tptp.nat_int_encode) tptp.top_top_set_int) tptp.top_top_set_nat))
% 6.39/6.74 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (= (@ tptp.nat_int_encode X) (@ tptp.nat_int_encode Y4)) (= X Y4))))
% 6.39/6.74 (assert (@ (@ (@ tptp.bij_betw_int_nat tptp.nat_int_encode) tptp.top_top_set_int) tptp.top_top_set_nat))
% 6.39/6.74 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X3 tptp.real) (Y6 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X3) Y6)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.39/6.74 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X3 tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X3) Y6)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.39/6.74 (assert (= (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int) tptp.semiring_1_Nats_int))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.inj_on_real_real (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N)))) tptp.top_top_set_real))))
% 6.39/6.74 (assert (= (@ (@ tptp.image_nat_int tptp.nat_int_decode) tptp.top_top_set_nat) tptp.top_top_set_int))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_int_encode (@ tptp.nat_int_decode N)) N)))
% 6.39/6.74 (assert (forall ((X tptp.int)) (= (@ tptp.nat_int_decode (@ tptp.nat_int_encode X)) X)))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (= (@ tptp.nat_int_decode X) (@ tptp.nat_int_decode Y4)) (= X Y4))))
% 6.39/6.74 (assert (@ (@ (@ tptp.bij_betw_nat_int tptp.nat_int_decode) tptp.top_top_set_nat) tptp.top_top_set_int))
% 6.39/6.74 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.39/6.74 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.semiri3842193898606819883omplex) (and (= (@ tptp.im Z) tptp.zero_zero_real) (exists ((I2 tptp.nat)) (= (@ tptp.re Z) (@ tptp.semiri5074537144036343181t_real I2)))))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.inj_on_int_nat tptp.nat_int_encode) A2)))
% 6.39/6.74 (assert (@ (@ tptp.inj_on_set_nat_nat tptp.nat_set_encode) (@ tptp.collect_set_nat tptp.finite_finite_nat)))
% 6.39/6.74 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inj_on2178005380612969504at_nat tptp.nat_prod_encode) A2)))
% 6.39/6.74 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.inj_on_nat_int tptp.nat_int_decode) A2)))
% 6.39/6.74 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.member_nat N2) N5) (@ (@ tptp.ord_less_eq_nat K) N2))) (@ (@ tptp.inj_on_nat_nat (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_nat N4) K))) N5))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (@ tptp.summable_real (@ (@ tptp.comp_nat_real_nat F) G)))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G))) (@ tptp.suminf_real F)))))))
% 6.39/6.74 (assert (@ (@ tptp.inj_on_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))))))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.inj_on_nat_nat G) tptp.top_top_set_nat) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (=> (forall ((X4 tptp.nat)) (=> (not (@ (@ tptp.member_nat X4) (@ (@ tptp.image_nat_nat G) tptp.top_top_set_nat))) (= (@ F X4) tptp.zero_zero_real))) (= (@ tptp.suminf_real (@ (@ tptp.comp_nat_real_nat F) G)) (@ tptp.suminf_real F))))))))
% 6.39/6.74 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (or (not (= X tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X) N))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))))))))))))
% 6.39/6.74 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima2)))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa) Y4) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y4 (not (= Xa tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y4 (not (and (= Deg2 Xa) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (= Xa tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (= Deg2 Xa) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (= Xa tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))))))
% 6.39/6.74 (assert (= tptp.complete_Sup_Sup_int (lambda ((X8 tptp.set_int)) (@ tptp.the_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X8) (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) X8) (@ (@ tptp.ord_less_eq_int Y6) X3)))))))))
% 6.39/6.74 (assert (forall ((X tptp.vEBT_VEBT) (Xa tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X) Xa) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Y4 (= Xa tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= Y4 (and (= Deg2 Xa) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X8))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X8)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X8 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X8)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))))))))))))
% 6.39/6.74 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I2 tptp.int) (N4 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.semiri5074537144036343181t_real N4))) (not (= N4 tptp.zero_zero_nat))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X) X4) (@ (@ tptp.ord_less_real X4) Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X)))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X) X4)))))
% 6.39/6.74 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I2 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I2)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.39/6.74 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ P (@ (@ tptp.fract A4) B3)))) (@ P Q2))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.gcd_gcd_int A) B))) (= (@ (@ tptp.fract (@ (@ tptp.divide_divide_int A) _let_1)) (@ (@ tptp.divide_divide_int B) _let_1)) (@ (@ tptp.fract A) B)))))
% 6.39/6.74 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract tptp.zero_zero_int) K) tptp.zero_zero_rat)))
% 6.39/6.74 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.zero_zero_int) tptp.zero_zero_rat)))
% 6.39/6.74 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 6.39/6.74 (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.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))))
% 6.39/6.74 (assert (forall ((A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.fract tptp.zero_zero_int))) (= (@ _let_1 A) (@ _let_1 C)))))
% 6.39/6.74 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 6.39/6.74 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.39/6.74 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.39/6.74 (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_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.39/6.74 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N)) tptp.one_one_rat)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.39/6.74 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.39/6.74 (assert (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.39/6.74 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))))
% 6.39/6.74 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 6.39/6.74 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.39/6.74 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (F2 (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F2 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F2 X4))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.39/6.74 (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 ((Q3 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 Q3)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 6.39/6.74 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.39/6.74 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))))))
% 6.39/6.74 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.39/6.74 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0))))))
% 6.39/6.74 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M5 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N4) (@ tptp.numeral_numeral_nat M5)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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 ((Q3 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q3)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 6.39/6.74 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M))))))
% 6.39/6.74 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q3 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q3)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.39/6.74 (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 ((Q3 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q3)))) (@ (@ tptp.bit_take_bit_num N4) M)))) N))))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 6.39/6.74 (assert (not (@ tptp.positive tptp.zero_zero_rat)))
% 6.39/6.74 (assert (forall ((X tptp.rat)) (=> (not (@ tptp.positive X)) (=> (not (= X tptp.zero_zero_rat)) (@ tptp.positive (@ tptp.uminus_uminus_rat X))))))
% 6.39/6.74 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y6 tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y6) X3)))))
% 6.39/6.74 (assert (= tptp.positive (lambda ((X3 tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa) Y4) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit0 N2))) (not (= Y4 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit1 N2))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (not (= Y4 (@ tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (=> (= Xa tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M4) N2)))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.39/6.74 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_snd_int_int X3)))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y4 tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa) Y4) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit0 N2))) _let_4)) (=> (=> _let_5 (=> (exists ((N2 tptp.num)) (= Xa (@ tptp.bit1 N2))) _let_1)) (=> (=> (exists ((M4 tptp.num)) (= X (@ tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (=> (=> (exists ((M4 tptp.num)) (= X (@ tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2)))))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa) Y4) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y4 tptp.none_num)))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ tptp.some_num (@ tptp.bit1 N2))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 N2))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (=> (= Xa tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (=> (= Xa tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit0 N2)) (not (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (=> (= Xa (@ tptp.bit1 N2)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))))))))))))))))))))
% 6.39/6.74 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.39/6.74 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 6.39/6.74 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.39/6.74 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.39/6.74 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.num) (Xa tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y4 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.some_num (@ tptp.bit1 N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit1 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit0 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit0 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X (@ tptp.bit1 M4)) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (=> (= Xa _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N2))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 6.39/6.74 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.39/6.74 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.39/6.74 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.39/6.74 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.39/6.74 (assert (= tptp.bit_take_bit_num (lambda ((N4 tptp.nat) (M5 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 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 ((P6 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q3 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q3)))) (@ (@ tptp.bit_take_bit_num O) P6)))) (lambda ((P6 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P6))))) X3))) A3))) (@ (@ tptp.product_Pair_nat_num N4) M5)))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y4) (exists ((Q4 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q4))) (and (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real _let_1) Y4)))))))
% 6.39/6.74 (assert (= tptp.plus_plus_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y6))) (let ((_let_2 (@ tptp.product_snd_int_int X3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 6.39/6.74 (assert (= tptp.inverse_inverse_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X3))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X3)) _let_1)))))))
% 6.39/6.74 (assert (= tptp.fract (lambda ((Xa4 tptp.int) (X3 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X3))))))
% 6.39/6.74 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.39/6.74 (assert (= tptp.times_times_rat (@ (@ (@ tptp.map_fu4333342158222067775at_rat tptp.rep_Rat) (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat)) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_fst_int_int Y6))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X3)) (@ tptp.product_snd_int_int Y6)))))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X))) (let ((_let_2 (@ tptp.product_snd_int_int Xa))) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X))) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.inverse_inverse_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ (@ 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 (@ tptp.product_snd_int_int X)) _let_1))))))))
% 6.39/6.74 (assert (= tptp.ratrel (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X3))) (let ((_let_2 (@ tptp.product_snd_int_int Y6))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_1))))))))
% 6.39/6.74 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.39/6.74 (assert (= tptp.ratrel (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X3))) (let ((_let_2 (@ tptp.product_snd_int_int Y6))) (and (not (= _let_1 tptp.zero_zero_int)) (not (= _let_2 tptp.zero_zero_int)) (= (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) _let_2) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_1))))))))
% 6.39/6.74 (assert (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa)) (@ tptp.product_snd_int_int X)))))))))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.positive (@ tptp.abs_Rat X)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.39/6.74 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L3 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L3))) (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 K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.39/6.74 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I) M))) (let ((_let_2 (@ tptp.upt I))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N) (= (@ (@ tptp.take_nat M) (@ _let_2 N)) (@ _let_2 _let_1)))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) (@ tptp.pred_numeral K))))))
% 6.39/6.74 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N)))))
% 6.39/6.74 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N) K) L)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N)) L) R2)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I)) (@ (@ tptp.minus_minus_nat N) I)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N)) I))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q2)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q2) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N) K) L)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N)) L)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M6) N)))) M))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M6)))) M))))
% 6.39/6.74 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q2) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.39/6.74 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q2) tptp.zero_z5237406670263579293d_enat)))
% 6.39/6.74 (assert (= tptp.inf_inf_int tptp.ord_min_int))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) N)))) N))))
% 6.39/6.74 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.39/6.74 (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))))))
% 6.39/6.74 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X8 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X8 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X8)))))
% 6.39/6.74 (assert (= tptp.divide_divide_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (@ (@ (@ tptp.if_nat (= N4 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N4)) M5))))))))
% 6.39/6.74 (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 ((D4 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D4))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.39/6.74 (assert (forall ((M10 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M10) (=> (not (= M10 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M10)) (= (@ tptp.gcd_Gcd_nat M10) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M5 tptp.nat)) (@ tptp.collect_nat (lambda ((D4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D4) M5))))) M10)))))))))
% 6.39/6.74 (assert (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D4 tptp.int)) (@ (@ tptp.dvd_dvd_int D4) N)))) (@ tptp.abs_abs_int N)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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 ((D4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D4))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (= tptp.upto_aux (lambda ((I2 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I2)) Js) (@ (@ (@ tptp.upto_aux I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X) (@ tptp.nat_list_encode Xs)))))))
% 6.39/6.74 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (forall ((X tptp.list_nat)) (=> (not (= X tptp.nil_nat)) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (not (= X (@ (@ tptp.cons_nat X4) Xs2))))))))
% 6.39/6.74 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 6.39/6.74 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.39/6.74 (assert (forall ((A2 tptp.set_list_nat)) (@ (@ tptp.inj_on_list_nat_nat tptp.nat_list_encode) A2)))
% 6.39/6.74 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (= (= (@ tptp.nat_list_encode X) (@ tptp.nat_list_encode Y4)) (= X Y4))))
% 6.39/6.74 (assert (@ (@ (@ tptp.bij_be8532844293280997160at_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 6.39/6.74 (assert (= (@ (@ tptp.image_list_nat_nat tptp.nat_list_encode) tptp.top_top_set_list_nat) tptp.top_top_set_nat))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((X tptp.list_nat) (Y4 tptp.nat)) (=> (= (@ tptp.nat_list_encode X) Y4) (=> (=> (= X tptp.nil_nat) (not (= Y4 tptp.zero_zero_nat))) (not (forall ((X4 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X4) Xs2)) (not (= Y4 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs2)))))))))))))
% 6.39/6.74 (assert (= tptp.upt (lambda ((I2 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I2) J3)) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J3))) tptp.nil_nat))))
% 6.39/6.74 (assert (forall ((X tptp.list_nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X) Y4) (=> (@ _let_1 X) (=> (=> (= X tptp.nil_nat) (=> (= Y4 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))) (=> (= X _let_1) (=> (= Y4 (@ 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)))))))))))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Xa tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y4 tptp.nil_int))) (not _let_1)))))))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I2) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.39/6.74 (assert (= tptp.upto (lambda ((I2 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I2) J3)) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.39/6.74 (assert (forall ((X tptp.int) (Xa tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y4) (and (=> _let_1 (= Y4 (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y4 tptp.nil_int)))))))
% 6.39/6.74 (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))))))
% 6.39/6.74 (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)))))))
% 6.39/6.74 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I2 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.39/6.74 (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)))))))))
% 6.39/6.74 (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))))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 6.39/6.74 (assert (= tptp.quotient_of (lambda ((X3 tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X3 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 6.39/6.74 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.abs_abs_int K)) L) (@ (@ tptp.algebr932160517623751201me_int K) L))))
% 6.39/6.74 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.algebr932160517623751201me_int K))) (= (@ _let_1 (@ tptp.abs_abs_int L)) (@ _let_1 L)))))
% 6.39/6.74 (assert (forall ((Q2 tptp.int) (P5 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P5) Q2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2) (=> (@ (@ tptp.algebr932160517623751201me_int P5) Q2) (= (@ tptp.normalize _let_1) _let_1))))))
% 6.39/6.74 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.39/6.74 (assert (forall ((A tptp.int) (D tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int D))) (let ((_let_2 (@ tptp.abs_abs_int C))) (let ((_let_3 (@ tptp.abs_abs_int B))) (let ((_let_4 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.algebr932160517623751201me_int A) D) (=> (@ (@ tptp.algebr932160517623751201me_int B) C) (= (= (@ (@ tptp.times_times_int _let_4) _let_2) (@ (@ tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.39/6.74 (assert (forall ((A tptp.int) (B tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ (@ tptp.algebr932160517623751201me_int A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ tptp.abs_abs_int X) tptp.one_one_int)))))))
% 6.39/6.74 (assert (forall ((Q2 tptp.rat)) (not (forall ((A4 tptp.int) (B3 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A4) B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (not (@ (@ tptp.algebr932160517623751201me_int A4) B3))))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (@ (@ tptp.algebr932160517623751201me_int A4) B3) (@ P (@ (@ tptp.fract A4) B3))))) (@ P Q2))))
% 6.39/6.74 (assert (forall ((Q2 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (= Q2 (@ (@ tptp.fract A4) B3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (=> (not (= A4 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A4) B3)))))) (= Q2 tptp.zero_zero_rat))))
% 6.39/6.74 (assert (forall ((R2 tptp.rat)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_fst_int_int X4))) (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y3))) (let ((_let_2 (@ tptp.product_fst_int_int Y3))) (=> (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y3 X4)))))))))))
% 6.39/6.74 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M5 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M5)) M5))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ tptp.order_mono_real_real F) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N4 tptp.nat)) (@ F (@ tptp.semiri5074537144036343181t_real N4)))) _let_1) tptp.at_top_nat) (@ (@ (@ tptp.filterlim_real_real F) _let_1) tptp.at_top_real))))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.algebr934650988132801477me_nat M) N))))
% 6.39/6.74 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N) (@ (@ tptp.algebr932160517623751201me_int K) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.algebr932160517623751201me_int (@ tptp.semiri1314217659103216013at_int N)) K))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.39/6.74 (assert (forall ((A tptp.nat) (D tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A) D) (=> (@ (@ tptp.algebr934650988132801477me_nat B) C) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) D)) (and (= A B) (= C D)))))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N)) N)))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc N))))
% 6.39/6.74 (assert (forall ((A tptp.nat) (B tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X tptp.one_one_nat)))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_mono_nat_real X9) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X9 I3)) B4)) (@ (@ tptp.bfun_nat_real X9) tptp.at_top_nat)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.39/6.74 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (@ tptp.order_mono_nat_real X9) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X9 I3)) B4)) (not (forall ((L5 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X9) (@ tptp.topolo2815343760600316023s_real L5)) tptp.at_top_nat) (not (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X9 I4)) L5))))))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N2)))))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4))) (=> (@ tptp.order_mono_nat_real F) (=> (@ tptp.order_5726023648592871131at_nat G) (= (@ (@ tptp.bfun_nat_real (lambda ((X3 tptp.nat)) (@ F (@ G X3)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_snd_int_int X3))))) (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_snd_int_int X3))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A7 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A7) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X9 N2))) A7)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X9 N4)) (@ Y7 N4))))))))
% 6.39/6.74 (assert (forall ((C tptp.rat)) (= (@ tptp.vanishes (lambda ((N4 tptp.nat)) C)) (= C tptp.zero_zero_rat))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X9) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X9 N4)) (@ Y7 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X9) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X9 N4)) (@ Y7 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.vanishes X9) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X9 N4)))))))
% 6.39/6.74 (assert (= tptp.vanishes (lambda ((X8 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N4))) R5)))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X9 N2))) R3)))))) (@ tptp.vanishes X9))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X9) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X9 N6))) R2))))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) tptp.ratrel)) (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B2)))) (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B2)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re6650684261131312217nt_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) tptp.semiri1314217659103216013at_int) tptp.semiri1314217659103216013at_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_eq_int) tptp.ord_less_eq_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.times_times_nat) tptp.times_times_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.times_times_int) tptp.times_times_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.divide_divide_int) tptp.divide_divide_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.bit_se7882103937844011126it_nat) tptp.bit_se7882103937844011126it_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4785983289428654063nt_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.bit_se7879613467334960850it_int) tptp.bit_se7879613467334960850it_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.bit_se4205575877204974255it_nat) tptp.bit_se4205575877204974255it_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4785983289428654063nt_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.bit_se4203085406695923979it_int) tptp.bit_se4203085406695923979it_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.bit_se2161824704523386999it_nat) tptp.bit_se2161824704523386999it_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4785983289428654063nt_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.bit_se2159334234014336723it_int) tptp.bit_se2159334234014336723it_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) tptp.suc) tptp.suc))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) tptp.minus_minus_int) tptp.minus_minus_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4)))) tptp.minus_minus_nat) tptp.minus_minus_nat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y5 tptp.num) (Z4 tptp.num)) (= Y5 Z4))) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4)))) (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M5)) (@ tptp.numeral_numeral_int N4)))) (lambda ((M5 tptp.num) (N4 tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M5)) (@ tptp.numeral_numeral_int N4)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_fst_int_int Y6))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X3)) (@ tptp.product_snd_int_int Y6))))) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_fst_int_int Y6))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X3)) (@ tptp.product_snd_int_int Y6))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re5228765855967844073nt_int tptp.ratrel) (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel)) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y6))) (let ((_let_2 (@ tptp.product_snd_int_int X3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y6))) (let ((_let_2 (@ tptp.product_snd_int_int X3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X3))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X3)) _let_1))))) (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X3))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X3)) _let_1))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y6))) (let ((_let_2 (@ tptp.product_snd_int_int X3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Y6)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1)))))) tptp.plus_plus_rat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X3))) (@ (@ (@ 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 (@ tptp.product_snd_int_int X3)) _let_1))))) tptp.inverse_inverse_rat))
% 6.39/6.74 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))) tptp.pcr_rat)) (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B2 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A3) B2)))) tptp.fract))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7627151682743391978at_rat tptp.pcr_rat) (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat)) (lambda ((X3 tptp.product_prod_int_int) (Y6 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_fst_int_int Y6))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int X3)) (@ tptp.product_snd_int_int Y6))))) tptp.times_times_rat))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X3)) (@ tptp.product_snd_int_int X3))))) tptp.positive))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6))) (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)))) tptp.times_times_int))
% 6.39/6.74 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) tptp.pcr_int) (lambda ((N4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N4) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X3)))) tptp.uminus_uminus_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat)) tptp.nat2))
% 6.39/6.74 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re7408651293131936558nt_int tptp.pcr_int) (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) U3)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat) (M tptp.nat)) (let ((_let_1 (@ tptp.produc457027306803732586at_nat A2))) (= (@ _let_1 (lambda ((Uu3 tptp.nat)) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 (lambda ((I2 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) I2))))) (@ _let_1 (lambda ((I2 tptp.nat)) (@ (@ tptp.set_or6659071591806873216st_nat (@ (@ tptp.minus_minus_nat M) I2)) M))))))))
% 6.39/6.74 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I2 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0))) tptp.inverse_inverse_real))
% 6.39/6.74 (assert (@ (@ tptp.pcr_real (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) tptp.zero_zero_real))
% 6.39/6.74 (assert (@ (@ tptp.pcr_real (lambda ((N4 tptp.nat)) tptp.one_one_rat)) tptp.one_one_real))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))) tptp.uminus_uminus_real))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y8 N4)))) tptp.plus_plus_real))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4695409256820837752l_real tptp.pcr_real) (@ (@ tptp.bNF_re3023117138289059399t_real tptp.pcr_real) tptp.pcr_real)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y8 N4)))) tptp.times_times_real))
% 6.39/6.74 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P6 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P6)))))
% 6.39/6.74 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q3 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q3) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4))))))))) tptp.positive2))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6))) (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)))) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6))) (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)))))
% 6.39/6.74 (assert (forall ((X tptp.nat) (Y4 tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y4)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U) Y4)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X3)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X3)))))
% 6.39/6.74 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.39/6.74 (assert (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (= (@ tptp.abs_Integ X) (@ tptp.abs_Integ Y4)) (@ (@ tptp.intrel X) Y4))))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y4) (@ tptp.positive2 (@ (@ tptp.times_times_real X) Y4))))))
% 6.39/6.74 (assert (not (@ tptp.positive2 tptp.zero_zero_real)))
% 6.39/6.74 (assert (forall ((X tptp.real) (Y4 tptp.real)) (=> (@ tptp.positive2 X) (=> (@ tptp.positive2 Y4) (@ tptp.positive2 (@ (@ tptp.plus_plus_real X) Y4))))))
% 6.39/6.74 (assert (forall ((X tptp.real)) (=> (not (@ tptp.positive2 X)) (=> (not (= X tptp.zero_zero_real)) (@ tptp.positive2 (@ tptp.uminus_uminus_real X))))))
% 6.39/6.74 (assert (let ((_let_1 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y5 tptp.nat) (Z4 tptp.nat)) (= Y5 Z4))) _let_1) _let_1)))
% 6.39/6.74 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y6 tptp.real)) (@ tptp.positive2 (@ (@ tptp.minus_minus_real Y6) X3)))))
% 6.39/6.74 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.39/6.74 (assert (= tptp.intrel (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U3 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X3) V4) (@ (@ tptp.plus_plus_nat U3) Y6)))) __flatten_var_0)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y6 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) Y6)))) __flatten_var_0)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.intrel) (lambda ((Y5 tptp.int) (Z4 tptp.int)) (= Y5 Z4))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) V4)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) V4)))) __flatten_var_0)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re3099431351363272937at_nat tptp.intrel) (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel)) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) U3)))) __flatten_var_0)))) (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y6 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 Y6) U3)))) __flatten_var_0)))))
% 6.39/6.74 (assert (= tptp.positive2 (lambda ((X3 tptp.real)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ (@ tptp.rep_real X3) N4))))))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re728719798268516973at_o_o tptp.realrel) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4))) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4))))))))) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4))))))))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y8 N4)))) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y8 N4)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re1962705104956426057at_rat tptp.realrel) (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y8 N4)))) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y8 N4)))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4)))))
% 6.39/6.74 (assert (@ (@ tptp.realrel (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)))
% 6.39/6.74 (assert (@ (@ tptp.realrel (lambda ((N4 tptp.nat)) tptp.one_one_rat)) (lambda ((N4 tptp.nat)) tptp.one_one_rat)))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re4521903465945308077real_o tptp.pcr_real) (@ (@ tptp.bNF_re4297313714947099218al_o_o tptp.pcr_real) (lambda ((Y5 Bool) (Z4 Bool)) (= Y5 Z4)))) tptp.realrel) (lambda ((Y5 tptp.real) (Z4 tptp.real)) (= Y5 Z4))))
% 6.39/6.74 (assert (@ (@ (@ (@ tptp.bNF_re895249473297799549at_rat tptp.realrel) tptp.realrel) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0))) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0))))
% 6.39/6.74 (assert (= tptp.positive2 (@ (@ (@ tptp.map_fu1856342031159181835at_o_o tptp.rep_real) tptp.id_o) (lambda ((X8 (-> tptp.nat tptp.rat))) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X8 N4)))))))))))
% 6.39/6.74 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.inverse_inverse_real (@ tptp.real2 X)) (@ tptp.real2 (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X N4)))))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((Y (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Y) Y) (@ P (@ tptp.real2 Y)))) (@ P X))))
% 6.39/6.74 (assert (= tptp.ring_1_of_int_real (lambda ((X3 tptp.int)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.ring_1_of_int_rat X3))))))
% 6.39/6.74 (assert (= tptp.field_7254667332652039916t_real (lambda ((X3 tptp.rat)) (@ tptp.real2 (lambda ((N4 tptp.nat)) X3)))))
% 6.39/6.74 (assert (= tptp.one_one_real (@ tptp.real2 (lambda ((N4 tptp.nat)) tptp.one_one_rat))))
% 6.39/6.74 (assert (= tptp.zero_zero_real (@ tptp.real2 (lambda ((N4 tptp.nat)) tptp.zero_zero_rat))))
% 6.39/6.74 (assert (= tptp.semiri5074537144036343181t_real (lambda ((X3 tptp.nat)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.semiri681578069525770553at_rat X3))))))
% 6.39/6.74 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X N4))))))))
% 6.39/6.74 (assert (forall ((Xa (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa) Xa) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 Xa)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ Xa N4)) (@ X N4)))))))))
% 6.39/6.74 (assert (forall ((Xa (-> tptp.nat tptp.rat)) (X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel Xa) Xa) (=> (@ (@ tptp.realrel X) X) (= (@ (@ tptp.times_times_real (@ tptp.real2 Xa)) (@ tptp.real2 X)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ Xa N4)) (@ X N4)))))))))
% 6.39/6.74 (assert (forall ((X (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.realrel X) X) (= (@ tptp.positive2 (@ tptp.real2 X)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X N4)))))))))))
% 6.39/6.74 (assert (= tptp.inverse_inverse_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X8 (-> tptp.nat tptp.rat)) (__flatten_var_0 tptp.nat)) (@ (@ (@ (@ tptp.if_nat_rat (@ tptp.vanishes X8)) (lambda ((N4 tptp.nat)) tptp.zero_zero_rat)) (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X8 N4)))) __flatten_var_0)))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X9)) (@ tptp.real2 Y7)) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X9 N4)) (@ (@ tptp.plus_plus_rat (@ Y7 N4)) R5))))))))))))
% 6.39/6.74 (assert (= tptp.pcr_real (lambda ((X3 (-> tptp.nat tptp.rat)) (Y6 tptp.real)) (and (@ tptp.cauchy X3) (= (@ tptp.real2 X3) Y6)))))
% 6.39/6.74 (assert (forall ((P (-> tptp.real Bool)) (X tptp.real)) (=> (forall ((X15 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X15) (@ P (@ tptp.real2 X15)))) (@ P X))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (not (@ tptp.vanishes X9)) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X9 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X9 N4)) (@ Y7 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X9 N4)))))))
% 6.39/6.74 (assert (forall ((X tptp.rat)) (@ tptp.cauchy (lambda ((N4 tptp.nat)) X))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X9 N4)) (@ Y7 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (@ tptp.cauchy (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X9 N4)) (@ Y7 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (@ (@ tptp.realrel X9) X9))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X9 N6))) B3)))))))
% 6.39/6.74 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y7) (=> (@ (@ tptp.ord_less_real X) (@ tptp.real2 Y7)) (exists ((N2 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.field_7254667332652039916t_real (@ Y7 N2))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y4 tptp.real)) (=> (@ tptp.cauchy X9) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.field_7254667332652039916t_real (@ X9 N2))) Y4)) (@ (@ tptp.ord_less_eq_real (@ tptp.real2 X9)) Y4)))))
% 6.39/6.74 (assert (forall ((Y7 (-> tptp.nat tptp.rat)) (X tptp.real)) (=> (@ tptp.cauchy Y7) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.field_7254667332652039916t_real (@ Y7 N2)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.real2 Y7))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (= (@ tptp.uminus_uminus_real (@ tptp.real2 X9)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X9 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.plus_plus_real (@ tptp.real2 X9)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X9 N4)) (@ Y7 N4)))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.times_times_real (@ tptp.real2 X9)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X9 N4)) (@ Y7 N4)))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (= (@ (@ tptp.minus_minus_real (@ tptp.real2 X9)) (@ tptp.real2 Y7)) (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X9 N4)) (@ Y7 N4)))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (=> (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X9 N4)) (@ Y7 N4)))) (@ (@ tptp.realrel X9) Y7))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (@ tptp.cauchy Y7) (= (= (@ tptp.real2 X9) (@ tptp.real2 Y7)) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X9 N4)) (@ Y7 N4)))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (not (@ tptp.vanishes X9)) (=> (@ tptp.cauchy Y7) (=> (not (@ tptp.vanishes Y7)) (=> (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X9 N4)) (@ Y7 N4)))) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ tptp.inverse_inverse_rat (@ X9 N4))) (@ tptp.inverse_inverse_rat (@ Y7 N4))))))))))))
% 6.39/6.74 (assert (= tptp.realrel (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat))) (and (@ tptp.cauchy X8) (@ tptp.cauchy Y8) (@ tptp.vanishes (lambda ((N4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ X8 N4)) (@ Y8 N4))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (not (@ tptp.vanishes X9)) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (exists ((K2 tptp.nat)) (or (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B3) (@ tptp.uminus_uminus_rat (@ X9 N6))))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B3) (@ X9 N6))))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (= (@ tptp.positive2 (@ tptp.real2 X9)) (exists ((R5 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat R5) (@ X9 N4)))))))))))
% 6.39/6.74 (assert (= tptp.uminus_uminus_real (@ (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2) (lambda ((X8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ tptp.uminus_uminus_rat (@ X8 N4))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (=> (not (@ tptp.vanishes X9)) (exists ((B3 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B3) (exists ((K2 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat B3) (@ tptp.abs_abs_rat (@ X9 N6))))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X9) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K2 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N6) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X9 M2)) (@ X9 N6)))) R2))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) M4) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X9 M4)) (@ X9 N2)))) R3)))))))) (@ tptp.cauchy X9))))
% 6.39/6.74 (assert (= tptp.cauchy (lambda ((X8 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M5) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M5)) (@ X8 N4)))) R5)))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.real2 X9)))) (let ((_let_2 (@ tptp.vanishes X9))) (=> (@ tptp.cauchy X9) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ tptp.real2 (lambda ((N4 tptp.nat)) (@ tptp.inverse_inverse_rat (@ X9 N4))))))))))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.rat))) (=> (@ tptp.cauchy X9) (= (not (@ tptp.positive2 (@ tptp.real2 X9))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K3 tptp.nat)) (forall ((N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N4) (@ (@ tptp.ord_less_eq_rat (@ X9 N4)) R5))))))))))
% 6.39/6.74 (assert (= tptp.times_times_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N4)) (@ Y8 N4))))))
% 6.39/6.74 (assert (= tptp.plus_plus_real (@ (@ (@ tptp.map_fu1532550112467129777l_real tptp.rep_real) (@ (@ tptp.map_fu7146612038024189824t_real tptp.rep_real) tptp.real2)) (lambda ((X8 (-> tptp.nat tptp.rat)) (Y8 (-> tptp.nat tptp.rat)) (N4 tptp.nat)) (@ (@ tptp.plus_plus_rat (@ X8 N4)) (@ Y8 N4))))))
% 6.39/6.74 (assert (= tptp.cr_real (lambda ((X3 (-> tptp.nat tptp.rat)) (Y6 tptp.real)) (and (@ (@ tptp.realrel X3) X3) (= (@ tptp.real2 X3) Y6)))))
% 6.39/6.74 (assert (@ tptp.bi_tot896582865486249351at_int tptp.pcr_int))
% 6.39/6.74 (assert (= tptp.pcr_real tptp.cr_real))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.rcis R2) A)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real tptp.one_one_real) R2)) (@ tptp.uminus_uminus_real A)))))
% 6.39/6.74 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.rcis R2) tptp.zero_zero_real) (@ tptp.real_V4546457046886955230omplex R2))))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.rcis R2) A) tptp.zero_zero_complex) (= R2 tptp.zero_zero_real))))
% 6.39/6.74 (assert (forall ((A tptp.real)) (= (@ (@ tptp.rcis tptp.zero_zero_real) A) tptp.zero_zero_complex)))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.cos_real A)))))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.sin_real A)))))
% 6.39/6.74 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R1) R22)) (@ (@ tptp.plus_plus_real A) B)))))
% 6.39/6.74 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real R1) R22)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.39/6.74 (assert (forall ((R2 tptp.real) (A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.rcis R2) A)) N) (@ (@ tptp.rcis (@ (@ tptp.power_power_real R2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.39/6.74 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.39/6.74 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S) N)))))
% 6.39/6.74 (assert (forall ((S tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.infini8530281810654367211te_nat S) N))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (Q (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P N) (=> (@ Q M) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K2 tptp.nat)) (= (@ P (@ tptp.suc K2)) (@ Q K2))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 6.39/6.74 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M5 tptp.nat)) (@ P (@ tptp.suc M5))))))))))
% 6.39/6.74 (assert (= tptp.comple1385675409528146559p_real (lambda ((X8 tptp.set_real)) (@ tptp.ord_Least_real (lambda ((Z5 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) X8) (@ (@ tptp.ord_less_eq_real X3) Z5))))))))
% 6.39/6.74 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.last_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A2)) (@ _let_1 A2)))))
% 6.39/6.74 (assert (forall ((N tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A2)) (@ (@ tptp.insert_nat N) (@ _let_1 A2))))))
% 6.39/6.74 (assert (forall ((F4 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F4)) (@ tptp.finite_finite_nat F4))))
% 6.39/6.74 (assert (forall ((X tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X)))))
% 6.39/6.74 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A2)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.39/6.74 (assert (forall ((F (-> tptp.nat tptp.real)) (M10 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N4) M10)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ F N2)) (@ F M4))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 6.39/6.74 (assert (forall ((X9 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.bfun_nat_real X9) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ X9 M4)) (@ X9 N2)))) (@ tptp.topolo7531315842566124627t_real X9)))))
% 6.39/6.75 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo7531315842566124627t_real (@ tptp.power_power_real X))))))
% 6.39/6.75 (assert (forall ((F (-> tptp.nat tptp.real)) (M10 tptp.nat)) (=> (@ (@ tptp.bfun_nat_real (lambda ((N4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N4) M10)))) tptp.at_top_nat) (=> (forall ((M4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M4) (=> (@ (@ tptp.ord_less_eq_nat M4) N2) (@ (@ tptp.ord_less_eq_real (@ F M4)) (@ F N2))))) (@ tptp.topolo7531315842566124627t_real F)))))
% 6.39/6.75 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat S2) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_less)))))
% 6.39/6.75 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat S2) T) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T))) tptp.fun_pair_leq)))))
% 6.39/6.75 (assert (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D))) (= (@ (@ tptp.filtermap_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real X3) D))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.39/6.75 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real X3) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.39/6.75 (assert (= (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)) (@ (@ tptp.filtermap_real_real tptp.inverse_inverse_real) tptp.at_top_real)))
% 6.39/6.75 (assert (= tptp.at_top_real (@ (@ tptp.filtermap_real_real tptp.inverse_inverse_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.39/6.75 (assert (= (@ (@ tptp.filtermap_real_real tptp.ln_ln_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_bot_real))
% 6.39/6.75 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M5 tptp.nat) (N4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M5) N4) (not (= M5 N4))))) tptp.zero_zero_nat))
% 6.39/6.75 (assert (@ (@ (@ tptp.ordering_top_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X3))) (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X3))) tptp.zero_zero_nat))
% 6.39/6.75 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.int) (Y4 tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.num) (Y4 tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.rat) (Y4 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.real) (Y4 tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X8 tptp.real)) (@ P X8)))))
% 6.39/6.75 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.complex) (Y4 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.list_int) (Y4 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.list_int) (Y4 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.list_nat) (Y4 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X (-> tptp.int tptp.int)) (Y4 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X (-> tptp.int tptp.int)) (Y4 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y4 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X (-> tptp.nat tptp.rat)) (Y4 (-> tptp.nat tptp.rat))) (= (@ (@ (@ tptp.if_nat_rat true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.option_num) (Y4 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.option_num) (Y4 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y4) Y4)))
% 6.39/6.75 (assert (forall ((X tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y4) X)))
% 6.39/6.75 (assert (forall ((X tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y4) Y4)))
% 6.39/6.75 (ass/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 21007 Alarm clock ( read result; case "$result" in
% 299.99/300.35 unsat)
% 299.99/300.35 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.99/300.35 ;;
% 299.99/300.35 sat)
% 299.99/300.35 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.99/300.35 ;;
% 299.99/300.35 esac; exit 1 )
% 299.99/300.36 Alarm clock
% 299.99/300.36 % cvc5---1.0.5 exiting
% 299.99/300.36 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------